Ryan Muller - Optimization of a non-Grashof compound four bar linkage mechanism for cutting surgical wires

STAFFORDSHIRE UNIVERSITY

Final Year Project (BEng) Optimization of a non-Grashof compound four bar

linkage mechanism for cutting surgical wires

Ryan Muller

Award: Mechanical Engineering

Student number: 08003271

Supervisor: Professor Peter Ogrodnik

4/7/2012

Final Year Project (BEng) 2012

a

Abstract

The following paper investigates the improvement of a non-Grashof conforming compound

four bar linkage mechanism by modification of the input link fixed pivot of the external

mechanism. The mechanism in question is an integral sub assembly found in a pair of wire

cutting pliers from the company GEOMED, a manufacturer of orthopaedic equipment, which

is used in order to magnify the input force by a factor of 9.5 in order to shear 2-3mm 316L

surgical wire.

Theoretical calculation is made of the original configuration in order to obtain a benchmark

value for the mechanisms mechanical advantage, which is then compared to a software model

using Working ModelTM

. The software model is then modified using a matrix of input link

fixed pivot coordinates in order to obtain an optimum position.

Finally, through a practical investigation, a Wheatstone bridge is created in order to measure

tensile strain and therefore the force output of the system indirectly, through use of a rapid

prototyped planar model. The results show that the revised input link fixed pivot position

yields a 37% increase in output force when compared to the original position used by

GEOMED and allows the product to be scaled by a factor of 0.73; allowing the manufacturer

to save on material and production costs.


b

Acknowledgements

First and foremost, I would like to thank Professor Peter Ogrodnik in giving me the

opportunity to carry out this project. Along with its challenges and points of triumph, the

project has allowed me to better myself in terms design, problem solving, research methods

and testing, which has allowed me apply all of the skills gained from modules taught at

University.

A special thanks also to the lab technicians in F12 at Staffordshire University, for providing

support and guidance during experimentation and demonstrating procedures for various

aspects of testing the physical prototype.

Finally, I would also like to thank my parents and friends for proof reading and suggesting

areas of improvement in order for ideas and statements to be conveyed as intended for any

reader.


I

Contents

List of figures ..................................................................................................................... V

List of tables ..................................................................................................................... IX

Nomenclature ................................................................................................................... IX

1 Introduction .......................................................................................................... 1

1.1 Development of cutting instruments with respect to cutting force ............................. 1

1.2 A brief history of kinematics ....................................................................................... 5

1.3 Linkage Mechanisms................................................................................................... 5

1.4 The four bar linkage .................................................................................................... 8

1.5 Practical investigations regarding four bar linkage mechanical advantage .............. 10

1.6 Degrees of freedom of planar mechanisms ............................................................... 13

1.6.1 Grashof’s criterion ........................................................................................................ 14

1.7 Dual or compound linkage mechanisms ................................................................... 15

1.8 Classical and current methods of linkage synthesis and analysis ............................. 15

1.8.1 Computer aided linkage synthesis and analysis ............................................................ 16

1.9 Existing Patents review ............................................................................................. 17

1.9.1 Non-Surgical cutting instruments ................................................................................. 17

1.9.2 Surgical cutting instruments ......................................................................................... 24

1.10 Current state of the art ............................................................................................... 29

1.11 Ergonomic analysis of hand tools ............................................................................. 31

1.12 British standards for surgical cutting instruments and maximum loading ................ 33

1.12.1 Stainless steels for surgical cutting instruments ........................................................ 33

1.12.2 Guideline cutting forces for lever assisted cutting pliers .......................................... 34

1.13 Conclusions from background literature and market research .................................. 36

2 Project aims and objectives based on background literature.............................. 37

2.1 Generalized method layout to fulfil project objectives ............................................. 38


II

3 Hypothesis .......................................................................................................... 39

4 Instantaneous transmission ratio based on the kinematic constraint equation ... 40

5 Linkage configuration analysis of Geomed-Gold Cut wire cutting Pliers ......... 43

5.1 Apparatus/Software required for obtaining linkage point coordinates ..................... 44

5.2 Method of obtaining linkage point coordinates / internal angles .............................. 45

5.2.1 Preliminary initial measurement with ruler: ................................................................. 46

5.3 Hercules Gold-cut join coordinates ........................................................................... 47

6 Reverse Engineering of Geomed wire cutting pliers ......................................... 48

6.1 Product design specification...................................................................................... 48

6.2 CAD development ..................................................................................................... 51

6.3 3-Dimensional computer model summary specification ........................................... 57

7 Theoretical kinematical and torque transmission analysis ................................. 57

7.1 Geomed internal four bar linkage transmission ratio (relaxed position) ................... 58

7.2 Geomed internal four bar linkage transmission ratio (3mm offset) .......................... 59

7.3 Combined mechanical advantage of Geomed wire cutting pliers ............................. 60

7.4 Mechanical advantage using lever ratio equation from BS 3087-7:1996 ................. 61

8 Excel analysis of internal linkage mechanism ................................................... 62

9 Working model analysis of standard configuration ........................................... 66

9.1 The test model and initial conditions ........................................................................ 66

10 Input link fixed pivot modification .................................................................... 67

11 Modification of Working Model analysis setup ................................................. 68

12 Working model results using input link matrix .................................................. 70

12.1 Output force using rigid member configuration ........................................................ 70

12.2 Output force using spring configuration ................................................................... 72

12.3 Theoretical results discussion.................................................................................... 72


III

13 Initial rapid prototype in order to compare theory with practise........................ 73

13.1 Creation of planar mechanism model in Pro EngineerTM

......................................... 73

13.2 Kinematic analysis in CAD of revised input link fixed pivot location and initial

problems encountered .......................................................................................................... 75

13.3 DXF drawing creation and CNC laser setup for initial prototype............................. 79

13.4 The finished planar acrylic model for analysis ......................................................... 80

14 Finite Element Analysis of planar mechanism ................................................... 81

14.1 FEA Analysis using COSMOSTM

............................................................................. 81

14.2 FEA analysis comparison using MSC NASTRANTM

............................................... 83

14.3 Comparison of Finite Element Analysis results ........................................................ 84

15 Method of testing the physical prototype ........................................................... 85

15.1 Preliminary equipment setup and calibration ............................................................ 86

15.1.1 Creating the Wheatstone bridge for strain measurement .......................................... 86

15.1.2 Calibration of the strain gauge .................................................................................. 89

15.1.3 The final physical test setup ...................................................................................... 90

16 Results of testing the physical model ................................................................. 92

16.1 Discussion ................................................................................................................. 96

16.2 Comparing results with theory .................................................................................. 96

16.3 Fair test factors .......................................................................................................... 98

16.4 Anomalous results and limitations of the experimental procedure ........................... 98

17 Conclusions ........................................................................................................ 99

17.1 Recommendations ................................................................................................... 100

18 References ........................................................................................................ 101

19 Appendix .......................................................................................................... 107

Appendix 1- BS EN ISO7153-1:2001 (Metallic materials for surgical instruments) ........ 107

Appendix 2 – Full derivation of the four bar kinematic constraint equation ..................... 108


IV

Appendix 3 – Four bar linkage force transmission ratio table data ................................... 109

Appendix 4 – Raw data for stress vs. strain when loading physical model ....................... 111

Appendix 5 - COSMOS Finite Element Analysis Report .................................................. 112


V

List of figures

Fig. 1-1: Surgical scissors from the Huntington and Marsh manuscripts (Spink and Lewis,

1973) followed by a non-surgical example in a similar time period (Ward-Perkins, 1940) ..... 2

Fig. 1-2: Modification of blade design with introduction of bevel (Brunschwig, 1497)

followed by a decreased blade to handle length ratio by Woodall (1639). ................................ 2

Fig. 1-3: Curved and compound surgical scissors with adjustable angle (Savigny, 1800) ....... 3

Fig. 1-4: Bone cutting pliers with curved handles and assisting opening spring (Kirkup, 1998)

.................................................................................................................................................... 3

Fig. 1-5: Nickel plated bone cutting pliers followed by compound Stainless Steel gouge

cutters ......................................................................................................................................... 4

Fig. 1-6: A cutting mechanism based on the four bar linkage (Eckhardt, 1998) ....................... 6

Fig. 1-7: The standard four bar linkage model (Phelan, 1988) .................................................. 8

Fig. 1-8: Free body diagram of the four bar linkage (Phelan, 1988) ......................................... 9

Fig. 1-9: Maximum and minimum allowable transmission angle in a four bar linkage (Patel,

2011) ........................................................................................................................................ 10

Fig. 1-10: Example of an Elastrator (Midha et al, 1984) ......................................................... 11

Fig. 1-11: Variation of mechanical output of the system based on input force (Midha et al,

1984) ........................................................................................................................................ 12

Fig. 1-12: Early cutting pliers / pinchers followed by variant products (right) utilizing a four

link mechanism (Lindsay, 1874).............................................................................................. 18

Fig. 1-13: Ergonomic design patent as opposed to complex linkage mechanisms or an

increase in overall size (Smith, 1876) ...................................................................................... 19

Fig. 1-14: A compound mechanism design with adjustable internal spring-back mechanism

(Porter, 1880) ........................................................................................................................... 19

Fig. 1-15: Compound mechanism with interchangeable single fixing blades (Broadbooks,

1902) ........................................................................................................................................ 20

Fig. 1-16: A portable hand held compound linkage mechanism with patented inverted "J"

cutting head (Geddes, 1940) .................................................................................................... 21

Fig. 1-17: Hand held compound rod cutters for use in the building trade, Shurtleff (1975) ... 22

Fig. 1-18: Multi-functional transportable cutting pliers, Rowe (1981) ................................... 23

Fig. 1-19: Cutting/gripping pliers with adjustable rack configuration, Caravello (2008) ....... 24

Fig. 1-20: Surgical combination tool with interchangeable cutting heads (Koeth, 1905) ....... 25

Fig. 1-21: Small surgical pliers for use in Endodontic applications, Rosen (1960) ................ 26


VI

Fig. 1-22: Surgical cutting pliers for use in jaw surgery and orthodontic procedures, Tippy

(1975) ....................................................................................................................................... 27

Fig. 1-23: The wire retention device proposed by Mooney (1999) for the cutting of softer

wires ......................................................................................................................................... 28

Fig. 1-24: A design patent for compound surgical wire cutters from GEOMED, 2003 .......... 29

Fig. 1-25: Grip force vs. handle size (Edgren et al, 2004) ....................................................... 31

Fig. 4-1: Generalized four bar linkage model for constraint equation derivation (Rothenhofer,

2010) ........................................................................................................................................ 40

Fig. 4-2: Modification of figure 4-1 to illustrate derivation of trigonometric terms ............... 41

Fig. 5-1: Geomed Hercules Gold-Cut wire cutting pliers (Geomed, 2011)............................. 43

Fig. 5-2: Geomed compound linkage break-down (Geomed, 2011) ....................................... 44

Fig. 5-3: Shadowgraph from Midland Metrology Ltd ............................................................. 45

Fig. 5-4: Physical Geomed wire cutting plier image ............................................................... 46

Fig. 5-5: Hercules Gold-Cut joint coordinates taken with shadowgraph ................................. 47

Fig. 6-1: The modelled LHS handle ........................................................................................ 51

Fig. 6-2: The modelled linkages .............................................................................................. 51

Fig. 6-3: CAD model representation of linkage constraints to set correct angles ................... 52

Fig. 6-4: CAD model of RHS cutter ........................................................................................ 52

Fig. 6-5: The modelled right hand side handle ........................................................................ 53

Fig. 6-6: The modelled Tungsten-Carbide blades .................................................................... 53

Fig. 6-7: The finished computer generated model ................................................................... 54

Fig. 6-8: Rendered images of the Geomed wire cutter computer generated model using the

standard linkage configuration ................................................................................................. 55

Fig. 6-9: Summary technical drawing to illustrate critical dimensions ................................... 56

Fig. 6-10: Model mass properties ............................................................................................ 57

Fig. 7-1: Internal four bar linkage analysis of Geomed wire cutting pliers ............................. 58

Fig. 7-2: Internal linkage angles for 3mm cutter offset ........................................................... 59

Fig. 7-3: Transmission quality compared to claimed value by Geomed (Geomed.de, 2011) . 60

Fig. 7-4: Cutting end gap between blades based on BS 3087-7:1996 ..................................... 62

Fig. 8-1: Torque transmission of Geomed wire cutting pliers with respect to input link angle

.................................................................................................................................................. 63

Fig. 8-2: Working model representation of internal mechanism in starting position .............. 64


VII

Fig. 8-3: Working model representation of internal mechanism in maximum force

transmission position ............................................................................................................... 64

Fig. 8-4: Working model representation of internal mechanism in negative torque region .... 65

Fig. 8-5: Illustration of non-Grashof conformance .................................................................. 65

Fig. 9-1: Working model analysis of original Geomed linkage configuration ........................ 67

Fig. 10-1: Modification of input link fixed pivot in order to create matrix grid for data

collection .................................................................................................................................. 68

Fig. 11-1: Measurement anomalies using the spring setup in Working model ....................... 69

Fig. 11-2: Rigid member setup in Working model for increased repeatability between tests . 69

Figure 12-1: Values on design model giving rise to highest output force when using rigid

member at cutting end .............................................................................................................. 71

Fig. 13-1: The planar model with relocated input fixed pivot ................................................. 74

Fig. 13-2: Bolt-on blade tips to eliminate shear condition of planar mechanism at the cutting

end ............................................................................................................................................ 74

Fig. 13-3: Insufficient cutter head travel relative to handle displacement ............................... 75

Fig. 13-4: adjustment position using data from table 6 to obtain input link fixed pivot location

yielding a significant increase in mechanical advantage of the mechanism ............................ 76

Figure 13-5: The finalized model to be laser cut to begin practical analysis followed by the

updated 3-dimensional model .................................................................................................. 77

Fig. 13-6: The final rendered model with modified input link fixed pivot positioning ........... 78

Fig. 13-7: DXF drawing template to be laser cut followed by the laser cut parts after

component placement revision to minimize waste .................................................................. 79

Fig. 13-8: The physical test model ........................................................................................... 80

Figure 14-1: Stress flow analysis of the original configuration and revised configuration ..... 81

Fig. 14-2: Stress analysis results at cutting head for each input link configuration ................ 82

Figure 14-3: FEA analysis of planar mechanism in NASTRAN with input link in original

position ..................................................................................................................................... 83

Figure 14-4: FEA analysis of planar mechanism in NASTRAN with input link in modified

position ..................................................................................................................................... 84

Figure 15-1: The Wheatstone bridge (U.A. Bakshi; A.V. Bakshi, 2003) ................................ 87

Fig. 15-2: The finished strain gauge with top-side and underside ........................................... 89

Fig. 15-3: Test setup for strain gauge calibration .................................................................... 89

Fig. 15-4: The final test setup in order to test the physical model ........................................... 91


VIII

Fig. 15-5: The cutter head wire loop in order to measure strain .............................................. 91

Fig. 16-1: Strain vs. load for original configuration ................................................................ 93

Fig. 16-2: Strain vs. load for modified configuration .............................................................. 94

Fig. 16-3: Comparison of strain vs. load between original and modified configuration ......... 95


IX

List of tables

Table 1: Common linkage designs employed by various manufacturers of surgical cutting

instruments ............................................................................................................................... 30

Table 2: Surgical steels suitable for wire cutting pliers (BSOL, 2011) ................................... 34

Table 3: Maximum permissible cutting force for lever assisted side cutting pliers (British

standards online, 2011) ............................................................................................................ 35

Table 4: Design requirements for 3-Dimensional model ......................................................... 50

Table 5: Output force in working model using rigid member (SPAR) .................................... 70

Table 6: Output force in working model using a spring .......................................................... 72

Table 7: Strain calibration ........................................................................................................ 90


X

Nomenclature

Notation Definition Units (SI)

Force

Compliance equivalent load

Load to main pivot length

Main pivot to load length

Normal force

Coefficient of friction

Torque (Tension)

Linkage angle

Input rubber band stretch

Output rubber band stretch

Mobility of a mechanism

No. of links

No. of joints

Longest link in system

Shortest link in system

Length of remaining links

Handle span open

Handle span closed

Relaxed cutting jaw distance

-

-

-

-


XI

Transmission angle

Stress

Transmission ratio

Resistor (circuit)

Current

Voltage

Galvanometer

Emf (Young’s Modulus)

Standard uncertainty

Standard deviation

Variance

-

-

-

-

-

-

Abbreviations

Mechanical advantage

Factor of safety

Tungsten mono-carbide


1

1 Introduction

Wire cutting pliers are commonly used in industry in order to trim lengths of cable or wire

to a specific length. The design of the pliers will depend on the type of application and will

therefore need to meet specific specifications set by the manufacturer or the customer; this

will ultimately determine what size the pliers depending on the thickness or gauge of the

wire (or cable) to be cut.

An important design consideration associated with cutting pliers is that of the input force

required to shear a specific gauge wire. From simple lever theory, an increased handle

length relative to the distance between the cutting end and the main fixed pivot or joint will

provide a greater moment of rotation and therefore allow for lesser load to be applied to the

handles. However, in applications where space is limited, an increase in handle length

becomes an inefficient method of increasing the mechanical advantage of the mechanism;

therefore another approach is needed in order to maintain a high mechanical advantage or

force transmission ratio with no appreciable increase in size of the mechanism.

1.1 Development of cutting instruments with respect to cutting force

Surgical instruments form an array of tools from which the surgeon can carry out a variety

of complex tasks and procedures. Some of the most common instruments available to the

surgeon include Retractors, Forceps, Scissors and Rongeurs with the roles of retracting

bone or flesh, grasping and cutting respectively. Scissors in a surgical environment for

example are estimated to have been used as early as AD 1000 for the use of eye surgery

and C-shaped blades for tonsillectomy, as illustrated by Spink and Lewis (1973) based on

drawings taken from the Marsh [1271-1272] and Huntington manuscript [1465-1466];

early non-surgical scissors are illustrated by Ward-Perkins (1940) whereby a domestic

example was found at Tuna, Sweden at a burial site and dated between AD 800-850 based

on association of coins found within the area.

The instruments uncovered from the Marsh and Huntington manuscripts alongside the find

in Tuna, Sweden are illustrated in figure 1-1.


2

According to Kirkup (1998), advancements of surgical wire cutters in order for increased

cutting capacity and efficiency were made by modification of the blade bevel and by

alteration of the cutter length relative to the handles; this allowed for more complex tasks

to be carried out and for an increased control of power over variations of tissue section

length. The highest ratio of 0.55 was most common for use during post-mortems where a

relatively low output force is required in order to shear through extended lengths of bowel

tissue followed by a ratio of 0.44 for use of cutting bandages. Lower ratios such as 0.3

were used for applications where a higher output force was needed at the cutting end and

include instruments used for bone cutting; these modifications are evident from the work

published by Brunschwig (1497) and Woodall (1639), shown in figure 1-2.

Fig. 1-1: (Left) Surgical scissors from the Huntington and Marsh manuscripts (Spink and Lewis, 1973)

followed by a non-surgical example (right) in a similar time period (Ward-Perkins, 1940)

Fig. 1-2: (Left) Modification of blade design with introduction of bevel (Brunschwig, 1497) followed

by a decreased blade to handle length ratio by Woodall (1639), right.


3

Kirkup also goes to describe the importance of adjustable compound joints which were

used in conjunction with blade ratios of less than 0.2 for use in scissor action cutters and

for linear cutters in order for increased efficiency and customizability of transferring power

from the input load; an example of the implementation of compound joints is illustrated in

figure 1-3 from the work of Savigny (1800).

Since the 19th

century, the development of scissors and other cutting instruments based on

their linkage configurations did not change significantly. However, subtle changes to the

handle shape meant that a more comfortable grip could be achieved and thus a more

controlled power input; the mechanism was also assisted by an opening spring in order to

retract properly when cutting through dense tissues such as bone. An example is illustrated

in figure 1-4.

Fig. 1-3: Curved and compound surgical scissors with adjustable angle (Savigny, 1800)

Fig. 1-4: Bone cutting pliers with curved handles and assisting opening spring (Kirkup, 1998)


4

Finally, an example of straight or linear (including compound) cutters, illustrated from the

work of Kirkup (from the manufacturers Arnold [1910] and Stille [1965]) are illustrated in

figure 1-5; these particular examples are Nickel plated and made from Stainless Steel

respectively.

The comprehensive study carried out by Kirkup illustrates the evolution of surgical cutting

instruments with minimal changes of the cutting tool design over a considerable time

period. The most noticeable changes arise from changes to the handle design (with respect

to the ergonomic properties of the product), modification of the number of joints (and more

importantly the customizability of the linkages) used and subtle changes to the design of

the blades.

In his other work on the evolution of materials used in surgical instruments, Kirkup (1993)

states that the first tools were most likely to have been made from Bronze with Steel

cutting blades, based on findings in Pompeii which date to AD 97. However, development

of the materials used in cutting instruments was needed due to ferrous metals corroding

and compromising the antiseptic qualities needed for surgery. More expensive tools would

have handles made from ivory, pearl or ebony during the 18th

and 19th

centuries with the

introduction of Nickel or Chrome plated blades which were introduced in 1883 and 1893,

with these materials being resistant to corrosion. Further sterilization was achieved by pre-

heating the instruments before use.

Fig. 1-5: (Above) Nickel plated bone cutting pliers followed by compound

Stainless Steel gouge cutters (below)


5

1.2 A brief history of kinematics

The design of the surgical cutting instruments illustrated in figures 1-3 and 1-4 (with the

exception of the compound cutting pliers in figure 1-5) is based a type of linkage

configuration known as the 2-bar linkage and can be easily identified due to two handles

(or bars) with one fixed revolute joint. This design is essentially based on simple lever

theory and can be dated back to the time of Archimedes [ca. 287–212 BC] in which the

theory of mechanical advantage was based on that of the principles of equilibrium (such as

a simple seesaw with a fixed pivot); this theory was used in order to raise water from wells

and in order to lift various other types of loads not manageable by man himself (Chondros,

2010).

Since this time period, there have been numerous attempts in the history of Engineering to

categorize machine linkages according to their application or type of motion they produce.

Some consider a particular mechanism as a whole while others examine the mechanism as

basic elements. It is agreed by many, including that of Ceccarelli and Moon (2007) that

Leonardo da Vinci attempted to describe the first collection of machine elements in the

Codex Madrid, 1493. Over three centuries after publication of the Codex Madrid, Franz

Reuleaux [1829-1905], often considered “the father of kinematics” (Hanfried and

Mauersberger, 2009) went to describe the mechanism elements as a kinematic chain; this

concept was defined as a system where the motion of a particular element or part is

constrained by all the other adjacent elements.

Engineers and mathematicians have carried out analyses on various configurations of

mechanisms for particular uses with the aim of converting one type of motion into another,

primarily for the function to transmit a force in order to do work (as used during the

industrial revolution) and can be traced back to the time of James Watt [1736-1819], who

utilized linkage mechanisms (from the work of Newcomen) based on the application of

thermodynamics in order to convert pressure energy into mechanical energy. This

mechanism could then translate rotary motion into straight line motion which would

eventually be used on modern steam engines and beguile the minds of other scholars in the

development of machinery and tools, as illustrated by Ferguson (1962).

1.3 Linkage Mechanisms

A linkage mechanism can be described as a closed chain consisting of links (or bars) and

joints with the role of transmission of a particular input force and to provide a means of


6

rotation respectively. In terms of scissors for example, the moving handles are described as

resistant bodies in which enough resistance to the input load is provided in order to allow

the mechanism to move (Eckhardt, 1998). Additionally, in order for a linkage system to be

defined as a mechanism, it is required that one of these resistant bodies remains rigidly

fixed and is known as a ground link, which constrains the other remaining links to follow a

predetermined motion path. In terms of scissors one handle is the ground and the other is

the remaining link.

With mechanisms consisting of more than 2 bars, the same rules still apply. Let us consider

the four bar linkage mechanism in figure 1-6 in the form of cutters where B does not move

relative to the ground and therefore is considered to be part of the ground. The 4 links or

bars are connected by 4 revolute joints and therefore form a 4-bar linkage; additionally, the

mechanism can clearly be seen to be a closed chain and is constrained by only one input

motion.

Suh and Radcliffe (1978) state that three common types of mechanical devices exist which

can be used as part of a mechanism, namely:

1. Gear systems where circular toothed elements in contact transmit a particular

motion between rotating shafts with the aim of maintaining a constant angular

Fig. 1-6: A cutting mechanism based on the four bar linkage (Eckhardt, 1998)

𝐹

𝐶

𝐿

𝐵

𝑃

𝐺𝑟𝑜𝑢𝑛𝑑


7

velocity. However non circular toothed elements are also used for non-uniform

motion transmission.

2. Cam systems whereby a uniform input motion is transformed into a non-uniform

motion at the output. The input motion can be converted into shaft rotation, slider

translations or other specific follower motions by creating a contact between the

particular input cam shape and the follower.

3. Plane and spatial linkages for creating mechanical motions for a point or a rigid

body which can be used for three different types of task

a. Rigid body guidance whereby a body is guided through a series of

predestined positions in space.

b. Path generation. A specific mechanism in which a point on a rigid body

is guided through a series of points on a pre-specified path in space

c. Function generation. A type of mechanism whereby a specific output

motion is generated relative to a particular input motion

In the context of cutting instruments, these particular mechanisms consist of planar and

spatial linkages and can be described as function generators due to the output motion

relying on the type of input motion which is constrained by the configuration of the joints

in the system.


8

1.4 The four bar linkage

According to Phelan (1988) the most common type of linkage used for planar movement

and function generation is the 4-bar linkage where the individual links can be classified as

a:

1. Rocker – A link which can only oscillate

2. Crank – For any link that rotates

3. Coupler – A link which connects a crank to a rocker or a rocker to a rocker

Figure 1-7 illustrates the standard four bar linkage model with an input crank A-D, a

rocker C-B and a coupler A-B.

It is usually the case that power must be transmitted through the linkage from the driver

(A-D) to the output or follower. Phelan also illustrates that if an assumption is made that

the parts within the linkage are frictionless and rotation is slow, that the effects of

acceleration and inertia can be considered as negligible. With reference to figure 1-7, link 3

is a “two-force” member which can only transfer a particular force to B via A and is either

in tension or compression.

Let us consider the output link which is rotating in a clockwise direction against a

counteracting torque from the output link. In order for the system to remain in

equilibrium, the sum of the torques about the output link fixed pivot must equal zero;

therefore the force on the follower as a result of a compressive or tensile force due to the

coupler link can be described by:

Fig. 1-7: The standard four bar linkage model (Phelan, 1988)

𝐴

𝐵

𝐶

𝐺𝑟𝑜𝑢𝑛𝑑

𝐷


9

(1.0)

A free body diagram is illustrated in figure 1-8.

By inspection of equation (1.0), the component of the force acting long the coupler link

will have a minimum value when is equal to 90 and will increase as becomes smaller,

eventually becoming infinite as A-B approaches a parallel condition with respect to B-C,

however a maximum moment on the output angle is applied when is equal to 90 . The

coupler or Transmission angle is of particular interest to the engineer as a mechanism with

a small coupler angle will to lock or jam due to not being able to overcome friction; hence

angles of less than 45-50 are to be avoided (Ambekar, 2007). The positions where the

torque transmission has a maximum value are called Toggle positions and allow for high

degrees of mechanical advantage of the output relative to the input link and are favoured

in applications such as bolt cutters where a high output force is required from a relatively

low input force.

The concept of a useful transmission angle is clearly illustrated by Patel (2011) in figure 1-

9, whereby the maximum and minimum angles are illustrated in order to do useful work.

The input crank link rotates in a clockwise fashion and transmits a force along A-B

whereby the maximum moment is placed on B-Bo when is 90 . However, once the link

Fig. 1-8: Free body diagram of the four bar linkage (Phelan, 1988)

𝐹 𝐷

𝐷

2

𝑇

𝐴 𝐹

𝐹 𝐴

3 𝐵

𝐹

𝐵

4

𝐹 𝐹 𝐶

𝐶

𝐹

𝛾

𝑇

𝐹


10

A-Ao has performed a revolution of 180 , no appreciable transmission of force is applied to

the output link (B-Bo) when becomes a minimum value.

According to Alt (1932), the consideration of the transmission angle of a particular

mechanical system is critical in order for optimum synthesis of a particular linkage

configuration; this relates directly to compound linkage configurations used in cutting tools

in which the transmission angle will determine the output path of the coupler alongside the

corresponding output force.

1.5 Practical investigations regarding four bar linkage mechanical advantage

An experiment carried out by Midha et al (1984) analysed the mechanical advantage of a

four bar double crank and slider mechanism with single-input and multiple-output ports

based on the instantaneous transmission angle over the global range of movement. The aim

of the study was to investigate the mechanical advantage of the system by use of an

opposing external force on the system with a simple spring. The rubber band tension and

the input handle force were obtained as functions of the rubber band displacement; this

meant that the input force could be directly correlated to the tension of the spring.

Assuming the conservation of incremental energy between the input and the rubber band

extension, the mechanical advantage could be given as:

(2.0)

Where is the rubber band tension, is the input force and and are the input and

output displacements (handle displacement and cutter displacement respectively); this

means that the mechanical advantage of mechanisms such as shears, bolt cutters and wire

Fig. 1-9: Maximum and minimum allowable transmission angle in a four bar linkage (Patel, 2011)

𝐴0 𝐴

𝐵

𝐵0 𝐴0

𝐴

𝐵

𝐵0

𝛾𝑚𝑎𝑥 𝛾𝑚𝑖𝑛


11

cutting pliers for example can be simply calculated from the ratio of the displacement of

the handles relative to the displacement of the cutting end.

The double crank and slider mechanism or Elastrator used in the investigation is shown in

figure 1-10 and illustrates the positioning of the input force relative to the main fixed pivot;

figure 1-11 illustrates the correlation between the input force and mechanical advantage of

the system as a function of the rubber band stretch.

𝑆𝑙𝑖𝑑𝑒𝑟

𝐹 𝑑𝑠𝑖

𝐹 𝑑𝑠𝑖

𝐿𝑖

𝐻𝑎𝑛𝑑𝑙𝑒

𝐹𝑖𝑥𝑒𝑑 𝑃𝑖𝑣𝑜𝑡 𝑅𝑖𝑔𝑖𝑑 𝐸𝑙𝑒𝑚𝑒𝑛𝑡

𝑇

𝑇

𝑇

𝑇

𝑑𝑠𝑜

𝐹𝑙𝑒𝑥𝑖𝑏𝑙𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡

Fig. 1-10: Example of an Elastrator, utilizing the double crank and slider mechanism (Midha

et al, 1984)


12

An investigation carried out by Balli and Chand (2002) concluded that the optimum

transmission angle of the coupler within a four bar linkage mechanism is dependent on a

particular link or element having a minimum transmission angle which is greater than the

minimum transmission angles of all the remaining links. It was also found, with reference

to Hall (1961), that the optimum transmission angle of 90 leads to less vibration in the

system and allows the mechanism to be used in high speed applications.

It is the case however, that when more than four bars are used in a particular linkage

configuration, that the transmission angle and therefore the mechanical advantage of the

system cannot be identified easily using standard linkage theory. It was concluded by Wu

(1990) that more than one transmission angle is needed to describe the quality of force and

motion transmission of a particular mechanism, this was suggested from work carried out

where the derivations of the dead centre configurations could be used in order to find the

modified transmission angles for any linkage configuration.

Fig. 1-11: Variation of mechanical advantage of the system based on input force (Midha et al, 1984)

𝑅𝑢𝑏𝑏𝑒𝑟 𝑏𝑎𝑛𝑑 𝑠𝑡𝑟𝑒𝑡𝑐 𝑠𝑜

𝐹𝑜𝑟𝑐𝑒 𝑀𝑒𝑐 𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒

. 916

0

0 0

~35𝑁

𝑀𝑒𝑐 𝑎𝑛𝑖𝑐𝑎𝑙 𝑎𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒

𝐹𝑜𝑟𝑐𝑒

𝑇𝑜𝑟𝑞𝑢𝑒


13

According to Cheung and Zhou (2004), the four bar linkage configuration can generate

multi-phase motion from the adjustment of the driven link fixed pivot which would allow

the system to generate a variety of non-linear motion paths; it was also found that the force

transmission (or mechanical advantage) of the linkage configuration remained at a

maximum with motion paths of high non-linearity. Other authors including Norton (2004)

state that more complex motion paths can be achieved with five and six bar mechanisms

with the introduction of additional position vectors; however the solution to the kinematic

motion of these linkage systems is more difficult to solve due more complex mathematics

which require an iterative solution.

1.6 Degrees of freedom of planar mechanisms

An important design consideration to the Engineer is to determine the number of degrees

of freedom of a particular mechanism and is determined by how the system is constrained

to carry out a particular motion path. For planar linkages, the mechanism is subject to

three degrees of freedom; namely one being rotational and two being translational.

According to Rothenhofer (2010) the number of discrete coordinates needed to describe

the motion of the system are reduced when links are joined together (for example by a

fixed revolute joint). The mobility or number of degrees of freedom of a mechanism can be

calculated using the Kutzbach-Gruebler equation:

3 1 2 (3.0)

Where the number of links is denotes the number of joints in the system.

For a mechanism with 4 links and 4 joints:

3 4 1 2 4 1 (3.1)

Therefore the four bar linkage has only one degree of freedom, or in other words, only the

movement of one particular link (be it the input, coupler or output) will cause the entire

system to move; it is however only the input or output which are usually defined.


14

1.6.1 Grashof’s criterion

In order to further understand the motion of four-bar linkages based on their mobility or

degrees of freedom, Grashof’s criterion allows the engineer to define a four-link kinematic

chain with respect to each link or elements length (Chang et al, 2005).

Where s is the shortest element in a mechanism and l is the longest link, p and q are the

lengths of the two remaining elements.

This can also be written as:

(4.0)

According to Grashof’s theorem, at least one a crank (or fully rotational element) is present

with respect to the remaining links if:

(4.1)

Grashof linkages can be defined in three groups of mechanism based on the position of the

shortest link, namely:

1. Crank-rocker– a mechanism where if the shortest link is adjacent to the ground,

that it is allowed to fully rotate where the remaining adjacent link to the ground is

left to rock or oscillate

2. Double-crank – a mechanism where if the ground link is the shortest link, that

both remaining ground adjacent links are allowed to fully rotate

3. Double-rocker – a mechanism where the coupler is the shortest and is allowed to

fully rotate. The remaining input and output links are only able to oscillate or rock

Therefore from the Grashof definitions, it can be determined that the Grashof’s theorem is

fulfilled if the shortest link can fully rotate with respect to the remaining links. Conversely,

a non-Grashof mechanism has three moveable links which are always in an oscillating

condition.


15

1.7 Dual or compound linkage mechanisms

Compound mechanisms are a means of increasing the total mechanical advantage of a

particular system relative to a mechanism which employs only one simple linkage. The

theory behind compound linkages is that two separate linkage configurations work in

unison in order to scale the total mechanical advantage as a product of each sub-system’s

individual mechanical advantage in order to create appreciable gains of output force, as

stated by Keenan (2006:442) “The total, or overall, mechanical advantage of a compound

machine is equal to the product of the mechanical advantages of the several machines that

make it up”.

1.8 Classical and current methods of linkage synthesis and analysis

The graphical method of determining the motion path of linkage mechanisms has been the

most common means of synthesis of a particular machine in order to carry out a particular

task. It is usually the objective to ascertain the optimal linkage lengths alongside the

transmission angle (also known as coupler geometry) in order for the machine to carry out

the desired motion (Anoop, 2009). In terms of a function generating mechanism, the

objective is to ensure that the constructed machine is designed such that the generated

motion path matches that of graphical methods based on known geometry. An example of

classic basic four bar linkage synthesis is based on the four bar kinematic constraint

equation which is based on the four natural coordinates and is characteristic of a four bar

linkage (Slocum, 2010) allowing the engineer to be able to predict the behaviour of the

mechanism based on the angles of the constituent links and their relative lengths;

Grashof’s theorem also aids the design process by determining how the system will behave

based purely on the linkage lengths; all information needed to kinematically model the

system is then known to the Engineer.

The main limitation of using graphical methods of characterizing the motion of a four bar

linkage is that of only being able to visualize an instantaneous position of all constituent

links; in order to analyse the system dynamically, the use of software integration is a key

tool in accelerating the design process before manufacture of a working model.


16

1.8.1 Computer aided linkage synthesis and analysis

Wang (1996) carried out an analysis of planar four bar linkages using the programmes

MATLAB and Working model. Synthesis of the models was accomplished by design of

one and two dimensional bodies acting as links which were connected by revolute joints

and allowed for analysis of the mechanisms instantaneous position, velocity and

acceleration and also allowed for the model to be analysed in real time; the models created

included the standard four bar linkage, a slider-crank and inverted slider-crank variations.

Wang states that MATLAB is able to solve a variety of numerical problems in much

shorter time periods instead of a bespoke programme written in FORTRAN or C.

MATLAB for example can also be used to analyse singularities of specific linkage

configurations according to when the mechanism reaches its toggle position; this is also an

indicator of the linkage configuration not satisfying the Grashof criterion. Additionally, the

software package is also able to determine when the torque required is too large for a

particular action and illustrates the problem by halting the simulation at discrete positions.

Finally, Working ModelTM

is a mechanism simulation package with the addition of being

able to analyse inertia. Additionally, the particular program is designed such that 2-

dimensional models of the mechanism can be created and analysed in real time and create

graphs of positional vectors, acceleration velocity and other dynamic properties such as the

mechanical advantage of the system.

Shirazi (2007) used 3-dimensional computer modelling techniques in order to construct a

Burmester curve based on Burmester theory for synthesis of spherical mechanisms. The

analysis was carried in order to determine the motion curves with reference to function

generation compared to spatial mechanisms for the role of carrying out complex tasks. The

author states that a variety of CAD (Computer Aided Design) packages can be used for 3-

dimensional motion analysis such as NASTRAN, COSMOS MOTION and ADAMS

VIEW in order to determine whether a designed linkage performs to the intended

specification.

The use of computer programmes also allows for complex calculation to be carried out

quickly and accurately with minimal human error. Other complex arithmetic can also be

carried out by various computer aided programs including that of Finite Element Analysis.

According to Ajuria et al (2010), Finite Element software allow for modelling of linkages

on methods based on energy concepts with the ability to calculate error functions of the


17

inherent design; the user is also able to solve linear and non-linear velocity, position and

acceleration problems with any number of degrees of freedom. In addition of the FEM

method using a global stiffness matrix for a particular set of elements as opposed to the

more complex Jacobian matrix method, no derivation of the inherent constraint equations

or closed loops are required in order for synthesis of a working model.

1.9 Existing Patents review

The following chapter reviews the development of non-surgical and surgical cutting tools

between 1874-2008 and 1903-2005 respectively in order to understand the evolution of

compound mechanisms for various uses.

1.9.1 Non-Surgical cutting instruments

An invention consisting of a compound four-bar linkage design which could be used for

cutting and gripping was suggested by Lindsay (1874) and is illustrated in figure 1-12. The

inventor claims that the design of the linkage allows the user to operate the cutting jaw

with a much greater force than previous designs and that a greater mechanical advantage of

the lever mechanism is achieved during the global travel of the handles.

The design works such that when the handles are in the relaxed position or open, the

pivoted ends of the cutting arms ( ) are brought inwards by the toggling action of the

inner handle pivots ( ), thus opening the shanks of the cutting end. When a load is

applied to the handles, the pivoted arrangement works such that the inner handle pivot

linkage applies a compressive force to the outer cutting shank which ultimately rotates the

blade arrangement around the centre fixed pivot.


18

Smith (1876) suggested the design of a small pair of wire cutting nippers which are

designed such that the curvature of the handles would aid the user apply a greater force

(and hence stress) to the wire. The Ergonomic feature of this design would be to ensure

that a maximum area of the hand is in contact with the handle as well as ensuring a

comfortable grip; this lead to a more convenient method of cutting small wires and allowed

for greater ease of transportation.

This particular design is illustrated in figure 1-13

Fig. 1-12: (Left) Early cutting pliers / pinchers followed by variant products (right) utilizing a

four link mechanism (Lindsay, 1874)


19

An invention by Porter (1880), illustrated in figure 1-14, utilized the theory of compound

mechanisms for the use in heavy duty wire/bolt cutters. This particular design claims that

the introduction of the arms and which are connected to and at one end and to and

on the other provide substantial adjustability when their positioning is modified by bolt

. The author states that this adjustment allows for less wear to be applied to the cutters by

variation of the force transmission for particular tasks.

Fig. 1-13: Ergonomic design patent as opposed to complex linkage

mechanisms or an increase in overall size (Smith, 1876)

Fig. 1-14: A compound mechanism design with adjustable internal spring-

back mechanism (Porter, 1880)


20

A similar but portable variation of this design can be seen from the invention by

Broadbooks (1902) in figure 1-15 in which a similar compound mechanism to figure 1-14

is utilized for smaller gauge wires.

The author states that the design is a “useful improvement” and provides compound

leverage of the cutting head in order for powerful but yet simple operation. The invention

also gives rise to a secondary design feature for a hand held wire cutting device in which

the blades are interchangeable with different cutting heads and are simply removed via two

bolts.

A hand held compound lever device designed for the military for the use of cutting heavy

duty barbed wire is presented by Geddes (1940), figure 1-16. This particular design

comprises of a cutting head lever in the form of an inverted “J” and is operated by a

compressive load being formed at “18” rotating about point “20”. The main revolute joint

at “14” allows for rotation of the cutting head and hence for the input load to be transferred

to the desired object to be cut. The author also states that the invention is based on a

previous patent by Francis T, Lind with patent number 2,239,852 and is designed such that

manufacturing costs are reduced alongside an increased cutting force due to the compound

nature of the linkages.

Fig. 1-15: Compound mechanism with interchangeable single fixing blades

(Broadbooks, 1902)


21

It is argued by Shurtleff (1975), that no compound mechanisms had existed which could

shear through mild steel rod by using only one hand due to inadequate power generation

without long handles or that a specific design utilized a ratchet mechanism. The invention

is intended for the building trade, in which brick-layers are substantially slowed down

when cutting steel rod which is used to reinforce bricks. The author claims that the

patented design can be used on site whilst holding mild steel rod in one hand, and being

able to cut with the other. Two moderately sized handles are shaped such that the input

force is applied in a perpendicular fashion which is then transferred to the cutting head due

to a revolute joint at point “57”. The addition of the compound mechanism where two links

are present either side of the cutting head allow for balanced force transmission and aid to

increase the mechanical advantage of the system. The second handle is mounted such that

maximum force multiplication is transferred to the second cutting jaw in order to provide a

maximum stress on the object to be cut.

The invention by Shurtleff is illustrated in figure 1-17.

Fig. 1-16: A portable hand held compound linkage mechanism with patented inverted

"J" cutting head (Geddes, 1940)


22

A patent applied for by Rowe (1981), suggested the use of multifunctional pliers for the

electrical trade in which various bladed through-holes performed the role of stripping

various sized cables (mainly for coaxial). The tool, illustrated in figure 1-18, is intended to

combine the roles of various tools which crimp, cut, strip, remove and tighten connectors.

One side of the handle is designed to loosen and remove fittings followed by a handle for

connecting and removing cable by virtue of an external thread on the lower boundary of

the handle with accompanying centre thread.

The main centre revolute joint or pivot allows for handle rotation; the length of the handles

relative to the distance of the blades from the fixed pivot allows for a fair mechanical

advantage to be placed on the wires to be cut or stripped. The arrangement of the locating

holes between the bladed segment allows for a greater force to be applied to thicker gauge

Fig. 1-17: Hand held compound rod cutters for use in the building trade,

Shurtleff (1975)


23

cabling followed by a lesser required force to be applied to smaller cables and hence is

positioned further away from the fixed pivot centre.

A final patent worth nothing which illustrates appreciable differences to other common

pliers and cutting tools is the invention by Caravello (2008), illustrated in figure 1-19.

Caravello states that previous products which have been manufactured and incorporate

linkage mechanisms such as levers, cams and gears to act as a compound mechanism for

force amplification have limitations in the sense that the usable gripping or cutting opening

size compared to the opening size of the handles is minimal. Whereas ratchet mechanisms

have been utilized to minimise this particular problem, they are not always the easiest tool

to use with a single hand and do not always release when wanted. Another consideration

which is stated by the author is that of adjustable rack systems in which the force

amplification ratio changes with modification of the rack positioning; this problem is also

evident on sliding fulcrum mechanisms where the distance of the main fixed pivot is

altered with respect to the cutting end and the length of the handles.

The particular invention stated by the author uses a rack system which is adjustable, but

where the pivot point locations are not modified and therefore changes in the mechanical

advantage are negligible.

Fig. 1-18: Multi-functional transportable cutting pliers, Rowe (1981)


24

1.9.2 Surgical cutting instruments

An invention by Koeth (1905) enabled for the user to have a spring assisted pair of multi-

functional pliers with interchangeable cutting heads. The Patent is based on the area of

being able to disassemble the handle configuration and replace the cutting heads with a

punch or wire cutting head for surgical applications; the pivot plate at “18” is allowed to

rotate about “20” and therefore allows for simple removal of the cutting head. This

invention is shown in figure 1-20.

Fig. 1-19: Cutting/gripping pliers with adjustable rack configuration, Caravello (2008)


25

An Endodontic device for securing silver points in root canals is proposed by Rosen

(1960), figure 1-21, in which a novel method cutter has been devised such that minimal

disturbance is caused to the surrounding pulp tissue followed by being able to retrieve cut

wire from the area by use of a special bevelled blade design. Although the pliers are not

particularly large, it is intended for the design to cut a sufficiently soft metal and to finally

produce a flush finish of the point without disturbance and without the possibility of

causing voids around the root canal.

The mechanism is a simple two bar linkage with a single fixed pivot and does not require

for a high mechanical advantage to be produced due to the application. Furthermore, the

smallness of the device is wanted in order to prevent disturbance to surrounding tissue of

the root canal.

Fig. 1-20: Surgical combination tool with interchangeable cutting heads (Koeth, 1905)


26

Tippy (1975) proposed a wire cutting design in which the wire cut-offs would be retained

by a “resilient member” against one of the cutting faces of the tool. The idea is such that

when carrying out orthodontic procedures or jaw surgery, that the user (i.e. surgeon) could

cut the wires shortly enough in order to eliminate interference to internal skin tissue from

excessive lengths of wire; the design encompasses a novel design in order to cut wires

cleanly with no left sharp edges. The design of the blades allows for a shearing action to

occur followed by being retained by the cutting blades in order for efficient and safe

removal without wire elements being left inside the patient’s mouth.

The wire cut-off holder concept can be clearly seen in figure 1-22.

Fig. 1-21: Small surgical pliers for use in Endodontic applications,

Rosen (1960)


27

A variation of the surgical cutting pliers suggested by Tippy is illustrated by Mooney

(1999), figure 1-23, in which several cavities are utilized near the cutting edge in order to

remove wire during certain applications where the excess is not simply allowed to fall after

being disposed from the shearing action. The cutting pliers which are designed for surgical

applications for wire cutting employs a simple 2-bar linkage configuration with a single

fixed pivot design and is characteristic of the size of wire to be cut for the intended

application; the author states that the intended device is best suited for the cutting of softer

metals such as copper, nickel and silver and also explains that harder metals are cut with

greater difficulty and are also less likely to be retained by the cutting head device for

removal.

Fig. 1-22: Surgical cutting pliers for use in jaw surgery and orthodontic procedures, Tippy

(1975)


28

Finally, a patent applied for by illustrates a novel design for a pair of wire

cutting pliers which are specified to be able to cut through 2mm wire with one hand and is

to be used for surgical applications (figure 1-24). The intended application for the product

is for the cutting of wire during operations on bone and joint fractures followed by the

cutting of seams; it is stated by the author that conventional wire cutters cut strands of

specific material individual rather than cutting across evenly and can cause issues for the

patient.

The point of interest for the project lies in the analysis of wire cutting mechanisms and

more specifically the linkage mechanisms employed. The Patent applied for by GEOMED

also encompasses a special linkage configuration which, from figure 1-24, is illustrated by

the intermediate linkage “21” which is allowed to rotate about “22” and transmit the force

from the handles to point “24”. It is to be noted that this particular type of mechanism

satisfies the condition for a “Compound mechanism” due to the fact of intermediate

mechanisms being used to further amplify the mechanical advantage of the system;

furthermore the compound mechanism can be seen to consist of two 4-bar linkages where

the linkage “21” is used to couple the torque to the output link “24”. Finally, to ensure that

the mechanical advantage remains sufficiently high to cut 2mm wire, the distance from the

cutting blades to the main fixed pivot “16” is far less in magnitude when compared to the

Fig. 1-23: The wire retention device proposed by Mooney (1999) for the cutting of

softer wires


29

length of the handle tips to the pivot; therefore it can be seen that this design utilizes all

features from previous surgical and non-surgical mechanisms in order to maximise the

force transmission to the cutting end.

1.10 Current state of the art

Despite the age of the design of scissors and other cutting instruments, the basic concept

has remained more or less the same despite some changes to the linkage design for variable

torque output depending on the application (as illustrated in figure 1-3). In order to gain an

appreciation into the “state of art” of surgical and non-surgical instruments, research is

needed into current products and how these differ to designs pre-dating the 21st century.

Market research on current surgical instruments available which employ various linkage

designs are illustrated in table 1 in order to determine commonly used linkages and if any

linkage configurations differ to the common four-bar link mechanism employed on other

hand cutting tools.

Fig. 1-24: A design patent for compound surgical wire cutters from GEOMED, 2003


30

Surgical wire cutters (other products other than wire cutters excluded, i.e. scissors)

Geomed Accrington Surgical Key surgical Sirag surgical Simplex medical

Hercules double action

wire cutters for 1-2mm

wires. Compound four

bar configuration

Accrington TC wire

cutters for 1.5mm wire.

Simple 2-bar

mechanism with one

fixed revolute joint

Basic wire cutters with

single fixed revolute

joint. No performance

figures are given on

website.

“Small” wire cutters

from Sirag surgical;

basic fixed pivot design

.

Single fixed pivot

design. Maximum

capable cutting

capacity, 1.1mm.

Hercules Gold cut wire

cutters consisting of a

compound four bar

mechanisms

Accrington TC wire

cutters for 2.5mm

wires. Compound four

bar linkage design

Basic wire cutters from

key surgical, no

performance figures

given. Compound Four

bar linkage

configuration

“Medium” wire cutters

from Sirag surgical;

same basic design with

increased handle

lengths

Medium sized wire

cutters with four bar

linkage. Maximum

cutting capacity,

2.4mm

Hercules Gold cut XS

wire cutters: same 2-four

bar configuration as

normal Hercules wire

cutters, however with

greater handle lengths

Accrington TC wire

cutters for 1.6mm hard

wire or 2.0mm soft

wire. Here the four bar

linkage seems to

increase mechanical

advantage.

Heavy duty wire cutters

from key surgical.

Greater mechanical

advantage is given by

longer handle lengths.

However, only one four

bar linkage is used; no

size constraints for this

application

“Heavy” wire cutters

from Sirag surgical.

Same basic single fixed

pivot design although

with longer handle (or

lever) length for

increased input

moment

Maximum sized wire

cutters from simplex

medical incorporating a

four bar link

mechanism and

550mm handles

Table 1: Common linkage designs employed by various manufacturers of surgical cutting instruments

http://www.accringtonsurgical.co.uk/includes/get_image.php?srcimage=http://www.accringtonsurgical.co.uk/cmsfiles/Image/Products/AS-01016 Wire cutter with tungsten carbide inserts 150mm for.jpg&mode=resize&maxw=613&maxh=456

http://www.accringtonsurgical.co.uk/includes/get_image.php?srcimage=http://www.accringtonsurgical.co.uk/cmsfiles/Image/Products/AS-01020 Wire cutter with tungsten carbide inserts hard wire.jpg&mode=resize&maxw=613&maxh=456

http://www.accringtonsurgical.co.uk/includes/get_image.php?srcimage=http://www.accringtonsurgical.co.uk/cmsfiles/Image/Products/AS-01022 Wire cutter with tungsten carbide inserts hard wire.jpg&mode=resize&maxw=613&maxh=456


31

1.11 Ergonomic analysis of hand tools

Edgren et al (2004) carried out an experiment to measure the magnitude of grip force on

different sized cylindrical handles where the aim of the investigation was to compare this

compressive force between 61 males and females of different age groups for an increased

knowledge for designers into the optimum size of handles for operators of varying hand

sizes. The particular apparatus consisted of a cylindrical strain gauge measuring forces in a

single direction across the cylinder length at 50 Hz, using an analogue to digital converter

and amplifier. This made it possible to record the grip force overtime and also allowed for

analysis of particular tendons in the forearm being used when gripping at different

orientations relative to the wrist positioning with different areas of the hand (a pinch-grip

for example, which subjects tendons in the forearms to a higher stress). The author states

that larger diameter handles are favoured to minimize contact stress between the hands but

could consequently lower the applied grip force when exceeding the optimum diameter; if

a handle is to be pulled, that the force should be normal to the surface of the palm in order

to further minimize tendon stress and the chance of injury. From the 61 subjects tested, the

maximum average grip force for males and females was at a span (or radius) of 3.81cm

with a force of 306N and 169N respectively and illustrates the importance of a comfortable

grip for the user for an increased efficiency of force transmission.

The results of the investigation can be viewed in figure 1-25.

0

50

100

150

200

250

300

350

0 2 4 6 8

Fo

rce

(N)

Handle size diameter (cm)

Grip force Vs. handle size

Males

Females

Fig. 1-25: Grip force vs. handle size (Edgren et al, 2004)


32

According to Mcgorry (2004), the main factors to consider when designing hand tools

include the frequency of use, the posture of the user when using the equipment, rest

periods between use and the magnitude of the force which is applied, where these design

considerations are crucial to avoid musculoskeletal injuries and disorders and of which

were a key factor of 9% of work related injuries during 1984 in industry.

Another important design criterion is that of the safety factor applied to hand tools relative

to grip stress. Theoretically, the minimum grip force required is that to provide equilibrium

by balancing the forces to prevent the object slipping. The force which essentially keeps

the device in the hand is based on grip and friction at the interface and depends on various

factors including the use of gloves or if vibration is present. The work force ratio can be

expressed as the working gripping force divided by the minimum force needed to keep the

device in the hand and is a useful quantitative measure of minimizing hand strain and/or

injury by excessive force for a particular application.

(5.0)

Working force ratio (which is also a form of a factor of safety) can then be expressed as:

(5.1)

Where the “FOS” will always be greater than one, however smaller numbers indicate a

lower working force ratio and therefore a lesser likelihood of hand strain due to repetitive

tasks with high grip forces.

Other factors also need to be considered for optimum ergonomic hand tool design and

depend on the application of the particular device; these include the specific shape of the

handles for varying degrees of force distribution along the handle and how the hand works

in conjunction with the mechanism in order to provide sensitive movement or a “power-

grip” which essentially maximises the generation of force along the handle major axis. For

screwdrivers for example, one of the design considerations is that of the shear force at the

interface between the hand and the handle and is a function of the handle radius.

A kinematic model of the human hand was proposed by Buchholz and Armstrong (1992)

for ergonomic and potentially orthopaedic uses, whereby the grip force was predicted for

varying hand postures using an algorithm to compute surfaces of contact between


33

simplified elliptical polygons in order to estimate the contact area of skin with cylinders

based on ideal joints. The algorithm was synthesized such that the degree of flexion could

be assessed for individual digits based on an increase in cylinder size (and therefore span

of the hand) alongside a measure of the joint angle of each digit in order to assess a

potential grip strength, which was estimated by a hypothetical model of the assumed soft-

tissue deformation. It was found that an increase in cylinder size for which to apply a

gripping force allowing for less flexion of the major joints. As expected, an increase in

hand length illustrated increased flexion of the hand for all four digits (where the thumb

was neglected due to negligible mobility).

1.12 British standards for surgical cutting instruments and maximum loading

British standards are a method of ensuring a particular process is carried out in a pre-

specified manner and is a means of providing an agreed document between buyers,

manufacturers, regulators and users in order to increase the reliability of particular

products and services (BSI group, 2011). In order to ensure the safe and intended use of

cutting instruments in an orthopaedic environment for example, regulations and guidelines

are given to ensure the product is chemically safe; for non-surgical applications, guidelines

are available in order to produce mechanically sound plier designs based on guideline

geometry.

1.12.1 Stainless steels for surgical cutting instruments

The British standard BS EN ISO7153-1:2001/BS 5194-1:1991 “Steels for surgical

instruments” lists the material compositions which are suitable for use in a surgical

environment (all of which are stainless steels); of the materials listed, only three are stated

as being preferable for use in surgical wire cutting pliers.

The stainless steel compositions allowed for wire cutting pliers in a surgical environment

are illustrated in table 2; the complete list of surgical steels suitable for varying instrument

use is illustrated in appendix “1”.


34

Steel grade Chemical compositions (%)

Ref Grade No.

According tob

C Si

(max)

Mn

(max)

P

(max)

S Cr Mo Ni Other

Elements

ISO

4957

ISO

683-13

Martensitic Steels

D

H

I

—

—

—

—

—

—

0,42 to 0,50

0,35 to 0,4

0,42 to 0,55

1

1

1

1

1

1

0,04

0,045

0,045

0,03 max.

0,03 max.

0,03 max.

12,5 to 14,5

14 to 15

12 to 15

—

0,4 to 0,6

0,45 to 0,9

1 max.

—

—

—

V: 0,1 to 0,15

V: 0,1 to 0,15

Table 2: Surgical steels suitable for wire cutting pliers (BSOL, 2011)

Realistically, all of the material compositions stated in BS EN ISO7153-1:2001/BS 5194-

1:1991 could potentially be used for wire cutting pliers so long the material properties meet

the intended specification of the manufacturer. It is stated by Baratz (1999) that common

Stainless Steel alloys used for biomedical applications include the types AISI 316 and

316L, where L denotes the reduced carbon content of 0.03% maximum 0.08% compared to

standard 316. The author also states that the Engineer is not limited to only using Stainless

Steel’s but has an extended choice covering other materials such as Titanium and certain

Ceramics; commonly used for biomedical implants.

The British Stainless Steel Association (BSSA, 2010), with reference to BS EN ISO7153-

1:2001/BS 5194-1:1991, states that the grades A, B and C are broadly classified as AISI

410 and 420 Steels and used comprehensively in the field of surgery and dentistry due to

good corrosion and wear resistance; additionally, these properties can be improved by

means of heat treatment. The BSSA also states that Martensitic Steels provide long service

lives for surgical equipment through proper maintenance and that some instruments can

have service lives of up to 30 years; although wear is to be expected from instruments with

the function of cutting for example, it is critical for the tool to be resistant to corrosion.

1.12.2 Guideline cutting forces for lever assisted cutting pliers

Additionally, wire cutters (surgical and non-surgical) should conform to BS 3087-7:1996,

ISO 5747:1995, a specification for dimensions of lever assisted side cutting pliers, end and

diagonal cutting nippers, which illustrates the geometry of a particular design with its

corresponding maximum guideline application of force. Table 3 illustrates the variable

input forces with respect to a maximum cutting force relative to a specific gauge wire and

mechanical advantage of the mechanism.


35

L L1

Lever ratio

(mechanical

advantage)

Cutting test Load test

Diameter

of hard test

wire

Db

Maximum

cutting

force

F1 (max)

Load

Maximum

permanent

set

smaxc

mm mm mm N N mm

125

140

160

200

60

75

90

125

15

15

15

15

1,25

1,4

1,6

2

260

310

370

530

360

450

540

750

1

1

2

3

Table 3: Maximum permissible cutting force for lever assisted side cutting pliers (British

standards online, 2011)

The equation relating to the maximum cutting force with the basic plier geometry is given

as:

(6.0)

Where:

is the measured distance from the applied load to the main fixed pivot

is the distance from the main fixed pivot to the applied load from that given in

table 3

F is the load given in table 3

is a compliance equivalent load.

For lever assisted side cutting pliers with specifications that do not match those details

given in table 3, the following equation can be used.

2

(6.1)

Where:

2 is a correction factor for hard wire

is the measured span of the handles when open

is the measured span of the handles in the closed position

is the relaxed distance of the cutting jaws


36

Additionally, the lever ratio (LR or MA) of the system can be expressed as:

(6.2)

However it is stated that the equations illustrated are for the purposes of verifying a

particular linkage design and does not affect the design of a particular product.

1.13 Conclusions from background literature and market research

An appreciation has been gained toward the historical development of surgical and non-

surgical cutting tools in the form of blade and linkage design in order for the instrument to

be used for a particular application; aside from increasing the efficiency and cutting

capacity of cutting instruments from an increase in overall size, the methods employed

include the re-design of the cutting heads with respect to their length ratio to the main fixed

pivot relative to the handles alongside wire removal features - which allow for variable

design to meet an intended specification.

Furthermore, limitations have been determined from using graphical methods of

interpreting the commonly used 4-bar linkage kinematic behaviour due to analysing the

mechanism at one instantaneous point in time. For this reason other methods are employed

in order to analyse the motion paths of mechanism by use of computer aided software such

as “Working Model”, “Nastran”, “Adams View” or “Cosmos Motion”; Finite Element

Software is also available for analysis of the distributions of stress within the system. It

has been established that the design of the individual linkage lengths alongside their

respective angles relative to the ground are crucial to determine the correct motion path

and for synthesis of the force transmission characteristics over the global range of travel

and ultimately determines the amplification of the force used in compound 4-bar link

mechanisms.

From the market research undertaken alongside a review of surgical and non-surgical

patents, the most commonly used type of mechanism is indeed the 4-bar linkage – most

notably used in compound configurations for increased output forces for use in cutting

instruments.

It has also been made clear to consider the shaping of cutting tool handles as well as the

form of loading (as illustrated by Mcgorry, 2004) to ensure that strain injury is minimized

from continuous high loading and/or repetitive use. From the work of Edgren et al (2004),

the importance of handle span of a particular hand tool has a substantial influence on the


37

gripping force with a maximum of 306N and minimum of 180N with a handle diameter of

3.81cm for males.

From research into British Standards regarding surgical and non-surgical wire cutting

pliers, it is understood that strict criteria need to be met in order to ensure that the material

used is non-reactive, non-corrosive and not susceptible to external influences

(heat/humidity changes); for this reason only a limited amount of Stainless Steels can be

used for surgical/orthopaedic applications. The Engineer does still however have

reasonable selections of materials and is not limited to one specific Steel alloy

composition; this is confirmed by the BSSA and authors such as Baratz (1999) who state

that other types can be used such as AISI 410 and 420 although 316 and 316L are the most

commonly used. Additionally, the guidelines on the maximum input and cutting forces

have been established with respect to the wire cutting plier’s geometry and are useful for

determining the performance of a particular linkage design.

2 Project aims and objectives based on background literature

The aim of this paper is to review the design of a particular pair of Hercules gold cut wire

cutting pliers from GEOMED, a manufacturer and supplier of premium surgical

equipment, due to possible improvement being made to the product’s linkage configuration

in order to increase the mechanical advantage of the system, allowing the user to apply a

reduced load to the handles whilst maintaining an equivalent output force. The scope of

the paper is to review both the theoretical model associated with the linkage configuration

on the GEOMED wire cutting pliers and to compare this model with experimentation in

order to determine an optimized solution for the mechanism.

The investigation to be carried out will continue from the work of Cheung and Zhou

(2004) by analysing the systems mechanical advantage (by inspection of the transmission

angle of the design) from adjustment of the driven link fixed pivot. The work will also be

taken further by considering the four bar linkage as part of a primary single fixed pivot

system rather than an individual mechanism (as utilized by GEOMED in their existing

products); this will require a more in-depth analysis of the flow of the force from the

predetermined input at the handles, through to the internal four bar linkage configuration

and will be analysed by using program’s such as “Working Model” to determine how the

linkage configuration affects the overall output of the system . Working model has been


38

chosen over other kinematic modelling software packages due to the programs simplicity

and versatility for analysing linkages.

From a practical investigation carried out by Midha et al (1984), the basis of determining

the mechanical advantage of the system can be related to using a force balance at the

output in order to analyse the mechanical advantage through the overall range of

movement of the handles; this also forms a basis for the project to carry out a practical

investigation for a proposed working model of the GEOMED Hercules Gold-Cut wire

cutters with variable input linkage positioning in order to verify the results obtained from

computer aided analysis.

2.1 Generalized method layout to fulfil project objectives

Based on the background literature the generalized project layout and methods of

accomplishing the project aims and objectives will be to:

1) Perform an initial analysis on the Geomed Hercules wire cutting pliers kinematically,

whereby measurement data is needed of the product’s joint coordinates in order to

determine the corresponding linkage lengths and internal angles; this is to be carried

out using a DS401SM/JT12A-B shadowgraph machine from Midland Metrology Ltd

and measured from the specified datum. The particular machine is capable of

measuring X,Y and Z coordinates with a sensitivity of 0.001mm in order to ensure

that measurements are taken as accurately as possible with minimal error;

additionally, the magnification of 20 used on the projecting screen, alongside a static

target display, ensures that any movement of the wire cutters is reduced and that

repeatable measurements can be taken to ensure the measurements are taken

correctly.

2) Obtain a transmission ratio index for the internal linkage mechanism which can be

multiplied with the mechanical advantage of the “scissor” or external linkage

mechanism associated with the handles and will give an estimated value for the total

mechanical advantage of the mechanism

3) Create a 3-dimensional model of the Hercules Gold-Cut wire cutting pliers based on

results taken from measurement data from step 1; the program of choice for this

process will be Pro EngineerTM

Wildfire 5 due to a robust interface for creating part

bodies / solids. Upon obtaining a finished model, an assembly of the model is to be

imported into a drawing sheet from which a particular view can be exported into


39

Working Model in DXF format; this is then to be constrained using pin joints in

order for the model follow an identical motion path to that seen on the Geomed wire

cutting pliers.

4) Compare initial kinematic analysis with that of the computer generated model to

validate the theoretical principle of mechanical advantage; the program of choice to

measure the overall output force of the system will be Working ModelTM

due to

effective results obtained by Wang (1996) and being able to visualize the

instantaneous mechanical advantage based on input displacement and spring

tension.

5) To modify the 3-Dimensional model with a series of adjustments to the driven link

fixed by variation of the joint in X and Y; using geometry, the input link will have

to be altered accordingly in order to prevent an increase or decrease in handle span.

This model modification can then be exported as a DXF back into working model

in order to verify an increase or decrease in the systems mechanical advantage

6) Obtain an appreciation of the stress distribution within the Geomed wire cutting

pliers by exporting the model into SolidworksTM

as individual components and

constrained in an assembly for subsequent analysis; this will allow to visually

(indirectly) gauge the flow of the force from the handle to the cutting end and allow

to visualize which areas are under high stress

3 Hypothesis

Based on the statement made by Phelan (1988) where the torque transmission of the

internal compound linkage should have a maximum value when the input link angle is

oriented such that the transmission angle is 90 degrees, in this position, the cutting pliers

should have be in a position of maximum force transmission through the coupler link; the

maximum force transmission will occur in the toggle position, or when the coupler link is

parallel with the output link.

From preliminary inspection of the Geomed Hercules wire cutters, the input link of the

internal patented mechanism is such that a maximum transmission angle is present at the

start of travel and approaches a perpendicular condition to the coupler link over the global

range of movement; for this reason it is expected that the mechanical advantage of the

system will be maximum at the end of travel and minimum at the start of travel.


40

Finally, it is predicted that the internal linkage mechanism should behave as a crank-

rocker, a double crank or a double rocker depending on the corresponding internal linkage

lengths. However if Grashof’s theorem is not satisfied where the longest link plus the

shortest link is less than the sum of the remaining link lengths; then the system is not a

Grashof linkage and can therefore not rotate fully. It is expected that the system will not

conform to Grashof’s criterion due to the application in which the mechanism is used (over

small distances/arcs); additionally, the torque would reverse if the input angle is greater

than that needed to create a toggle position and would therefore not be practical for use in

wire cutter design.

4 Instantaneous transmission ratio based on the kinematic constraint

equation

In order to truly understand how the transmission ratio changes with respect to the input

and output link angles (relative to the ground), let us again consider the generalized four

bar linkage (figure 4-1). Rothenhofer (2010) discusses that any angle can be found in the

four bar linkage mechanism based on all instantaneous values of the remaining angles

(with reference to the Kutzbach-Gruebler equation) by use of the kinematic constraint

equation and can be derived by use of simple trigonometry

Fig. 4-1: Generalized four bar linkage model for constraint equation derivation (Rothenhofer, 2010)

𝑏

𝑏

𝑎

𝑎

𝑐

𝑐

𝑑

𝑑

𝜃 𝜃

𝜃

𝜃

𝛾

𝜇


41

With reference to figure 4-1, it can be clearly seen that application of the cosine rule with

respect to links d and c must yield the same answer of applying the same method to b and

a. Using this relationship, the derivation of the constraint equation can be carried out.

Modifying figure 4-1 for ease of illustration to create figure 4-2:

Using the cosine rule:

2 1 0 2 1 0 (7.0)

Also:

(7.1)

And:

(7.2)

By using basic rules of trigonometry, the constraint equation can be described as:

2 2 2 0 (7.3)

𝜃 𝜃

𝜃

𝜃

𝛾

𝜇

𝑎

𝑎

𝑏

𝑏

𝑐

𝑐

𝑑

𝑑

𝑅

𝑅

Fig. 4-2: Modification of figure 4-1 to illustrate derivation of trigonometric terms

𝑐𝑠𝑖𝑛 𝜃

𝑐𝑐𝑜𝑠 𝜃

𝑎𝑠𝑖𝑛 𝜃1

𝑎𝑐𝑜𝑠 𝜃1

𝑆𝑡𝑎𝑡𝑖𝑐 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑒 𝑗𝑜𝑖𝑛𝑡


42

In order to obtain an instantaneous torque transmission value, equation (7.3) needs to be

differentiated with respect to time.

2 2 2 0 (7.4)

Where:

(7.5)

From simple gear theory where the ratio of the angular velocities of each element gives

rise to a constant, namely the ratio of torques, the ratio of

can also be used for four bar

mechanisms due to the movement being a particular motion about an arc.

Then dividing by yields:

(7.6)

Hence an expression has been developed which relates the transmission ratio to the

instantaneous angular position of all the links within the system.

A full derivation of equation (7.6) is illustrated in appendix 2.


43

5 Linkage configuration analysis of Geomed-Gold Cut wire cutting

Pliers

It has been determined that the most common types of linkage configuration used in

cutting pliers is that of the four bar linkage, usually in compounded form in order to

increase the mechanical advantage of the mechanism further; by inspection, the Hercules

Gold-Cut wire cutting pliers also employ a compounded four bar linkage configuration in

order for boring wires up to 3.0 mm in diameter.

The Hercules Gold-Cut wire cutting pliers are illustrated in figure 5-1.

Figure 5-2, a modification of figure 5-1, illustrates each simple mechanism configuration

in order to create the patented GEOMED design; the orange and green links denoting the

simple lever and internal compounding mechanisms respectively. The green line represents

the shared link between the two mechanisms and is responsible for transferring the force

from the handles to the cutting end. Additionally, this is ultimately the input link to the

second mechanism and can be treated as link “a” – as denoted in previous examples.

Fig. 5-1: Geomed Hercules Gold-Cut wire cutting pliers (Geomed, 2011)


44

As the shared link (green) is the input link and the ground being the fixed link associated

with the right hand side handle (with respect to figure 5-2), it is straight forward to

determine the coupler and output links and therefore a force transmission ratio. However,

in order for accurate analysis to be carried out on the Hercules Gold-Cut wire cutters,

accurate measurement data is required alongside the corresponding linkage angles in order

to obtain sensible and reliable results

5.1 Apparatus/Software required for obtaining linkage point coordinates

DS401SM/JT12A-B shadowgraph from Midland Metrology Ltd

Protractor to take initial angle data

GEOMEDTM

Hercules Gold-Cut wire cutting pliers

Pro-Engineer Wildfire 5TM

(Also known as Creo)

Ruler for initial measurement of basic plier dimensions

The shadowgraph is illustrated in figure 5-3.

Fixed joint

Moving joint

Main fixed pivot (Datum)

Fig. 5-2: Geomed compound linkage break-down (Geomed, 2011)


45

5.2 Method of obtaining linkage point coordinates / internal angles

The method of obtaining the linkage point coordinates, in sequential order, was to:

1) Position the wire cutting pliers on the glass table of the shadowgraph, ensuring the

entire model sits on the projected face with no overlap

2) Use the main datum of the model as a reference for all other dimensions to avoid

anomalies caused by moving the model

3) Move the table in X and Y to measure the centre points of the remaining links with

respect to the main datum; the projected image on the screen of the shadowgraph

(magnification of 20X) would allow for precise measurement with minimal error in

the deviation of results from the centre line

4) To plot these points in Pro Engineer in order to obtain the internal angles of the

linkages which would be used for subsequent analysis to calculate the systems

mechanical advantage

Critical dimensions needed are illustrated in figure 5-4.

Fig. 5-3: Shadowgraph from Midland Metrology Ltd


46

Fig. 5-4: Physical Geomed wire cutting plier image

5.2.1 Preliminary initial measurement with ruler:

Relaxed cutting end gap width - 5mm

Relaxed handle span – 105mm

Closed handle span – 70mm

Wire cutter weight – 4.134N (421.3 grams)

Tip of handle to datum – 185mm

Distance of cutting end to fixed pivot – 25mm

These measurements would be verified with joint positions of the relaxed wire cutting

pliers and would therefore be used in the creation of a 3-dimensional computer aided

design model in order to replicate the product as closely as possible. Variations in handle

breadth and cutter head shape should not have affected final results with the positioning of

joint rotation and spacing between static joints being most critical.

Relaxed

cutting end

width

Relaxed

handle

span

Handle tip to datum Distance of cutting end to

fixed pivot


47

5.3 Hercules Gold-cut join coordinates

Measurement data taken with the shadowgraph is illustrated in figure 5-5. The dimensions

have been plotted on a drawing sheet in order to log the joint positions visually where all

measurements are in mm. The reason for measuring all joint positions with respect to the

main static joint was to prevent movement of the cutting pliers between each reading; this

would allow for the product to remain in a static position whilst measuring each data point

and minimize the chance of induced errors.

Fig. 5-5: Hercules Gold-Cut joint coordinates taken with shadowgraph


48

6 Reverse Engineering of Geomed wire cutting pliers

In order to analyse the Geomed wire cutters dynamically with eventual modification of the

driven link fixed pivot, a Computer Aided design model needed to be created using Pro

Engineer. This would form the basis for subsequent Finite Element Analysis and for the

ability to import the 3-dimensional geometry as a drawing (2-Dimensional DXF) into

Working Model in order to validate theory with against practical results.

The computer generated model would allow for kinematic analysis of the internal and

external linkage mechanisms combined and how the movement varies upon modification

of the input link fixed pivot. The dimensioning of the model could then be checked through

the use of measurement tools within the CAD package to ensure that the specific tolerances

were met in order to obtain a good product benchmark.

6.1 Product design specification

In order to ensure the correct targets were met and that accurate analysis could be carried

out on the computer generated model, a product design specification would act as a means

to ensure all the relevant criteria had been met in order to obtain reliable results (based on

background literature). For example, the most commonly used Stainless Steel is that of

316L (Baratz, 1999), therefore the specification for the model material would be 316L in

order to utilize coherent mechanical properties for a specific material alloy.

The cutting blades were however made of Tungsten Carbide (Geomed, 2011) and therefore

have a significant difference in mechanical properties relative to the 316L used for the wire

cutter handles and linkages. According to Matweb (2011), a material library consisting of

over 86,000 metals, ceramics and polymers, Tungsten Carbide

(WC) has a Young’s modulus of 682.5Gpa (average), density of 15.7g/cc and ultimate

tensile strength of 344Mpa. For 316L (with negligible differences between annealed

bar, sheet plate and strip) the mechanical properties are 193Gpa for Young’s modulus,

a tensile strength of 560Mpa and a density of 8g/cc.

This data could then be used for subsequent Finite Element Analysis to ensure the model

behaved as closely as possible to that of the Geomed wire cutting pliers. Finally, the

product design specification (see table 4) is generated to ensure that the design dimensions

are as close to the existing product as possible, despite only having taken measurements of

the key joint positions. An estimation of how closely the model represents the ideal


49

(Existing product) would be to take a final mass measure once the relevant materials had

been applied to the 3-Dimensional design model.

# Need Metric Importance

(out of 10,

10 being

highest)

Units Marginal

value

Ideal value

1 Wire cutters

have

increased

mechanical

advantage

over

standard

product

Output force 10 N 1.75-2.25 1.9

2 For product

to remain

comfortable

for use

without

significant

alteration to

handle span

Handle span

from centre

line

8 mm 100-110 105(measured)

3 For mass to

remain at

current

value of

original

product

Product mass 5 g 400-500 420 (weighed)

4 Cutter

geometry to

match

original

product

Cutter-head

span

7 mm 4.5-5.5 5

5 Wire cutters

to have

same input

torque from

handles

Handle length 9 mm 185-190 185


50

Table 4: Design requirements for 3-Dimensional model

6 Output

torque to

match

existing

product

Distance of

cutter head to

main fixed

datum

9 mm 30-40 35

7 Closed

handle span

to match

existing

product to

determine

correct

benchmark

value of

total

mechanical

advantage

Closed handle

span

9 mm 70-75 70

8 Ensuring

body of

pliers

behaves

identical to

existing

product

Handle and

body to be

created as

316LStainless-

Steel

8 UTS

560Mpa

0 560

E

193Gpa

0 193

Density

8g/cc

0 8.0

9 Identical

deformation

of wire

Cutters to be

constructed

from Tungsten

Carbide (WC)

9 UTS

344Mpa

0 344

E

682.5Gpa

0 682.5

Density

15.7g/cc

0 15.7


51

6.2 CAD development

The first step of designing a 3-Dimensional model of the Geomed wire cutters in order to

obtain benchmark values of force transmission before modification of the input link

positioning would be to model the left side handle, due to this component incorporating the

main fixed datum from which all other measurements are taken relative to; figure 6-1

illustrates the initial design component.

This would be followed by designing all constituent linkages to gauge the positioning of

the remaining components due to knowing the lengths of the linkages from preliminary

measurement; illustrated in figure 6-2.

Fig. 6-1: The modelled LHS handle

Fig. 6-2: The modelled linkages


52

Figure 6-3 illustrates the linkages in the constrained condition using the preliminary

measurement data. Data points could be set at the coordinates obtained, followed by

measuring the angles between these coordinates.

As the main datum had already been implemented into the left side handle, the right cutter

could be designed with respect to this datum. The right blade was created using a mirror of

the left handle and split with a plane normal to the datum axis; this would create a direction

for the joint to be connected to the coupler link. The right cutter model is illustrated in

figure 6-4.

Fig. 6-3: CAD model representation of linkage constraints to set correct angles

Fig. 6-4: CAD model of RHS cutter


53

The Right hand side handle shown in figure 6-5 could now be created with respect to the

span of the internal linkage configuration due to constraints applied in earlier stages; this

would also allow for correct joint placement on the right handle in order to obtain an exact

replica position of the original Geomed wire cutters.

The final critical components before component assembly would be to model the

Tungsten-Carbide blades (figure 6-6). This was achieved by using the left hand side handle

as a reference and sketching on a plane normal to the under-side of the cutter-head. The

blade was then mirrored to create a right hand part and finessed in order to ensure either

side would create a parallel touch condition.

Fig. 6-5: The modelled right hand side handle

Fig. 6-6: The modelled Tungsten-Carbide blades


54

Using the constrained linkages from preliminary measurement, all constituent components

could then be constrained together using pin joints order to create a model which could be

analysed kinematically and exported into working model.

Figure 6-7 illustrates the finished model with added fixings and foam wire grips in order to

replicate the model weight as closely as possible.

A rendered image using Autodesk ALIASTM

is shown in figure 6-8 in order to view a

higher detailed model; figure 6-9 illustrates the dimensions which are needed to meet the

intended specification.

Fig. 6-7: The finished computer generated model


55

Fig. 6-8: Rendered images of the Geomed wire cutter computer generated model using the standard linkage configuration


56

Fig. 6-9: Summary technical drawing to illustrate critical dimensions


57

6.3 3-Dimensional computer model summary specification

Using Tungsten as the material for the cutting blades and Stainless Steel for the cutter body

from Pro Engineer’s material library, the overall mass of the wire cutters was in the region of

405g (as seen in figure 6-10).

From table 4 and figure 6-9, the computer generated model met the intended specification,

lying in the specified ranges for each design criteria as generated from preliminary

measurement data.

As the computer generated model met the intended specification which therefore matched the

original wire cutters from Geomed, front views of the major components (handles, cutting

blades and linkages) could be exported into a drawing sheet and subsequently saved as a

DXF file, this would then be imported into working model to obtain a benchmark value for

the mechanical advantage.

7 Theoretical kinematical and torque transmission analysis

The following chapter will analyse the mechanical advantage of the Geomed wire cutting

pliers with respect to the external and internal linkages in order to create the compounded

four bar configuration. With reference to Rothenhofer (2010), the constraint equation will be

used to analyse the internal four bar linkage transmission ratio based on instantaneous

internal angles, followed by multiplying this value by the external linkage mechanism with

respect to the input. Finally, this value is then to be compared with the lever ratio stated by

the British standard BS 3087-7:1996 to check each method’s validity.

Fig. 6-10: Model mass properties


58

7.1 Geomed internal four bar linkage transmission ratio (relaxed position)

Using the coordinates from figure 5-5 and joining the points to create lines and hence

measurable angles allows for creation of figure 7-1 where the mechanism is in the relaxed

state:

Fig. 7-1: Internal four bar linkage analysis of Geomed wire cutting pliers

Where 64. , 140.1 , and 133.3 .

Using the kinematic constraint equation (equation 7.6):

Then:

( 20.311 66.641 64. 20.311 34.443 64. 140.1

34.443 66.641 140.1 20.311 34.443 64. 140.1 ) (8.0)

1223. 2 6 6.9

14 2.33 6 6.9 0.69 (8.1)

The transmission ratio of the internal linkage in the open position is then:

1

0.69 1.45 (8.2)

𝐴 20.311𝑚𝑚

𝐵 = 31. 0𝑚𝑚

𝐶 34.443𝑚𝑚

𝐺𝑟𝑜𝑢𝑛𝑑 𝑅𝐻𝑆 𝐻𝑎𝑛𝑑𝑙𝑒

𝛾

𝜃

𝜃

𝐷 66.641𝑚𝑚


59

7.2 Geomed internal four bar linkage transmission ratio (3mm offset)

From having created the three dimensional Pro EngineerTM

model and constraining the

assembly in order to obtain a fully functioning kinematic mechanism, the handles could be

closed in CAD based on measurement data in the relaxed position; this gave the angles 63.2

and 139.0 degrees for and respectively; as illustrated in figure 7-2.

`

Then:

( 20.311 66.641 63.2 20.311 34.443 63.2 139.0

34.443 66.641 139.0 20.311 34.443 63.2 139.0 ) (9.0)

120 .16 6 .20

1505. 6 6 .50 0.64 (9.1)

The transmission ratio of the internal linkage in the 3mm offset position is then:

1

0.64 1.56

(9.2)

The answer obtained from equation (9.2) may seem low initially, but this value is not too

dissimilar from that claimed by Geomed themselves (figure 7-3). With a transmission ratio of

1.56 compared to a value of 1 with no internal compound linkage, only 64% of the input

force is required to create an equal output force; thus allowing the user to apply a load 36%

less.

Fig. 7-2: Internal linkage angles for 3mm cutter offset


60

As the value for mechanical advantage of the patented compound mechanism illustrated a

close correlation to the calculated theoretical value in the cutting position, kinematic analysis

using the kinematic constraint equation of a four bar linkage proves to be a valid method of

determining the instantaneous force transmission index (mechanical advantage) for any given

input angle – furthermore, the results also confirmed that the 3-dimensional Pro-Engineer

model had been created with a minimal deviation in geometry to the GEOMED wire cutting

pliers.

7.3 Combined mechanical advantage of Geomed wire cutting pliers

From Keenan (2006), the total mechanical advantage of a machine is the sum of the

individual simple mechanisms. Therefore the total mechanical advantage of the Geomed

cutting pliers would be the product of the internal and external linkage mechanisms.

From simple lever theory:

Fig. 7-3: Transmission quality compared to claimed value by Geomed (Geomed.de, 2011)


61

(10.0)

Where the torque is exerted on the handles due to a perpendicular force acting to the

input linkage of the external mechanism (the handles) and is the output torque at the

cutting end. The output force relative to an input at the handles is simply then a ratio between

the length of the handle relative to its point of rotation and the distance between the cutting

end and the main fixed pivot or:

(10.1)

Then the lever ratio for the external mechanism (for maximum leverage) and using figure 6-9

is:

1 6.2 1 .0

24.0 .0 (10.2)

From Keenan (2006), the total mechanical advantage in the 3mm offset position is then:

.0 1.56 10.92 (10.3)

7.4 Mechanical advantage using lever ratio equation from BS 3087-7:1996

From BS 3087-7:1996, where the overall lever ratio is based on the displacement of the

handles relative to the cutting end (using equation (6.2)):

The total mechanical advantage or lever ratio based on angular displacement is then:

104. 1.9

3.0 10.93 (10.4)

Figure 7-4 illustrates the process of choosing 3mm as the offset gap for the cutting position.


62

Fig. 7-4: Cutting end gap between blades based on BS 3087-7:1996

From a preliminary theoretical analysis, equation’s (10.3) and (10.4) gave extremely similar

results with negligible differences in mechanical advantage (less than 0.1%), illustrating the

validity of each method of calculation; hence proving the notion that the overall mechanical

advantage for a complex system is the product of the mechanical advantage of each

constituent simple mechanism.

Most importantly, the results showed that either method of calculation could be used in order

to determine the systems mechanical advantage for any instantaneous position of either the

handles (using the method from BSI) or the product of the mechanical advantage of the

internal compounded mechanism at the corresponding instantaneous linkage angles and that

of the external mechanism, i.e. the ratio of distances between the cutting end to specified

product datum (cutting end pivot) and the point of loading to the handle pivot.

8 Excel analysis of internal linkage mechanism

Inspection of figure 8-1 illustrated that the maximum force transmission quality is present

when the coupler link is parallel to the input link and supports the hypothesis based on the

work of Phelan (1988). From equation (1.0), it could be seen that when this condition was

approached, that the sin of the transmission angle approached zero causing the coupler force

to tend to infinity and therefore reaching its toggle position; these same results were

encountered by Chang and Lin (2002) who plotted the FTI (force transmission index) as a


63

function of input link rotation and witnessed this index tending to infinity at the mechanisms

toggle position.

The data table for figure 8-1 can be viewed in appendix 3.

However, as the blades were oriented such that to cut the wire in question, this toggle

position was not reached due to having a value of 63.2 degrees and not the ideal 31 degrees

where the coupler and input link are in a parallel condition. It could therefore be the case that

a more suitable modification would be to use a shorter input link in the internal mechanism or

to use blades with a lower breadth in order to allow the internal input link to reach this toggle

position rather than adjusting the input link of the external mechanism.

Fig. 8-1: Torque transmission of Geomed wire cutting pliers with respect to input link

angle

-200

-100

0

100

200

300

400

500

0 10 20 30 40 50 60 70 80

Mec

ha

nic

al

ad

va

nta

ge

Theta 1 (degrees)

Torque transmission of internal four bar linkage Vs input link angle

Theta 1


64

A simple 2-Dimensional drawing (created in Working Model) of the internal four bar linkage

utilized in the Geomed wire cutting pliers illustrated the process of the transmission angle

approaching the ideal 90 degrees as approaches 31degrees

1. By analysing figure 8-2, it was clear that at the starting position (when the pliers are

in the relaxed position) the output force had a minimum value due to the transmission

angle having a value near to 180 degrees and a coupler angle of a near 90 degrees.

2. From figure 8-3, as the transmission angle approached 90 degrees (or approached

31 degrees) the coupler force and torque transmission value had a combined

maximum value.

Fig. 8-2: Working model representation of internal mechanism in starting position

Fig. 8-3: Working model representation of internal mechanism in maximum force transmission

position


65

3. As the input link passed 31 degrees a negative torque as applied to the output link

through the coupler and is illustrated in figure 8-4.

Additionally, it could be shown the internal linkage did not satisfy Grashof’s criterion due to

the linkage locking under complete rotation of the input link and can be seen in figure 8-5

where the mechanism could not crank completely when being rotated clockwise or counter-

clockwise.

Fig. 8-4: Working model representation of internal mechanism in negative torque region

Fig. 8-5: Illustration of non-Grashof conformance


66

9 Working model analysis of standard configuration

The next step of the investigation would be to analyse the original configuration in working

model in order to obtain a value of the torque transmission (mechanical advantage) which

could be compared the theoretical values in chapter 7.

From the work carried out by Wang (1996), the method of obtaining a value for the

mechanical advantage of the mechanism would be to incorporate a spring balance into the

system (i.e. a counter-acting spring at the cutting end) which would measure the output force

as a function of the spring displacement and therefore tension. The simulation would be run

to neglect effects of mass/inertia with the left hand side handle being anchored to provide a

rigid support for all the remaining components.

9.1 The test model and initial conditions

Various configurations of spring tension were tested in order to obtain a maximum value for

the mechanical advantage; the values chosen for the spring in order to meet this requirement

whilst maintaining a non-touch condition between the two blades was achieved using a spring

stiffness (k) of 0.38N/mm at a length of 4.684mm (as measured from preliminary data).

A force vector of -100N was applied in the X direction on the right hand side handle whilst

anchoring the left hand side handle, yielding a maximum output force of -975N (the negative

sign denotes a compressive force) or a mechanical advantage of 9.75. This value correlates

closely to the theoretical value of 10.925 with a percentage difference of only 10.8% and

demonstrates the validity of the theoretical calculations.

The graph of output force versus spring displacement is illustrated in figure 9-1 alongside the

initial applied conditions and model representation.


67

As a benchmark value had been obtained with a mechanical advantage which closely

represents the theoretical data, the modification of the driven link fixed pivot could be carried

out; this would be achieved by adjusting the pivot in X and Y using a matrix positioning

system in order to correlate data between rows and columns. Modification of the input link

would have the effect of modifying the force transmission index to the internal linkage

mechanism due to a different input moment from different input link lengths and varying

components of the input force along the coupler link.

10 Input link fixed pivot modification

In order to obtain a suitable test sample size, the fixed input link joint was patterned in 0.8

degree increments about the corresponding axis created for the right hand side handle to

allow for correct spacing of the 5mm diameter fixing rivets; seven joint locations were

created above the standard location (in Y) with 2 being below. In order to obtain results in X,

ten holes were patterned in X relative to each input link joint on the right hand side handle;

this would allow for analysis of the force transmission as the input angle approaches a

perpendicular condition to the second link within the system and beyond (relative to the

input). Figure 10-1 illustrates the modified handle to allow for a suitable number of data

Fig. 9-1: Working model analysis of original Geomed linkage configuration


68

points in order to determine a fixed input joint location for an improved overall system

mechanical advantage.

11 Modification of Working Model analysis setup

It was found that using a spring to measure the tension between the cutting blades proved

unreliable due to the compound mechanism locking and in fact causing a state of tension

rather than compression when using the coordinate points furthest away from the handle in X;

for this reason the analysis was modified by using a rigid member to measure the tension with

the cutting blades offset by 3mm (due to the most commonly cut cable with the device being

2-3mm) which to provide greater repeatability between tests without the appearance of

sudden anomalies. Additionally, a single value would be obtained for the mechanical

advantage compared to a sinusoidal curve obtained in the initial Working model analysis; this

would aid to take readings rather than predicting the maximum from the graph plot

illustrating the tension versus time.

Fig. 10-1: Modification of input link fixed pivot in order to create matrix grid for data collection


69

An example of an anomaly obtained using a spring configuration with the modified handle is

illustrated in figure 11-1 alongside the revised model setup for more accurate measurement;

illustrated in figure 11-2.

Fig. 11-1: Measurement anomalies using the spring setup in Working model

Fig. 11-2: Rigid member setup in Working model for increased repeatability between tests


70

When re-constraining the right hand side handle and running the analysis using the standard

positioning (as used by Geomed), a slight discrepancy between output forces was seen

compared with the initial analysis (possibly due to errors during the constraint procedure by

not using pin joints exactly concentric to the linkage ends). An output force of -986N was

achieved compared with the initial model analysis of -975N; for this reason the latter value

would be used to maintain fair and accurate data for use of comparison to the standard

position.

12 Working model results using input link matrix

The following chapter illustrates the results obtained using the modified handle in order to

obtain a suitable number of data points from which to identify the optimum external input

link position at the fixed pivot.

12.1 Output force using rigid member configuration

Table 5 illustrates the results obtained using the matrix where each row and column directly

correlates to the row and column from the matrix of the right hand side modified handle; this

means that column 1 row 1 would be the uppermost data point on the right hand side handle

in the top left corner.

Table 5: Output force in working model using rigid member (SPAR)

Top 10 (values with highest mechanical advantage)

Legend

Greater magnitude of output force than control

Control value

1 2 3 4 5 6 7 8 9 10

1 -3.23E+02 -5.56E+02 1.07E+03 -3.56E+03 -4.80E+03 -1.68E+03 -1.10E+03 -8.60E+02 -7.26E+02 -6.40E+02

2 560.569 999.19 2128.629 3.40E+04 -3135.87 -1616.63 -1157.73 -925.233 -791.93 -703.141

3 943.908 1686.284 4816.12 -8910.47 -2550.91 -1587.64 -1105 -981.477 -847.356 -755.293

4 1432.11 2869.578 1.98E+04 -4.81E+03 -2302.16 -1576.9 -1230.42 -1028.86 -899.1 -804.122

5 2133.687 5316.551 -1.81E+04 -3.69E+03 -2158.99 -1572.58 -1262.9 -1071.47 -942.855 -847.296

6 3292.632 1.34E+04 -7.65E+03 -3.17E+03 -2.07E+03 -1.58E+03 -1.29E+03 -1.11E+03 -9.82E+02 -8.88E+02

7 5354.072 -1.13E+05 -5.37E+03 -2.87E+03 -2.02E+03 -1.58E+03 -1.32E+03 -1.14E+03 -1.02E+03 -9.25E+02

8 1.01E+04 -1.39E+04 -4.38E+03 -2.68E+03 -1.98E+03 -1.59E+03 -1.35E+03 -1.18E+03 -1.05E+03 -986.322

9 3.30E+04 -8.27E+03 -3.83E+03 -2.56E+03 -1.96E+03 -1.60E+03 -1.37E+03 -1.21E+03 -1.09E+03 -1.00E+03

10 -4.24E+04 -6.27E+03 -3.50E+03 -2.47E+03 -1.94E+03 -1.62E+03 -1.40E+03 -1.24E+03 -1.12E+03 -1.03E+03

Max 3.30E+04 1.34E+04 1.98E+04 3.40E+04 -1.94E+03 -1.57E+03 -1.10E+03 -8.60E+02 -7.26E+02 -6.40E+02

Min -4.24E+04 -1.13E+05 -1.81E+04 -8.91E+03 -4.80E+03 -1.68E+03 -1.40E+03 -1.24E+03 -1.12E+03 -1.03E+03

Matrix positioning (force in Newtons, negative sign denotes compression)


71

The data from table 5 illustrated surprising results due to previous working model analyses

locking when using a spring arrangement rather than a rigid member between the cutting end.

The yellow cells in the matrix illustrated the locations which appear to give rise to the highest

mechanical advantage despite the fact that realistically at least, these positions would not

allow for the transmission of torque from the external mechanism to the cutting end via the

internal compound mechanism. This was due to the component of the force not being able to

provide a reaction from the input link of the internal mechanism. An explanation for these

anomalous results could be due to the external and internal input links reaching a parallel

condition and causing peak values as discussed in chapter 8 whereby a toggle position is

reached in terms of force output but no moment to transmit the force.

Figure 12-1 illustrates the top ten values for output force on the design model.

Figure 12-1: Values on design model giving rise to highest output force when using

rigid member at cutting end


72

12.2 Output force using spring configuration

In order to validate the data using a rigid member at the cutting end, the test was re-run using

a spring configuration in order to analyse the output force over the global range of

movement; this would confirm whether the data cells from table 5 could be used to transmit a

suitable torque from the handles to the cutting end and would also allow to confirm the

results from any preliminary analysis in case of errors induced when re-constraining parts

between tests.

Table 6 illustrates the results from the second experiment using the modified handle by

measuring spring tension versus displacement.

12.3 Theoretical results discussion

From the secondary test carried out using the spring arrangement, the matrix position which

gave rise to the highest compressive output force was located in row 10, column 6 with a

value of -2030N or a mechanical advantage of 20.3 – a value almost twice the control value

of -1188N (a higher value compared to using the 3mm offset due to the cutting end closing

completely) and would allow the user to only need apply an input force which is 30% the

value of when in the original position due to a 70% increase in mechanical advantage. In this

Table 6: Output force in working model using a spring

1 2 3 4 5 6 7 8 9 10

1 FAIL FAIL FAIL FAIL FAIL -1.47E+03 -1.16E+03 -9.61E+02 -8.02E+02 -7.69E+02

2 FAIL FAIL FAIL FAIL FAIL -1620 -1301 -1090 -967 -864



5 FAIL FAIL FAIL FAIL -1180 -1767 -1454 -1307 -1120 -969

6 FAIL FAIL FAIL FAIL -1.21E+03 -1.80E+03 -1.51E+03 -1.34E+03 -1.13E+03 -1.03E+03


8 FAIL FAIL FAIL FAIL -1.29E+03 -1.94E+03 -1.53E+03 -1.38E+03 -1.24E+03 -1188



Max 0.00E+00 0.00E+00 0.00E+00 0.00E+00 -1.18E+03 -1.47E+03 -1.16E+03 -9.61E+02 -8.02E+02 -7.69E+02

Min 0.00E+00 0.00E+00 0.00E+00 0.00E+00 -1.32E+03 -2.03E+03 -1.60E+03 -1.41E+03 -1.38E+03 -1.26E+03

Matrix positioning (force in Newtons, negative sign denotes compression using spring)

Top 10 (values with highest mechanical advantage)

Legend

Greater magnitude of output force than control

Control value

Values which are not greater in magnitude than control


73

particular location using the Geomed patented internal compounded linkage configuration,

the total increase in mechanical advantage over a mechanism which is simple class 1 lever (a

simple lever with an MA of 5.28 giving an output of 528N with an input of 100N) was now

284%

It is also worth mentioning that the locations which gave rise to the highest mechanical

advantage were to the right of the input link of the internal mechanism and furthest away

from the point of rotation – as would be expected due to torque being dependent on the

distance from the pivot multiplied by a force normal to the direction of travel.

13 Initial rapid prototype in order to compare theory with practise

Due to having found the input link fixed position which yields the highest mechanical

advantage of the system, the next step of the investigation would be to compare the

theoretical values obtained for mechanical advantage with that of a prototype model.

Rather than creating a full 3-dimensional FDM rapid prototype for the initial practical testing

phase, an initial planar acrylic model would need to be created using the University on-site

acrylic sheet laser cutter in order minimize costs in case of the mechanism not behaving as

intended and therefore also allowing for ease of modification – simple 2.5 mm screws could

also be used on an acrylic sheet model for ease of assembly.

13.1 Creation of planar mechanism model in Pro EngineerTM

In order to create the intended model, a similar method of creating the initial Working

ModelTM

components was carried out whereby top views were taken of the model followed

by extracting the edges of the each component and projecting them on a plane parallel to the

top view; this would then give a planar outline from which a simple extrude function could be

used to create a 3mm thick stamped sheet.

Figure 13-1 illustrates the planar (or sheet) version of the existing Geomed wire cutters with

the revised input link fixed pivot location.


74

Due to the left and right cutting blades being stacked on-top one another, any object being

placed in-between these blades would be subject to a shear condition; to eliminate this, two

separate bolt-on blade tips were created which could be fixed on the front and rear of the left

and right hand side respectively in order to be able to place a spring or strain gauge in

between the cutting end.

This modification is illustrated in figure 13-2.

Fig. 13-1: The planar model with relocated input fixed pivot

Fig. 13-2: Bolt-on blade tips to eliminate shear condition of planar

mechanism at the cutting end


75

13.2 Kinematic analysis in CAD of revised input link fixed pivot location and

initial problems encountered

Despite the theoretical value for mechanical advantage being highest in the revised location,

it was now the case that the cutting pliers could not close completely due to the right hand

side handle approaching a condition of rotation where the input link fixed pivot would not

transmit a component of force along the coupler link of the internal mechanism.

Figure 13-3 illustrates the problem encountered:

Having obtained a higher mechanical advantage at a 3mm offset where the cutters would

theoretically begin to the cut the wire had come at the expense of decreased cutter head travel

based on the displacement at the input; this particular finding also illustrated the balance

needed between the maximum mechanical advantage of the mechanism and allowable handle

travel without causing mechanism lock-out.

Fig. 13-3: Insufficient cutter head travel relative to handle displacement


76

The second highest reading obtained for mechanical advantage from table 6 was located in

row 10 column 7 with an output force of -1600N (a reduction of 21.2% in mechanical

advantage from the reading from row 10 column 6). This location for the input link fixed

pivot of the external mechanism could then be tested to analyse whether a similar condition

would be obtained as seen in figure 13-3; this would be carried out by copying the coordinate

for the row 10 column 7 from the 3-dimensional model over into the planar mechanism in Pro

Engineer.

Figure 13-4 illustrates the remaining input coordinates of the external mechanism in row 10

from which the highest values of mechanical advantage had been obtained when using a

resisting spring arrangement. Using the second highest value of mechanical advantage from

row 10 column 7 would allow for the mechanism to fully close whilst not creating a clash

condition between the left and right hand side handles.

Fig. 13-4: adjustment position using data from table 6 to obtain input link fixed pivot

location yielding a significant increase in mechanical advantage of the mechanism


77

To finalize the modification, all other input link fixed pivot locations were deleted where the

model was left only with the modified position which would provide the highest mechanical

advantage. Figure 13-5 illustrates the final test setup which would be compared with a

practical experiment after being laser cut from 3mm thick acrylic sheet; the updated 3-

dimensional model is also shown.

The original location had been included in order to have a control value during the practical

analysis and would also provide a data point from which the theoretical values from linkage

theory and working model could be compared.

A final render of the finished 3-dimensional model with the modified input link fixed pivot is

illustrated in figure 13-6.

Figure 13-5: (Left) The finalized model to be laser cut to begin

practical analysis followed by the updated 3-dimensional model

(right)


78

Fig. 13-6: The final rendered model with modified input link fixed pivot positioning


79

13.3 DXF drawing creation and CNC laser setup for initial prototype

The final process before creating a practical planar model would be to create a drawing of the

top views of each component to be able to create a DXF (or Drawing Exchange Format)

which could be recognised by the AutocadTM

software linked to the CNC laser cutting

machinery. All top views of each component were projected onto a drawing sheet and

subsequently saved in DXF format – upon importing these views into Autocad, each view

could be “closed” in order to be seen as a filled surface and rearranged for minimal waste of

the available acrylic sheet. 2 sets of acrylic sheet would be cut to create a “doubled up”

version (a total of 6mm in depth) in order to increase stiffness and minimize erroneous

results due to insufficient rigidity when using a single sheet acrylic model, and therefore

resulting component deformation.

The top view component DXF drawing sheet and laser cut parts are shown in figure 13-7.

Fig. 13-7: Above: DXF drawing template to be laser cut followed by the

laser cut parts after component placement revision to minimize waste

(below)


80

13.4 The finished planar acrylic model for analysis

In order to fix each component together, M2.5 nuts and screws were used in order to

minimize friction and for ease of component disassembly in case of modification and for

when interchanging the input link of the external mechanism.

The finished physical model is illustrated in figure 13-8.

Fig. 13-8: The physical test model


81

14 Finite Element Analysis of planar mechanism

As stated in the project proposal for this paper, a Finite Element Analysis was to be carried

out on the design model in order to gain an appreciation into the flow of the force across the

entire assembly for the original and revised input link fixed pivot positioning. In order for an

investigation such as this to be carried out, the model had to be constrained such that

sufficient contact surfaces, points of rotation and interaction types (penetrable / non

penetrable) were set up correctly in order to fully represent the system – Appendix “5”

illustrates the model setup with corresponding initial conditions and model configuration.

An applied clockwise torque of 13.384Nm would represent the input load as was applied to

the Working Model analysis (of 100N) due to the fixed pivot location on the original

configuration being 133.84mm from the point of rotation; this would also provide more

accurate results when analysing the revised input link fixed pivot location as no interpolation

of where to position the point load would need to be carried out.

14.1 FEA Analysis using COSMOSTM

The initial stress analyses of the original and revised configurations are illustrated in figure

14-1:

Figure 14-1: Stress flow analysis of the original configuration (left) and revised configuration (right)


82

From initial inspection, the revised input link fixed pivot position evidently showed a greater

number of stress lines across the handle, cutter head and cutting wire; however in order to

quantify the stress accurately at the cutting head and wire, all assembly components other

than the cutting heads and wire were made rigid in order to eliminate displacement along

components perpendicular to the cutting plane which could cause possible anomalies.

The results after re-running the simulation for each configuration is shown in figure 14-2.

Fig. 14-2: Stress analysis results at cutting head for each input link

configuration


83

14.2 FEA analysis comparison using MSC NASTRANTM

In order to validate the data obtained from Solidworks COSMOSTM

and in order to check for

any inconsistencies in model constraints, mesh and initial conditions, another analysis was

run using MSC NASTRANTM

whereby the Von Mises stress distribution was analysed

throughout the model.

The same initial conditions were used by fixing the left hand side handle, using frictionless

pin constraints and rigid bodies and using a torque of -13.384Nm on the right handle main

pivot.

The results are illustrated in figures 14-3 and 14-4.

Figure 14-3: FEA analysis of planar mechanism in NASTRAN with input link in original

position


84

Figure 14-4: FEA analysis of planar mechanism in NASTRAN with input link in modified

position

14.3 Comparison of Finite Element Analysis results

The results from the two FEA analyses illustrated extremely similar results – as would be

expected using the same initial conditions and mesh size (see appendix 5). The maximum

stress (Von Mises) at the cutting end using COSMOSTM

for the original and modified input

link positions were observed as being 74.7Mpa and 94.3MPa respectively; this closely

matched the NastranTM

analysis results with 75.0Mpa and 93.8Mpa. The differences in stress

values were due to the alignment of the wire within the jaws when specifying tangency


85

between the wire and cutter head faces; a slight deviation from the ideal 24mm from the main

datum would alter the amount of force applied to the cutting wire due to a change in the ratio

of lengths between the handle and cutting head.

A further observation aside from obtaining an increase value of stress applied to the cutting

wire with the input link in the modified position is that the handle was now subjected to

higher peak stresses (an increase of around 120%). This was due to the input link of the

internal mechanism (link 2) providing link 1 with a normal reaction force at the point of

cutting; link 1 (the input link of the external mechanism) was also then in a perpendicular

condition relative to the cutting head, thus causing the highest bending moment on the

handle.

15 Method of testing the physical prototype

In order to obtain an equivalent output force of the physical model at the cutting end, a force

balance system would be set up by loading the handle with a series of weights (0g-100g) and

measuring the corresponding output force at the cutter head using a force balance, as carried

out by Midha et al (1984). The setup would be slightly modified due to the low loads (as a

consequence of the models low stiffness) by incorporating strain gauges into the system to

measure minute changes in displacement of the cutter head; the procedure would be carried

out as follows:

1) To correctly create a Wheatstone bridge for two strain gauges measuring in tension

2) To calibrate the strain gauges using a series of weights (0-1000g) to measure strain

versus load

3) To test the setup by hanging weights on the loading arm (right hand side, using

weights 0-100g in order to create predicted 1000g output force with 100gram load on

input) and measuring the corresponding strain at the cutter head

4) To repeat each experiment three times (original input and modified input link

position) in order to obtain reliable data

The equipment needed to carry out these tasks would be:

2 Tokyo Sokki Kenkyujo linear strain gauges Type FLA-5-11 (2.11+/-1 gauge factor,

120+/-0.3 ohm gauge resistance)

An TQ-SM1010 Digital Strain Display using a gauge factor of 2.1


86

An Aluminium strip in order to mount two strain gauges measuring in tension

o Acetone to remove grease from Aluminium surface

o Super Glue to stick strain gauge onto Aluminium surface

o Sellotape to provide insulation between strain gauge terminal and aluminium

strip

o Scoring tool

o Set square for scoring perpendicular lines for strain gauge alignment

o Digital vernier callipers in order to measure aluminium cross-sectional area

(sensitive to 0.01 )

4 wire telephone cable

Soldering Iron / Solder

Wire to attach cutter head to strain gauge

2 G-Clamps

Chemistry clamp

2 “dummy” strain gauges to complete Wheatstone bridge

Multimeter to ensure circuit has been soldered correctly

15.1 Preliminary equipment setup and calibration

The following chapter illustrates the processes which were carried out in order to create a test

setup for subsequent data analysis.

15.1.1 Creating the Wheatstone bridge for strain measurement

In order to obtain quantitative data for the deflection of the cutter head under tension with an

applied load, a Wheatstone bridge needed to be created using two strain gauges attached to a

13.86mm x 0.96mm cross-section aluminium strip on either side measuring tension.

U.A. Bakshi; A.V. Bakshi (2003) state that bridge circuits, consisting of four resistor arms in

order to form a closed circuit, operate on a null-indication principle whereby the bridge

compares an known electrical current with that of a known standard component. In a standard

bridge circuit the bridge is said to be balanced when no current flows through the null

detector (generally a galvanometer, a device for measuring small electric currents); this leads

to a relationship between the four resistors (or strain gauges in the context of the project)

whereby a balancing condition/equation can be synthesized in order to measure the current

through an unknown value when the bridge becomes unbalanced.


87

U.A. Bakshi; A.V. Bakshi (2003) continue to illustrate the principle of a Wheatstone bridge

by means of demonstrating the derivation of the balance condition. The authors state that for

zero current to flow through the galvanometer, that points C and D must be in a state of equal

potential, thus arms AD and AC also being subject to the same potential.

Figure 15-1 illustrates the Wheatstone bridge circuit.

As AC and AD are equipotential:

(11.0)

With the galvanometer current being zero in a balanced state and considering the current

flow:

(11.1)

(11.2)

𝑆𝑤𝑖𝑡𝑐

𝐸𝑚𝑓

𝐴

𝐺

𝑅

𝑅

𝑅

𝑅 𝐵

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑎𝑟𝑚 𝑈𝑛𝑘𝑛𝑜𝑤𝑛 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝐶 𝐷

𝐼

𝐼

𝐼

𝐼

𝑅𝑎𝑡𝑖𝑜 𝑎𝑟𝑚𝑠

Figure 15-1: The Wheatstone bridge (U.A. Bakshi; A.V. Bakshi, 2003)


88

Substituting (11.2) and (11.1) into equation (11.0):

(

) (

2 4

) (11.3)

2 4 1 3 (11.4)

Expanding the brackets:

(11.5)

And finally, due to being equal on both sides:

(11.6)

Then:

(11.7)

Equation (11.7) is called the balance condition of the Wheatstone bridge (U.A. Bakshi; A.V.

Bakshi, 2003); if this balanced condition is no longer present in the bridge, a current is passed

through the galvanometer due to AC and AD not being equipotential.

For the Lab, preparation was begun by scoring perpendicular lines on the surface of the

Aluminium strip in order to align the strain gauges correctly, this was followed by gluing the

strain gauges to the aluminium strip and provide a contact by using a terminal in order to

solder the telephone wire to the strain gauges; Sellotape was used to insulate the strain gauge

contact from the Aluminium surface and two “dummy” strain gauges were used in order to

complete the Wheatstone bridge.

The gauges were finally checked using a Multimeter to ensure the resistance read 120 Ohms,

as stated by the manufacturer.

The finished strain gauge is illustrated in figure 15-2.


89

15.1.2 Calibration of the strain gauge

In order to verify which loads correspond to a particular strain, the strain gauge was

calibrated by hanging weights directly from the aluminium strip using copper wire and a

chemistry clamp.

The results are illustrated in table 7.

Fig. 15-2: The finished strain gauge with top-side (Left) and underside (Right)

Fig. 15-3: Test setup for strain gauge calibration

𝐶 𝑒𝑚𝑖𝑠𝑡𝑟𝑦 𝑐𝑙𝑎𝑚𝑝

𝑆𝑡𝑟𝑎𝑖𝑛 𝑔𝑎𝑢𝑔𝑒

𝐶𝑜𝑝𝑝𝑒𝑟 𝑤𝑖𝑟𝑒

𝑊𝑒𝑖𝑔 𝑡 𝑎𝑛𝑔𝑒𝑟

𝐶𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 0.96𝑚𝑚

13. 6𝑚𝑚


90

load (grams) Strain ( )

0 0

100 1

200 2

300 3

400 4

500 5

600 6

700 7

800 8

900 9

1000 10

Table 7: Strain calibration

15.1.3 The final physical test setup

As a corresponding strain had been obtained for a particular load, the physical prototype

could be clamped and connected to the strain gauge. This was achieved by filing a groove

into the moving cutter head, and looping the welding wire around the cutter head in order to

indirectly measure the reaction force as the cutting end moves throughout its travel.

The final test setup and cutter head wire loop are illustrated in figures 15-4 and 15-5

respectively.


91

Fig. 15-4: The final test setup in order to test the physical model

Fig. 15-5: The cutter head wire loop in order to measure strain


92

16 Results of testing the physical model

The following chapter presents the experimental findings using the method from chapter 15

and the test setup from figure 15-4. All associated raw data for chapter 15 is illustrated in

appendix 4.

Error bars for each graph have been generated using the standard uncertainty of the mean

or:

√ (12.0)

Where s is the standard deviation of the mean and n is the number of results for each data set.

The graph plots from experimentation are shown in figures 16-1, 16-2 and 16-3.


93

Fig. 16-1: Strain vs. load for original configuration

-2

0

2

4

6

8

10

12

0 20 40 60 80 100 120

Str

ain

(μ

ε)

Applied load (grams)

Original input link position strain vs. load readings

Strain original 1st test"

Strain original 2nd test

Strain original 3rd test

Strain original averages


94

Fig. 16-2: Strain vs. load for modified configuration

-2

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100 120

Str

ain

(μ

ε)


Modified input link position strain vs. load readings

Strain modified 1st test"

Strain modified 2nd test

Strain modified 3rd test

Strain modified averages


95

Fig. 16-3: Comparison of strain vs. load between original and modified configuration

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0 20 40 60 80 100 120

Str

ain

(μ

ε)


Original vs. modified input link position strain readings

Avg. Strain original

Avg. Strain modified

3mm offset marker


96

16.1 Discussion

From figure 16-3, it is evident that the modified input link position yields higher output

forces upon applying larger masses (due to a decrease in cutter-head span when under

tension) and supports the project hypothesis whereby a larger output force is present within

the system due to the input link approaching a parallel condition to the cutter head blades and

a perpendicular condition to the input force; thus creating a maximum moment about the

point of rotation.

In other words, the main reason as to why the modified linkage configuration yields a higher

output force at greater applied loads is due to the modified input link fixed pivot position

allowing for the input link of the external mechanism to reach a parallel condition with the

cutting head in a shorter space of time when compared to the input link in the original

position.

It is also worth noting that the original configuration would appear to provide a greater output

force at increased cutter head spans; one of the main objectives of GEOMEDTM

whereby the

patented linkage configuration is intended to maximise the cutting force at larger cutter head

spans in order to shear higher gauge wires. However another explanation as to why the

original configuration yields a higher output force at lower applied loads could be due to the

original position of the input link fixed pivot providing a 45 degree incident angle which

provides a greater amount of rotation on the input link of the internal mechanism. The

modified position on the other hand, starts in a lower position than the original configuration

and therefore does not provide the same amount of rotation, but allows the mechanism to

reach a toggle position more quickly; yielding a higher maximum output force.

Above a loading of 50 grams however, when the cutter head jaws are allowed to travel when

overcoming friction, the revised input link configuration yields substantially higher strain

values than the original configuration whereby the differences in strain value become larger

as the mass (and therefore cutter-head travel) is increased; thus producing functions in the

form of a polynomial, as suggested by Phelan (1988).

16.2 Comparing results with theory

In order to gauge the reliability of the results obtained, let us consider the aluminium test strip

under tension, whereby the equivalent tensile force can be calculated from experimental

strain.


97

With the aluminium strip having a cross-sectional area of 13.86mmx0.96mm and a Young’s

Modulus of 70Gpa (Efunda, 2012), then the maximum force applied in order to cause 10

(for the original configuration) is:

(12.1)

Then:

( 13. 6 10 0.96 10 10 10 0 10 ) (12.2)

9.314 949 (12.3)

Which corresponds closely to the weight added (100grams, where the theoretical mechanical

advantage was calculated as being 10.93), indicating the experiment was carried out in an

accurate and sensible manner with a minimal deviation from the theoretical values; the slight

loss in mechanical advantage of the system would be due to friction in the mechanism.

Additionally, for completeness, calculating the maximum output force using the strain value

obtained for the modified linkage position

( 13. 6 10 0.96 10 13. 10 0 10 ) (12.4)

12. 6 1300 (12.5)

Equation (12.5) illustrates a strong correlation to the theoretical Working ModelTM

calculations (see table 6) whereby the predicted mechanical advantage in the modified

position was calculated to be 1600N as opposed to 1188N using the original configuration,

yielding a percentage increase of 34.7%.

With the experimental data, the percentage increase from 949grams to 1300grams is:

100 (1300 949

949) 3 .0 (12.6)

thus confirming the experimental data to match that of the maximum predicted value using

working model, and that of the theoretical calculation from chapter 7.


98

16.3 Fair test factors

It is worth mentioning that several considerations were made to ensure the investigation was

carried out in a fair and sensitive manner in order to obtain reliable data.

These considerations include:

Ensuring the same area of testing was used for each repeat using the same equipment

Using an area away from sources of draft which could potentially alter strain readings

due to temperature changes

Using 2 G-clamps to lock the model to a planar surface to minimize/eliminate rotation

of the model between tests

Re-setting the strain gauge display between tests to eliminate sources of residual

strain / heat changes

Using the most sensitive equipment available with digital displays in order to

eliminate parallax error

Calibrating the strain gauges before use

Repeating each experiment 3 times

16.4 Anomalous results and limitations of the experimental procedure

From figures 16-1 and 16-2, the majority of data points lie outside of the experimental error

bars indicating that, despite obtaining results which match the theory, that the experiment

could further be improved in order to obtain data points situated closer to the mean, and

hence trend line; the most obvious way of achieving this would be to carry out further tests in

order to increase the test sample size , thus reducing the standard uncertainty.

However, it must be remembered that the high sensitivity of the equipment used would make

it increasingly difficult to obtain the same value of strain for subsequent repeats of the same

test. Additionally, despite using an area with minimal fluctuation in ambient temperature,

some sporadic strain values had been recorded in preliminary measurement whereby strains

were displayed without having added any weights to the system; thus subjecting the

experiment to compounded errors combined with friction between contact linkages and

friction between the pin joints (M2.5 bolts).


99

17 Conclusions

From the theoretical and practical data obtained, the project can be deemed a complete

success due to the modified linkage configuration yielding an increased maximum

mechanical advantage of 34.7% and 37.0% for the theoretical and experimental analyses

respectively, compared to the standard configuration produced by GEOMEDTM

for the

Hercules Gold-cut wire cutting pliers. This means that the product could in theory be scaled

by a factor of 0.73 the overall size of the original product in order to maintain an equivalent

mechanical advantage as the existing product, potentially saving manufacturing and material

costs for the manufacturer.

However, from the results obtained, the original linkage configuration provides a higher

output force with minimal cutter-head travel, as opposed to the revised linkage configuration

which yields a higher maximum output force, although at greater cutter-head displacements;

thus making the revised linkage configuration more suitable for similar or smaller gauge

wires of a higher stiffness or shear modulus. Additionally, with each linkage configuration,

an increase in cutter-head displacement (with the cutters approaching a shear condition or

3mm offset) directly correlated to an increase in mechanical advantage, as predicted in the

project hypothesis (from the work of Phelan, 1988) due to the coupler and output links of the

internal mechanism approaching a parallel condition. It was also proven (although obvious

from inspection) that the internal compounded mechanism does not conform to Grashof’s

criterion, due to the input link not being able to act as a crank, making the compounded

linkage configuration significantly powerful over small displacements.

To conclude, the project has successfully:

Reverse engineered the GEOMEDTM

Hercules Gold-cut wire cutting pliers from

preliminary measurement, followed by testing a physical prototype

Managed to obtain an almost identical mechanical advantage for the standard patented

internal linkage configuration through theoretical calculation

Obtained values of mechanical advantage from practical testing which closely

correlate to the theoretical data

Carried out a Finite Element Analysis of the original and revised linkage

configurations in order to indirectly identify the flow of the force from input to output


100

Created a linkage configuration which yields a higher maximum output force than the

original product.

17.1 Recommendations

The project could be continued further by considering an alternative method of transferring

an input force from the handles to the cutting end other than using rigid members in the form

of links. The project has shown that the patented internal linkage configuration of the

Hercules Gold-cut wire cutting pliers can be deemed as “perfect” due to the input link

becoming parallel to the coupler link as the output link approaches a perpendicular condition

to the coupler when cutting 2-3mm wires; it is therefore the case that other potential

modification with the implementation of rigid bodies is limited by using similar arrangements

without increasing the size of the product.

In terms of testing, the experiment could be improved by using a material which is stiffer

than acrylic, meaning that thinner sheet could be used to further minimize friction between

the pin-joints (M2.5 bolts) and each link; this would improve readings when using a lower

weight and allow for more sensitive data plots at increase cutter head spans, rather than only

being able to measure the maximum output force upon reaching the point of cutting (2-3mm

offset).


101

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107

19 Appendix

Appendix 1- BS EN ISO7153-1:2001 (Metallic materials for surgical instruments)

Steel grade Chemical compositions (%)

Ref Grade No.

According tob

C Si

(max)

Mn

(max)

P

(max)

S Cr Mo Ni Other

Elements

ISO

4957

ISO

683-13

Martensitic Steels

A

B

C

D

E

F

G

—

27

28

—

—

—

—

3

4

5

—

—

—

—

0,09 to 0,15

0,16 to 0,25

0,26 to 0,35

0,42 to 0,50

0,47 to 0,57

0,6 to 0,7

0,65 to 0,75

1

1

1

1

0,5

0,5

1

1

1

1

1

1

1

1

0,04

0,04

0,04

0,04

0,03

0,03

0,04

0,03 max.

0,03 max.

0,03 max.

0,03 max.

0,025 max.

0,025 max

0,03 max.

11,5 to 13,5

12 to 14

12 to 14

12,5 to 14,5

13,7 to 15,2

12 to 13,5

12 to 14

—

—

—

—

—

—

0,5 max.

1 max.

1 max

1 max.

1 max.

0,5 max.

0,5 max.

1 max.

H

I

K

R

—

—

30

—

—

—

—

0,35 to 0,4

0,42 to 0,55

0,33 to 0,43

0,85 to 0,95

1

1

1

1

1

1

1

1

0,045

0,045

0,03

0,045

0,03 max.

0,03 max.

0,03 max

0,03 max.

14 to 15

12 to 15

15 to 17

17 to 19

0,4 to 0,6

0,45 to 0,9

1 to 1,5

0,9 to 1,3

—

—

1 max

—

V: 0,1 to 0,15

V: 0,1 to 0,15

—

V: 0,07 to

0,12

Ferritic Steels

L - 8a 0,08 max 1 1,5 0,06 0,15 to 0,35 16-18 0,6 max 1 max

Austenitic Steels

M

N

O

P

-

-

-

-

11

17

14

20

0,07 max

0,12 max

0,15 max

0,07 max

1

1

1

1

2

2

2

2

0,045

0,06

0,045

0,045

0,03

0,15 to 0,35

0,03 max

0,03 max

17 to 19

17 to 19

16-18

16,5 to 18,5

- c

2 to 2,5

8 to 11

8 to 10

6 to 8

10,6 to 13,5

a The reference letters are used for the purpose of cross-referencing.

b The grade numbers are provisional and will be subject to alteration when the relevant International Standards are published.

c The manufacturer has the option of adding molybdenum up to 0,7 %.


108

Appendix 2 – Full derivation of the four bar kinematic constraint equation

With reference to figure 4-2 and using the following rules of Trigonometry:

Let us also call 180 where 180 = radians (allowing for simplification) and also substitute

( for A and for B:

Then:

2

2

2

And finally for lengths a and b:

2

Then for lengths c and d:

2 2

2

Due to geometry for figure 27, 0, then:

0 2 2

2

2 ( ( ) ( )

)

Then finally:

2 2 2 0


109

Appendix 3 – Four bar linkage force transmission ratio table data

Theta 1

(radians)

Theta 2

(radians)

Transmission

ratio

Theta 1

(degrees)

Theta 2

(degrees) T2/T1

1.19 2.35 0.616 68 134.50 1.62

1.17 2.34 0.597 67 133.50 1.68

1.15 2.33 0.578 66 132.50 1.73

1.13 2.32 0.559 65 131.50 1.79

1.12 2.31 0.541 64 130.50 1.85

1.10 2.30 0.522 63 129.50 1.91

1.08 2.29 0.504 62 128.50 1.98

1.06 2.28 0.486 61 127.50 2.06

1.05 2.27 0.468 60 126.50 2.14

1.03 2.26 0.451 59 125.50 2.22

1.01 2.25 0.433 58 124.50 2.31

0.99 2.24 0.416 57 123.50 2.40

0.98 2.23 0.399 56 122.50 2.51

0.96 2.22 0.382 55 121.50 2.62

0.94 2.21 0.365 54 120.50 2.74

0.93 2.20 0.348 53 119.50 2.88

0.91 2.19 0.331 52 118.50 3.02

0.89 2.18 0.315 51 117.50 3.18

0.87 2.17 0.298 50 116.50 3.35

0.86 2.16 0.282 49 115.50 3.55

0.84 2.15 0.266 48 114.50 3.77

0.82 2.14 0.249 47 113.50 4.01

0.80 2.14 0.233 46 112.50 4.29

0.79 2.13 0.217 45 111.50 4.60

0.77 2.12 0.201 44 110.50 4.96

0.75 2.11 0.186 43 109.50 5.39

0.73 2.10 0.170 42 108.50 5.88

0.72 2.09 0.154 41 107.50 6.48

0.70 2.08 0.139 40 106.50 7.20

0.68 2.07 0.123 39 105.50 8.11

0.66 2.06 0.108 38 104.50 9.27

0.65 2.05 0.093 37 103.50 10.80

0.63 2.04 0.077 36 102.50 12.93

0.61 2.03 0.062 35 101.50 16.10

0.59 2.02 0.047 34 100.50 21.28

0.58 2.01 0.032 33 99.50 31.34

0.56 2.00 0.017 32 98.50 59.20

0.54 1.99 0.002 31 97.50 516.72

0.52 1.98 -0.013 30 96.50 -77.13

0.51 1.97 -0.028 29 95.50 -35.96


110

0.49 1.96 -0.043 28 94.50 -23.47

0.47 1.95 -0.057 27 93.50 -17.44

0.45 1.94 -0.072 26 92.50 -13.88

0.44 1.93 -0.087 25 91.50 -11.54

0.42 1.92 -0.101 24 90.50 -9.88

0.40 1.91 -0.116 23 89.50 -8.64

0.38 1.90 -0.130 22 88.50 -7.68

0.37 1.89 -0.145 21 87.50 -6.91

0.35 1.88 -0.159 20 86.50 -6.28

0.33 1.87 -0.173 19 85.50 -5.76

0.31 1.86 -0.188 18 84.50 -5.33

0.30 1.86 -0.202 17 83.50 -4.95

0.28 1.85 -0.216 16 82.50 -4.62

0.26 1.84 -0.230 15 81.50 -4.34

0.24 1.83 -0.245 14 80.50 -4.09

0.23 1.82 -0.259 13 79.50 -3.87

0.21 1.81 -0.273 12 78.50 -3.67

0.19 1.80 -0.287 11 77.50 -3.49

0.17 1.79 -0.301 10 76.50 -3.33

0.16 1.78 -0.315 9 75.50 -3.18

0.14 1.77 -0.329 8 74.50 -3.04

0.12 1.76 -0.342 7 73.50 -2.92

0.10 1.75 -0.356 6 72.50 -2.81

0.09 1.74 -0.370 5 71.50 -2.70

0.07 1.73 -0.384 4 70.50 -2.61

0.05 1.72 -0.397 3 69.50 -2.52

0.03 1.71 -0.411 2 68.50 -2.43

0.02 1.70 -0.425 1 67.50 -2.35


111

Appendix 4 – Raw data for stress vs. strain when loading physical model

Original input link position

mass (g) με

1st test 2nd test 3rd test stdev u Average xq 1st xq 2nd xq 3rd

0 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0

10 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0

20 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0

30 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0

40 1 1 2 0.58 0.33 1.3 0.3 0.3 0.7

50 3 3 2 0.58 0.33 2.7 0.3 0.3 0.7

60 4 4 4 0.00 0.00 4.0 0.0 0.0 0.0

70 6 7 6 0.58 0.33 6.3 0.3 0.7 0.3

80 6 7 6 0.58 0.33 6.3 0.3 0.7 0.3

90 8 9 8 0.58 0.33 8.3 0.3 0.7 0.3

100 9 11 10 1.00 0.58 10.0 1.0 1.0 0.0

Modified input link position

mass (g) με

1st test 2nd test 3rd test Stdev u Average xq 1st xq 2nd xq 3rd

0 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0

10 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0

20 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0

30 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0

40 1 0 0 0.58 0.33 0.3 0.7 0.3 0.7

50 2 3 2 0.58 0.33 2.3 0.3 0.7 0.3

60 4 4 4 0.00 0.00 4.0 0.0 0.0 0.0

70 8 8 7 0.58 0.33 7.7 0.3 0.3 0.3

80 9 8 9 0.58 0.33 8.7 0.3 0.7 0.3

90 11 11 12 0.58 0.33 11.3 0.3 0.3 0.3

100 13 14 14 0.58 0.33 13.7 0.7 0.3 0.7


112

Appendix 5 - COSMOS Finite Element Analysis Report

Model Information

Model name: Planar wire cutter

Current Configuration: Default

Solid Bodies

Document Name and

Reference Treated As Volumetric Properties

Document Path/Date

Modified

Body.3

Solid Body

Mass:0.00634121 kg

Volume:7.92651e-007 m^3

Density:8000 kg/m^3

Weight:0.0621438 N

G:\Uni Level 3\Final

year project\2d part

files in Catia for laser

cutter\FOR SOLID

WORKS

2012\cutterightdepthc

orrect.SLDPRT

Feb 04 19:12:52 2012

Body.2

Solid Body

Mass:0.00634142 kg

Volume:7.92677e-007 m^3

Density:8000 kg/m^3

Weight:0.0621459 N




cutter\FOR SOLID

WORKS

2012\cutterleftdepthc

orrect.SLDPRT

Feb 04 19:14:06 2012

Model Information


113

PartBody

Solid Body

Mass:0.0245649 kg

Volume:3.07061e-006 m^3

Density:8000 kg/m^3

Weight:0.240736 N




cutter\FOR SOLID

WORKS

2012\cutterright.SLD

PRT

Feb 04 19:11:50 2012

PartBody

Solid Body

Mass:0.0670188 kg

Volume:8.37734e-006 m^3

Density:8000 kg/m^3

Weight:0.656784 N




cutter\FOR SOLID

WORKS

2012\lefthandlepart.S

LDPRT

Feb 05 11:04:16 2012

PartBody

Solid Body

Mass:0.0257342 kg

Volume:3.21677e-006 m^3

Density:8000 kg/m^3

Weight:0.252195 N




cutter\FOR SOLID

WORKS

2012\link1hundredmi

ll.SLDPRT

Feb 05 11:04:16 2012

PartBody

Solid Body

Mass:0.0066088 kg

Volume:8.261e-007 m^3

Density:8000 kg/m^3

Weight:0.0647662 N




cutter\FOR SOLID

WORKS

2012\link2.SLDPRT

Feb 05 11:04:16 2012

PartBody

Solid Body

Mass:0.00936136 kg

Volume:1.17017e-006 m^3

Density:8000 kg/m^3

Weight:0.0917413 N




cutter\FOR SOLID

WORKS

2012\link3.SLDPRT

Feb 04 19:17:28 2012

Boss-Extrude1

Solid Body

Mass:0.000502655 kg

Volume:6.28319e-008 m^3

Density:8000 kg/m^3

Weight:0.00492602 N




cutter\FOR SOLID

WORKS

2012\wire.SLDPRT

Feb 04 19:52:16 2012


114

Study Properties

Study name Study 1

Analysis type Static

Mesh type Mixed Mesh

Thermal Effect: On

Thermal option Include temperature loads

Zero strain temperature 298 Kelvin

Include fluid pressure effects from

SolidWorks Flow Simulation

Off

Solver type FFEPlus

Inplane Effect: Off

Soft Spring: Off

Inertial Relief: Off

Incompatible bonding options Automatic

Large displacement Off

Compute free body forces On

Friction Off

Use Adaptive Method: Off

Result folder SolidWorks document

(c:\users\ryan\appdata\local\temp)

Units

Unit system: SI (MKS)

Length/Displacement mm

Temperature Kelvin

Angular velocity Rad/sec

Pressure/Stress N/m^2


115

Material Properties, loads and fixtures

Model Reference Properties Components

Name: AISI 316 Annealed

Stainless Steel Bar

(SS) Model type: Linear Elastic

Isotropic Default failure

criterion: Max von Mises

Stress Yield strength: 1.37895e+008

N/m^2 Tensile strength: 5.5e+008 N/m^2 Elastic modulus: 1.93e+011 N/m^2

Poisson's ratio: 0.3 Mass density: 8000 kg/m^3

Thermal expansion

coefficient: 1.6e-005 /Kelvin

SolidBody

1(Body.3)(cutterightdept

hcorrect-1),

SolidBody

1(Body.2)(cutterleftdepth

correct-2),

SolidBody

1(PartBody)(cutterright-

1),

SolidBody

1(Imported1)(latestmodif

iedhandlereadyfortesON

EHOLE-1),

SolidBody

1(PartBody)(lefthandlepa

rt-1),

SolidBody

1(PartBody)(link2-2),

SolidBody

1(PartBody)(link3-1),

SolidBody 1(Boss-

Extrude1)(modifiedinputl

ink-2),

SolidBody 1(Boss-

Extrude1)(wire-1)

Curve Data:N/A


116

Model Reference Connector Details Strength Details

Pin Connector-1

Entities: 2 face(s) Type: Pin

Connection type: With retaining

ring (No

translation) Rotational stiffness

value: 0

Units: SI

No Data

Connector Forces

Type X-Component Y-Component Z-Component Resultant

Axial Force (N) 0 0 13.242 13.242

Shear Force (N) -42.237 -534.16 0 535.82

Torque (N-m) -0 -0 -1.2565e-012 -1.2565e-012

Bending moment (N-m) -0.55729 -0.26937 0 0.61898

Pin Connector-9



ring (No


value: 0

Units: SI

No Data

Connector Forces


Axial Force (N) 0 0 53.63 53.63

Shear Force (N) -500.97 -41.942 0 502.73

Torque (N-m) 0 0 1.4413e-012 1.4413e-012

Bending moment (N-m) -0.42284 0.088695 0 0.43204

Pin Connector-10



ring (No


value: 0

Units: SI

No Data


117

Connector Forces


Axial Force (N) -0 -0 -66.997 -66.997

Shear Force (N) 411.13 548.91 0 685.8

Torque (N-m) 0 0 1.4413e-012 1.4413e-012

Bending moment (N-m) 0.80581 -0.98481 0 1.2725

Pin Connector-11



ring (No


value: 0

Units: SI

No Data

Connector Forces


Axial Force (N) -0 -0 66.998 -66.998

Shear Force (N) -411.12 -548.91 0 685.8

Torque (N-m) -0 -0 7.2671e-013 -7.2671e-013


Pin Connector-12



ring (No


value: 0

Units: SI

No Data

Connector Forces


Axial Force (N) 0 0 -183.06 183.06

Shear Force (N) 1239.5 538.61 0 1351.5

Torque (N-m) -0 -0 7.2672e-013 -7.2672e-013

Bending moment (N-m) -1.2934 2.1145 0 2.4787



ring (No


value: 0

No Data


118

Pin Connector-13 Units: SI

Connector Forces


Axial Force (N) -0 -0 -4.0973 -4.0973

Shear Force (N) 201.66 24.543 0 203.15

Torque (N-m) 0 0 9.596e-018 9.596e-018


Pin Connector-14



ring (No


value: 0

Units: SI

No Data

Connector Forces


Axial Force (N) 0 0 0.93239 0.93239

Shear Force (N) 169.29 -46.199 0 175.48

Torque (N-m) -0 -0 -9.7603e-017 -9.7603e-017


Pin Connector-15



ring (No


value: 0

Units: SI

No Data

Connector Forces


Axial Force (N) -0 -0 -20.075 -20.075

Shear Force (N) 91.532 24.709 0 94.808

Torque (N-m) 0 0 9.3458e-013 9.3458e-013



119

Pin Connector-16



ring (No


value: 0

Units: SI

No Data

Connector Forces


Axial Force (N) -0 -0 -16.253 -16.253

Shear Force (N) 129.46 -9.8637 0 129.84

Torque (N-m) 0 0 7.9454e-013 7.9454e-013


Pin Connector-21



ring (No


value: 0

Units: SI

No Data

Connector Forces


Axial Force (N) 0 0 13.383 13.383

Shear Force (N) 89.3 -506.95 0 514.75

Torque (N-m) -0 -0 -1.7166e-012 -1.7166e-012


Pin Connector-22



ring (No


value: 0

Units: SI

No Data

Connector Forces


Axial Force (N) -0 -0 -13.367 -13.367

Shear Force (N) -89.848 506.96 0 514.86


120

Torque (N-m) -0 -0 -1.7166e-012 -1.7166e-012

Bending moment (N-m) 1.813 0.45891 0 1.8702

Load name Load Image Load Details

Force-4

Entities: 1 face(s)

Reference: Face< 1 >

Type: Apply torque

Value: -13.384 N-m

Fixture name Fixture Image Fixture Details

Fixed-1

Entities: 1 face(s)

Type: Fixed Geometry

Resultant Forces

Components X Y Z Resultant

Reaction

force(N) 132.089 27.2037 0.125037 134.862

Reaction

Moment(N-m) -1.08504 2.48097 0.00245652 2.70787


121

Contact Information

Contact Contact Image Contact Properties

Contact Set-1

Type: Bonded

contact pair

Entites: 3 face(s)

Contact Set-2

Type: Bonded

contact pair

Entites: 3 face(s)

Global Contact

Type: Allow

Penetration

Components: 1

component(s)

Mesh Information

Mesh type Mixed Mesh

Mesher Used: Standard mesh

Automatic Transition: Off

Include Mesh Auto Loops: Off

Jacobian points 4 Points

Jacobian check for shell On

Element Size 1.50839 mm

Tolerance 0.0754193 mm

Mesh Quality High

Remesh failed parts with incompatible mesh Off


122

Mesh Information - Details

Total Nodes 66647

Total Elements 36630

Time to complete mesh(hh;mm;ss): 00:00:41

Computer name: Staffordshire IS Labs

Resultant & Reaction forces

Selection set Units Sum X Sum Y Sum Z Resultant

Entire Model N 132.089 27.2037 0.125037 134.862

Reaction Moments

Selection set Units Sum X Sum Y Sum Z Resultant

Entire Model N-m -1.08504 2.48097 0.00245652 2.70787


123

Study Results

Name Type Min Max

Stress1 VON: von Mises

Stress

0 N/m^2

Node: 40028

9.43181e+007

N/m^2

Node: 39713

Assem1-Study 1-Stress-Stress1

Name Type Min Max

Displacement1 URES: Resultant

Displacement

0 mm

Node: 7309

0.0217917 mm

Node: 46722


124

Assem1-Study 1-Displacement-Displacement1

Name Type Min Max

Strain1 ESTRN: Equivalent

Strain

0

Element: 23313

0.000423608

Element: 23251


125

Assem1-Study 1-Strain-Strain1

Image – Stress concentration close-up (with deformation, modified input link

position)


126

Documents

Ryan Muller - Optimization of a non-Grashof compound four bar linkage mechanism for cutting surgical wires