Chapter 02 - Mechanism and Linkages

8/2/2019 Chapter 02 - Mechanism and Linkages

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EE 2333 Mechanics of Machines

Chapter II Mechanism and Linkages

By

Syed Fawwaz Al-Attas


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Mechanisms

Terminology


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PAIRING ELEMENTS

Pairing elements: the geometrical forms by which twomembers of a mechanism are joined together, so that the

relative motion between these two is consistent.

Such a pair of links is called Kinematic Pair.


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Courtesy:www.technologystudent.com

PAIRING ELEMENTS


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KINEMATICKINEMATICPAIRSPAIRS

Based on nature of contact between elements

(i) Lower pair : The joint by which two members areconnected has surface contact.

Sliding pair Turning pair


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Examples: Sliding pairs (lower pairs)


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Examples: Turning pairs (lower pairs)


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(ii) Higher pair: The contact between the pairing elementstakes place at a point or along a line.

KINEMATICKINEMATICPAIRSPAIRS


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Examples: 2 DOF pairs (higher pairs)


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Based on relative motion between pairing

elements

(a) Siding pair [DOF = 1]

(b) Turning pair (revolute pair) [DOF = 1]

KINEMATICPAIRSKINEMATICPAIRS


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Based on relative motion between pairingelements

(c) Cylindrical pair [DOF = 2]

(d) Rolling pair [DOF = 1]



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Based on relative motion between pairing

elements

(e) Spherical pair [DOF = 3]

Eg. Ball and socket joint

(f) Helical pair or screw pair [DOF = 1]



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Based on the nature of mechanical constraint

(a) Closed pair

(b) Unclosed or force closed pair



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Kinematic Chain

Definition: Akinematic c

hain is an assembly of links connected together eitherjoined together or arranged in a manner that permits them to move

relative to one another, without specifying the base link (i.e., a fixed link)

Joints

Binary LinksBinary Links

TernaryTernary

LinkLink

Fig. Devices with diverse link components.

4-link kinematic

chain

That is, whenThat is, when allall linkages in a system are movably and connectedlinkages in a system are movably and connectedtogether bytogether byjointsjoints, they are said to form a, they are said to form a kinematic chainkinematic chain..


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LOCKED CHAIN ORSTRUCTURE

LinksLinks connectedconnected inin suchsuch aa wayway thatthat nono relativerelative

motionmotion isis possiblepossible..

Kinematic Chain


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Types ofLinks in a Kinematic Chain

BinaryBinary

linklinkBinaryBinary

linkslinks

Ternary linkTernary link

Fig. Mechanism with diverse link types.

Binary LinksBinary Links

TernaryTernary

LinkLink

Fig. Devices with diverse link components.

Joints

Kinematic chains might contain different types of links and joint.Kinematic chains might contain different types of links and joint.

Links containing only 2 par element connections are calledLinks containing only 2 par element connections are calledbinary linksbinary links;;

Those having 3 are calledThose having 3 are called ternary linksternary links,,

Those having 4 are calledThose having 4 are called quaternary linksquaternary links, and so on, and so on


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Closed vs. Open kinematic chains

Closed Chain Mechanisms:

If every link is connected to at least two other

links, the chain forms one or more closed loops

and it is called a closed kinematic chain.

Fig. Walking robot using a4-bar mechanism

4-bar kinematic chain

5-bar link mechanism


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Open Chain Mechanisms:

A kinematic chain that is not closed

(has no closed loops) is an open kinematic chain..

PUMARobot:

3-link open chain mechanism

Skeleton

Real robot

Robot simulation

Closed vs. Open kinematic chains


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MechanismsDefinition:Definition:A mechanism is a kinematic chain where one of its linkages

does not move (such link is fixed and its called the base link).

A mechanism is a constrained kinematic chain.

Motion of any one link in the kinematic chain will give a definite and predictable motion relative

to each of the others. Usually one of the links of the kinematic chain is fixed in a mechanism

Fixed link or base link

Fixed link

or base link


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Some Common Types of Mechanisms 4-bar mechanism

5-bar & 6-bar mechanisms

Slider-crank mechanism

Cam-follower mechanism

Gear Trains mechanism

Etc.

Figure. (a) Slider crank mechanism.

(b) Skeleton representation.

slider

crank

Figure. Slider crank

mechanism with offset.

Figure. Gear train.

Cam Disk

Follower


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LinksIndividual parts of machines or mechanisms

are also referred to as links.

Types ofLinks:

Links can be non-rigid: cables and belts.

Links can also be rigid bodies: cranks, levers, wheels, bars or

gears.

Non-rigid link:

timing belt

Rigid links:

pulleys,

cam,

crank, etc.

Example:

Links


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Slider-crank mechanism

Figure. Slider crank mechanism with offset.

This mechanism incorporates 5 mainelements:

1. A stationarybase link(link1). The otherlinks can move relative to the base link .

2. The crank(link2) rotates about a basepivot/joint.

3. The sliderorpiston (link4) moves in alinear motion.

4. A coupler(link3) connects the crank totheslider.

5. The line of action is the straight-linepath of the center of theslider.

The slider-crank mechanism might havean offsetbetween the line of action andthe base line.

Figure. Slider-crank mechanism.

slider

crank

coupler


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Skeleton of a Mechanism

Askeleton is a highly simplified drawing of amechanism.

Use:

Skeletons are use for analyzing the

motions of the mechanism.

theoretical

The dimensions in the skeleton diagramare critical for determining motions.

The skeleton includes links andjoints:

Joints are represented with a symbol thatdepends on the type of joint.

Links are, in general, represented bystraight lines (regardless of the actualshape of the real link).

Figure. (a) Slider crank mechanism.

(b) Skeleton representation.

slider

crank

joints


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Four-Bar Mechanism

4-bar mechanisms are among the most common and useful mechanisms:

Components in a 4-bar mechanism:

It has 4 bars (links)

A stationary orbase link(link1) and 3 moving links.

The crank(link2 or link4) rotates about a base pivot/joint (O2 or O4) and move

the mechanism.

A coupler (link3) connects the crank to the output link.

Figure. Skeleton

representation.

Figure. Example 4-bar

mechanism.

AngularAngular

displacementsdisplacements


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Complex mechanisms can be built from simple mechanisms by adding more links.

FIG. 4-bar mechanism

Skeleton.

FIG. Complex mechanism

FIG. 4-bar mechanism used in a

washing machine.

12

3 4

Gears

This gear drives the agitator

to provide the washing action

Four-Bar Mechanism


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Compound Mechanisms

A compound mechanism is system/machine

composed of basic/simple mechanisms

forming a complex machine.

The entire machine can be completely

analyzed by independently analyzing all the

individual (simple) mechanisms comprising

the overall system.

...

4-Bar mechanism

4-Bar mechanism

4-Bar mechanism

Example: compound

mechanism: ExcavatorCompound

mechanism


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Though all machines are mechanisms, allThough all machines are mechanisms, all

mechanisms are not machinesmechanisms are not machines

Machines


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Planar vs. Spatial Mechanisms Planar Mechanisms:

When all the links of a mechanism have plane motion, it is called as a planar

mechanism. All the links in a planar mechanism move in planes parallel to the

reference plane.

Spatial Mechanisms:

A mechanisms where links move in 3 dimensions.

Examples of spatial

mechanisms A gear train system (for example)

can be a planar or spatial

mechanisms depending on the

configuration of the system.


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Mechanisms

Degrees of Freedom(DOF)


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DOF of a System

DOF: Mechanisms (e.g., Robot manipulators and mobile robots) can move

in one or more dimensions.

The dimensions in which a mechanism can move arecalled its Degrees of Freedom (DOF)

NOTENOTE:: A DOF is any of the minimum number of coordinates required tocompletely specify the motion of a mechanical system (how many DOF a

mechanism such as a robothas is important in determininghow it can impact its

world, andhow well, it can accomplish its task).


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TranslationalandRotationalDOF General:

In general, a free body in 3D space has a total of 6 DOF.

3 of those are called translational DOF as they allow the body to movewithout turning (rotation), while the other 3 are called rotational as theyallow the body to rotate without moving (translation):

Translation DOF:usually labeledx,y andzby convention.RotationDOF:

usually labeled roll,pitch andyawby convention (in robotics)


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Examples of robot leg mechanisms with 2 & 3 DOF

Sch

ematic configuration ofor walking machines (3D

Hip abduction

angle (U)Hip flexion

angle (N)

Knee flexion

angle (])

U

N

]

A mammal type leg with

a two-joint actuator

(2DOF leg)

A m

a tw

(2D

3DOF leg


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Controllable vs. Uncontrollable DOF General:

If a mechanism has an actuator for every DOF, then all DOF are

controllable (this is an ideal scenario but it is not always the case).

The DOF that are not controllable are called uncontrollable:

ControllableDOF(CDOF) : DOF that we can control.

UncontrollableDOF(UDOF): DOF that we cannot control.

IMPORTANT NOTE:IMPORTANT NOTE: Any body in 2D can potentially move in 3 ways but it can only do so if it

has actuators that can control those 3 DOF (and cars DO NOT parallelparking is difficult)

This also happens in 3D where bodies can potentially move in 6 ways.


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N

umber of degrees of freedom of a mechanism is given by

Where,

F = Degrees of freedom

n = Number of links in the mechanism.

l = Number of lower pairs, which is obtained by counting thenumber of joints. If more than two links are joinedtogether at any point, then, one additional lower pair is to

be considered for every additional link.

h = Number of higher pairs

GRUBLERS CRITERIONGRUBLERS CRITERION

F = 3(n-1)-2l-h


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F = 3(n-1)-2l-h

Here, n = 4, l = 4 & h = 0.

F = 3(4-1)-2(4) = 1

i.e., one input to any one link will result in definite motion of all

the links.

ExamplesExamples -- DOFDOF


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F = 3(n-1)-2l-h

Here, n = 5, l = 5 and h = 0.

F = 3(5-1)-2(5) = 2

i.e., two inputs to any two links are required to yield definite

motions in all the links.



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F = 3(n-1)-2l-h

Here, n = 6, l = 7 and h = 0.

F = 3(6-1)-2(7) = 1

i.e., one input to any one link will result in definite motion of all

the links.



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F = 3(n-1)-2l-h

Here, n = 6, l = 7 (at the intersection of 2, 3 and 4, two lower pairs

are to be considered) and h = 0.

F = 3(6-1)-2(7) = 1



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F = 3(n-1)-2l-h

Here, n = 11, l = 15 (two lower pairs at the intersection of 3, 4, 6; 2,4, 5; 5, 7, 8; 8, 10, 11) and h = 0.

F = 3(11-1)-2(15) = 0



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Chapter 02 - Mechanism and Linkages