Lecture 5-6 Fundamentals of Mechanics and Mechanisms

8/10/2019 Lecture 5-6 Fundamentals of Mechanics and Mechanisms

1/137


2/137


3/137

Technical University of Cluj-Napoca

Faculty of Mechanics

Department of Mechanisms, Precision Mechanics and Mechatronics

Lecture 5-6 Fundamentals of Mechanics and Mechanisms

ef Lucr. Dr.ing. Sergiu-Dan Stan

Kinematic Analysis of Mechanisms


Aim

Determining the positions, velocities and accelerations of the driven

elements (without taking into account the forces that influence the

movement) knowing the movement of the driver element(s).


4/137


5/137








6/137






MOTIONSTUDY

Study of position, displacement, velocity and

acceleration of different elements ofmechanism.

Given input Desired output

Motion study is important in Mechanisms and Machine Theory


7/137






Kinematic Analysis of Mechanisms usingTransfer functions

In kinematic analysis of the mechanisms the transfer functions represents those

functions that establish a link between the kinematic state of a driven elementand kinematic state of the driver element.

Thus,

is defined as the function that establish the link

between parameter that is the driven element and is the driver element.

Transfer functions method


8/137






If we differentiate

where

Where represents the transfer function of 1storder (establish the link between

The velocity of driven and driver link).



9/137






If we differentiate 2 times:

where

Where represents the transfer function of 2ndorder (establish the link between

the acceleration of driven and driver link).



10/137






Example 1. Kinematic Analysis of Four-bar Mechanism

Kinematic analysis of four-bar mechanism


11/137

h l f ld l f h d h


12/137






Kinematic analysis of four-bar mechanism

2


13/137


14/137


15/137

Technical University of Cluj NapocaLecture 5 6 Fundamentals of Mechanics and Mechanisms


16/137






Example 2.

Technical University of Cluj-NapocaLecture 5-6 Fundamentals of Mechanics and Mechanisms


17/137








18/137

Technical University of Cluj Napoca



Lecture 5 6 Fundamentals of Mechanics and Mechanisms



19/137



20/137

Technical University of Cluj Napoca



Lecture 5 6 Fundamentals of Mechanics and Mechanisms


Kinematic analysis of a the planar four-bar linkage



21/137

y j p




Kinematic analysis of a the planar four-bar linkage



22/137

y j p






23/137

y j p




Kinematic analysis of a the slider-crank linkage

Example 3



24/137




Constante Variabile

l1

l2

l3=e

3=270

4=180

l4

1

2



25/137




3=270

4=180



26/137





27/137


F l f M h i


f L D i S i D S


28/137





F lt f M h i


f L D i S i D St


29/137





30/137




ef Lucr Dr ing Sergiu Dan Stan


31/137




Example 4




ef Lucr Dr ing Sergiu Dan Stan


32/137




Constante Variabile

l1

l3

l4

4=180

l2

1

2

3




ef Lucr Dr ing Sergiu-Dan Stan


33/137




4=180




ef Lucr Dr ing Sergiu-Dan Stan


34/137



ef Lucr. Dr.ing. Sergiu Dan Stan






35/137









36/137









37/137

y


g g






38/137

y


g g

Example 5


39/137


40/137






41/137







42/137







43/137


Technical University of Cluj-NapocaFaculty of Mechanics

D f M h i P i i M h i d M h i

Lecture 5-6 Fundamentals of Mechanics and Mechanismsef Lucr. Dr.ing. Sergiu-Dan Stan


44/137


Example 6


45/137


Department of Mechanisms Precision Mechanics and Mechatronics



46/137


2





47/137






48/137






49/137


Example 7





50/137


I

II

OABO

BCDEB

OAdriving link

EDdriven link





51/137






52/137






53/137

p ,





54/137

p ,





55/137


56/137





57/137





58/137





59/137


60/137


61/137





62/137


63/137





64/137





65/137





66/137





67/137





68/137

Differential





69/137

Cam Mechanisms


70/137





71/137

The cam has a very important function in the

operation of many classes of machines,

especially those of the automatic type, such asprinting presses, shoe machinery, textile

machinery, gear-cutting machines, and screw

machines. In any class of machinery in which automatic

control and accurate timing are paramount, the

cam is an indispensable part of mechanism. Thepossible applications of cams are unlimited,

and their shapes occur in great variety.

Applications of Cam Mechanisms





72/137

The transformation of one of the simple

motions, such as rotation, into any other

motions is often conveniently accomplishedby means of a cam mechanism.

A cam mechanism usually consists of two

moving elements, the cam and the follower,mounted on a fixed frame.

Cam Mechanisms
http://en.wikipedia.org/wiki/Image:Nockenwelle_ani.gif


73/137





74/137

Engine 4 stroke





75/137

Examples for cam mechanisms

In IC engines to operate the inlet and exhaust valves





76/137


77/137


78/137





79/137

Cam Mechanisms





80/137





81/137

Cam Mechanisms




CAM N l t


82/137

Cam profile:The outer surface

of the disc cam.

Base circle: The circle with

the shortest radius from the

cam center to any part of thecam profile.

Trace point: It is a point on the

follower, and its motion

describes the movement of

the follower. It is used to

generate the pitch curve.

CAM Nomenclature




CAM Nomenclat re


83/137

CAM Nomenclature

Pitch circle:A circle

drawn from the cam

center and passes

through the pitch point is

called Pitch circle

Stroke:The greatest

distance or angle through

which the follower movesor rotates




CAM Nomenclature


84/137

Pressure angle:The angle

between the direction of

the follower movement

and the normal to the

pitch curve.

Pitch point:Pitch point

corresponds to the point

of maximum pressureangle.

CAM Nomenclature




CAM Nomenclature


85/137

Pitch curve :The path

generated by the trace

point as the follower is

rotated about a

stationery cam.

Prime circle:The smallest

circle from the cam

center through the pitchcurve

CAM Nomenclature





86/137





87/137


88/137


89/137







90/137

Rotating camoscillating follower







91/137

Cam profiles







92/137

FLAT POINT/KNIFE ROLLER OFFSET

Cam Mechanisms






Fl t f d f ll


93/137

Flat faced follower







94/137







95/137

An eccentric cam is a disc with its centre of rotation positioned offcentre.This means as the cam rotates the flat follower rises and falls at a constant

rate. This type of cam is the easiest to make and yet it is one of the most

useful.

PRACTICAL EXAMPLE - ECCENTRIC CAM

ECCENTRIC CAM







96/137

THE SNAIL / DROP CAM

A snail (melc!) drop cam is used where the drop or fall of the follower must be

sudden.

THE SNAIL / DROP CAM






SWASH PLATE CAMS


97/137

SWASH PLATE CAMS

A swash plate cam is usually a disc that rotates around a shaft. The discis set at an angle so that the follower moves up and down as the disc

rotates.

SWASH PLATE CAMS







98/137

The mechanical display below is a dancing puppet.

SWASH PLATE CAMS







99/137

BOX CAMS

A box cam consists of a rotating disc, normally made from steel. A groove is cut /

milled into its surface to a specific depth (this is the profile). The groove may be anunusual shape as seen in the example below. As the disc rotates the follower

follows the path of the groove. Cams of this type are used in a range of machines

where a repetitive motion is needed.

BOX CAMS







100/137

End cams

It is also

similar to

cylindrical

cams, but the

follower

makes

contact at

periphery of

the cam as

shown in fig






FLAT PLATE CAM / LINEAR CAM


101/137


FLAT PLATE CAMS

The diagram below shows a basic example of a flat plate cam / linear cam. As the flat plate cam profile

moves to the left the follower moves up and down, matching the shape of the profile. The flat plate cam

then reverses in the opposite direction and the follower drops and rises again.








102/137

FLAT PLATE CAMS


103/137






Motion of the follower


104/137

Motion of the follower

As the cam rotates the follower movesupward and downward.

The upward movement of follower is called

rise (Outstroke) The downward movement is called fall

(Returnstroke).

When the follower is not moving upward anddownward even when the cam rotates, it iscalled dwell.






Sine motion law


105/137

Imposing the limit conditions for advance phase:

If we derive 2 times:

Space s made by the follower, function of rotation angle of the cam, after the law:







106/137

Maximum value of velocity for is:







107/137

Maximum value of acceleration for

Legea de variatie a spatiului s,

a vitezei vsi acceleratiei a,

ale tachetului:


108/137





ef Lucr. Dr.ing. Sergiu-Dan Stan;;


109/137

Maximum value of velocity for is:






Maximum value of acceleration for


110/137

Legea de variatie a spatiuluis,a vitezei vsi acceleratiei a,

ale tachetului:


111/137


112/137


Faculty of MechanicsDepartment of Mechanisms, Precision Mechanics and Mechatronics




113/137






114/137






115/137






116/137


117/137


118/137






119/137

Motion events

Motion events Technical University of Cluj-Napoca





120/137

Cam Mechanisms Technical University of Cluj-Napoca



http://en.wikipedia.org/wiki/Image:Nockenwelle_2005.jpg


121/137




http://en.wikipedia.org/wiki/Image:4-Stroke-Engine.gifhttp://en.wikipedia.org/wiki/Image:Nockenwelle_2005.jpg


122/137

Rotating cam-translating follower

Cam Mechanisms


123/137





C Sh


124/137

Grooved cam

Cam Shape

Cam Mechanisms


125/137






126/137






127/137






128/137

Dual cam






129/137

Cylindrical cam and end cam






130/137






131/137






132/137






133/137


134/137






135/137






136/137






137/137

Documents

Lecture 5-6 Fundamentals of Mechanics and Mechanisms