Dr. Hanafy M. Omar

1

Chapter 5: Cams

CAM - Definition A cam is a machine element used to drive another element,

called a follower, through a specified motion by direct contact.

Cam-and-follower mechanism are simple and inexpensive , have few moving parts, and occupy very little space.

Furthermore, follower motion having almost any desired characteristics are not difficult to design.

For these reasons, cam mechanisms are used extensively in modern machines.

Cam

Follower

Examples for cam

In IC engines to operate the inlet and exhaust valves

Classification of CAM Mechanism

Based on the basic shapes

(a)plate cam,

(b) wedge cam

(c) barrel cam

(d) face cam.

Classification of CAM Mechanism

Based on modes of Input / Output motion

Rotating cam Translating follower

Rotating cam Oscillating follower

Translating cam Translating follower

Rotating cam Translating follower

Rotating cam oscillating follower

Translating cam Translating follower

Classification of followers

According to the shape of follower

Knife edge follower

Roller follower

Flat faced follower

Spherical faced follower

Knife edge follower

Roller follower

Flat faced follower

Spherical faced follower

According to the path of motion of follower

a) Radial follower

b) Offset follower

When the motion of the follower is along an axis passing through the centre of the cam, it is known as radial followers.

The above figures are examples of this type.

Radial follower

Offset follower

When the motion of the follower is along an axis away from the axis of the cam centre, it is called off-set follower. Above figures are examples of this type.

CAM Nomenclature 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 the cam 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 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

pitch curve Stroke: The greatest distance or angle through which the follower

moves or rotates

Motion of the Follower As the cam rotates the follower moves upward 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 and downward even

when the cam rotates, it is called dwell.

Displacement diagram for a cam Displacement is the distance that a follower moves during

one complete revolution (or cycle) of the cam while the follower is in contact with the cam.

It is the plot of linear displacement, y() of follower versus angular displacement () of the cam for one full rotation of the cam.

y=y()

Types of follower motion 1. Uniform motion ( constant velocity)

2. Simple harmonic motion

3. Uniform acceleration and retardation motion

4. Cycloidal motion

Uniform motion (constant velocity)

Since the follower moves with uniform velocity during its rise and fall, the slope of the displacement curve must be constant as shown in figure

This motion is not useful for the full lift because of the sharp corners produced at the boundaries wit the other segment of the displacement curve.

To solve this problem, the modified displacement curve is used

Displacement diagram

Modified Uniform motion (constant velocity)

The sharp corners are eliminated in the modified uniform motion displacement diagram

Displacement diagram

Cam Profile Design It is required to determine the exact

shape of a cam surface required to deliver a specified follower motion.

We assume here that the required motion has been completely determined graphically as well as analytically.

Let us address the case of plate cams.

Basic Principle In constructing the cam profile, we employ the principle of

kinematic inversion, imagining the cam to be stationary and allowing the follower to rotate opposite to the direction of cam rotation.

Taking the cams with knife-edge follower for example, the locus generated by the trace point as the follower moves relative to the cam is identical to cam surface. By this way cam surface can be figured out.

Graphical Layout of Cam Profiles

For the case of reciprocating knife-edge follower

As shown in left figure, the displacement diagram of the follower is given, y=y (). Construct the plate cam profile.

Graphical Layout of Cam Profiles (the case of reciprocating knife-edge follower) Step1: divide the displacement-diagram abscissa into a number of segments.

Step2: divide the prime circle into corresponding segments.

Step3: transfer distances, by means of dividers, from the displacement diagram directly onto the cam layout to locate the corresponding positions of the trace point.

Graphical Layout of Cam Profiles (the case of reciprocating knife-edge follower)

Step4: draw a smooth curve through these points. The curve is just the required cam profile.

Graphical Layout of Cam Profiles (the case of reciprocating knife-edge follower)

Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)

As shown in left figure, the displacement diagram of the follower is given, y=y ().

Construct the plate cam profile.

Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower) Step1: construct the prime

circle with radius r0.

Step2: construct the offset circle with radius equal to the amount of offset e.

Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)

Step3: divide the displacement-diagram abscissa into a number of segments.

Step4: divide the offset circle into corresponding segments and assign station numbers to the boundaries of these segments.

Step5: construct lines tangent to the offset circle from these station, dividing the prime circle into corresponding segments.

Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)

Step6: transfer distances, by means of dividers, from the displacement diagram directly onto the cam layout to locate the corresponding positions of the trace point, always measuring outward from the prime circle.

Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)

Step7: draw a smooth curve through these points. The curve is just the required cam

profile.

Step8: draw the roller in its proper position at each station and then construct the cam profile as a smooth curve tangent to all these roller positions.

Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)

Graphical Layout of Cam Profiles (the case of reciprocating flat-face follower)

As shown in left figure, the displacement diagram of the follower is given, y=y ().

Construct the plate cam profile.

Graphical Layout of Cam Profiles (the case of reciprocating flat-face follower)

Step1: divide the displacement-diagram abscissa into a number of segments.

Step2: divide the prime circle into corresponding segments.

Step3: transfer distances from the displacement diagram directly onto the cam layout.

Step4: construct a line representing the flat face of the follower in each position.

Graphical Layout of Cam Profiles (the case of reciprocating flat-face follower)

Step5: construct a smooth curve tangent to all the follower positions. This curve is the required cam profile.

Low Speed Cams This cams are sometimes composed of a combination of curves, such as

straight lines are circular arcs, which can be produced easily by

machine tools (easy to manufacture), as shown in following two cams.

In these cams, the acceleration changes abruptly at each of the tangency

points because of the instantaneous change in the radius of curvature of

the cam profile.

Graphical Layout of Cam Profiles (the case of reciprocating flat-face follower)

High Speed Cams Although cams with discontinuous acceleration

characteristics have sometimes been accepted to save cost in low speed applications

However, for high speed applications (to increase the productivity), such cams exhibit major problems like high noise and wear

To overcome these problems, It is extremely important that not only the displacement and the velocity curve but also the acceleration curve be made continuous for the entire motion cycle.

2

2 )(,

)(),(

d

yd

d

dyy

must be continuous

Note 2

22

2

2

,

d

yd

dt

yd

d

dy

dt

dy

Parabolic Motion If the rotation angle of the cam is , the displacement

diagram equation for a parabolic motion of rise L is given by

First Half Rise: second Half 2

2

Ly

2

121

Ly

After differentiation we found that

First Half

L

d

yd

L

d

dy

4

4

2

2

Second Half

L

d

yd

Ld

dy

4

14

1

2

2

There is a discontinuity in the velocity and acceleration

Parabolic Motion

Displacement diagram and derivatives for full-rise parabolic motion

Simple Harmonic Motion

Displacement diagram and derivatives for full-return simple harmonic motion

Displacement diagram and derivatives for full-rise simple harmonic motion

The velocity and acceleration are continuous

cos1

2

Ly

cos1

2

Ly

Rise Return