##
28. Cam Design

• Cams are basically shaped surfaces that are typically not round. The cam is rotated or translated, and a follower (possibly a small wheel) is displaced as it moves over the surface.

• Cams can generate complex motion profiles in a compact area.

• Engine values are a well known application of cams. They can open and close the cylinders with a large force, but will also dwell in open or closed positions.

28.1 Cam Types
• Typical cams are pictured below,

• Some types of reciprocating followers include,

• Some oscillating followers include,

28.2 Cam Motion
• We can often describe a cam by drawing the displacement profile on a graph.

• Consider possible displacement curves for,

• The curve above can be broken into sections and described with a mathematical function,

• Of these two functions, the parabolic will allow a greater level of control, but harmonic motion will permit smooth transitions between motions.

• Some of the general design rules,

1. fulfil the basic motion requirements. (cam profiles are not exact and decisions are required.)

2. The displacement, velocity and acceleration curves must be continuous, but the jerk must not be infinite. This means that the positions and first and second derivatives must be equal at the segment ends.

3. Minimize the velocities and accelerations.

• The first step in developing a cam is to develop a motion profile. Consider example 5-2 from Shigley and Uicker,

• Now,

• You may have recognized that the previous design assumed that the follower must have a point contact with the curve.

• In actual practice we will have surfaces that are in contact, the surfaces can be identified using the equations developed previously.

• Consider the flat-face follower.

• We can develop the a modified cam profile based on the flat faced follower. (Note: the proof is done as if a milling cutter is used, but this turns out to be more a matter of convenience)

• Using the derivation of the basic relationships, we can now develop a method to plot out a complete cam profile.

• Now, develop a cam for example 3-52 from Shigley and Uicker,

• Keep in mind that when designing cam-follower pairs that the radius of the follower is not zero. Therefore it may be necessary to compensate for this during the design.

• Consider the effect of a round follower on a wedge cam.

• Consider the effect of a round follower on a radial cam.

• Other arrangements are possible, and some proofs are provided in the text.

28.3 Using Cams as Joints and Links in Mechanisms
• We can use cams to give complex joint motion,

28.4 Problems
Problem 28.1 You were recently hired as a Fuel Containment and Monitoring specialist for Generous Motors. Your first job is to design a mechanical gauge for an instrument panel. The tank holds up to 10 gallons of fuel. It has been determined that the needle on the gauge should remain steady at the full ‘F’ mark while the tank contains 8 to 10 gallons. When the tank has less than 3 gallons the gauge should read empty ‘E’. The last design was a failure ‘F’, and your boss fired the engineer responsible. It seems that he his design did not follow good cam design rules: the velocity and accelerations were not minimized: and so the gauge would wear out, and jam prematurely. Design a new cam to relate the float in the tank to the gauge on the instrument panel.

Problem 28.2 The motion profile curve below has 4 segments. Segments A and C are based on polynomials. Segment D is based on a harmonic/cosine function. Segment B is a constant velocity segment.

a) Write the equation for curve segment B.

b) What effect does the follower shape have when converting the motion profile to a cam profile. Draw a figure to illustrate this with a round follower.

c) Write the coefficients for the curve segment C.

28.5 References
Problem 28.3 Erdman, A.G. and Sandor, G.N., Mechanism Design Analysis and Synthesis, Vol. 1, 3rd Edition, Prentice Hall, 1997.

Problem 28.4 Shigley, J.E., Uicker, J.J., “Theory of Machines and Mechanisms, Second Edition, McGraw-Hill, 1995.