Background Information -- Become a mechanical engineer on the spot!

A cam is a device used to convert a constant velocity rotary motion into a reciprocating motion which has the kinematic features that we desire. (Reciprocating means "back and forth" or "up and down" in this case.) A common application of the cam is in the engine of a car. A rotating cam shaft is used to cause the valves in the engine to move up and down. Here is a two dimensional picture of a cam mounted on its shaft, and contacting its follower.

The difference between the radius at the point of contact and the radius of the cam's base circle (shown in lighter color in the figure) is called the lift. It is the linear displacement of the follower in the case shown. The lift is an important feature of the design. In this case, a significant portion of the cycle the cam's surface and the base circle coincide. This is called a dwell. So, in the case shown, we have a dwell at zero lift. Here is a plot of the lift as a function of rotation angle q.

The lift function is a displacement. Its first derivative can be used to compute the velocity, v, and the acceleration, a, of the follower. If w is the angular velocity in radians per second of the camshaft, then v = w y' and a = w2 y''. There is a third derivative quantity the "jerk" which is the time derivative of acceleration, j = w3 y'''. The jerk is the time rate of change of acceleration. The larger its value, the more likely the cam is to create undesirable vibrations in the engine.

THE PRINCIPLE LAW of CAM DESIGN: The jerk must be finite.

This means that the acceleration must be continuous. We want the cam to operate as smoothly as possible. We also want the acceleration to be as small as possible. Making the acceleration small minimizes the forces needed to hold the cam in place.

There, you are now initiated into the wonderful world of cam design. Time to try for a problem.