Cams

§1Cam and follower

A cam rotates (or slides) and, through its profile, drives a follower in a precisely timed motion — a valve opening, a tool advancing, a mechanism indexing. It turns steady rotation into any motion you can draw.

The pairing is simple: the cam is the driver with the worked profile; the follower is held against it by a spring or gravity and traces that profile as motion. A full cam cycle is built from segments — a rise (follower moves out), a dwell (follower held stationary while the cam turns), a return (follower moves back), and often another dwell. The designer specifies what motion is wanted in each segment, and the cam profile is then whatever shape delivers it. Everything therefore starts with the graph of that motion.

§2The displacement diagram

The displacement diagram plots follower lift s against cam angle θ over one revolution. It is the specification of the cam, drawn before any profile is laid out.

Reading it is a chain of derivatives against angle: the slope of the displacement curve is the follower velocity, the slope of that is the acceleration, and the slope of the acceleration is the jerk. Each matters for a different reason — velocity for the follower’s speed, acceleration because it sets the inertia force (F = m·a) the spring must overcome and the contact stress it drives, and jerk because sudden changes in acceleration cause vibration, noise and wear. A good cam law keeps acceleration finite and, ideally, continuous. The hero shows the four standard laws for one rise, and their acceleration is where they differ most.

§3The motion laws

Four displacement laws cover most cam design, each a different compromise between simplicity and smoothness. All raise the follower by the same lift h over the same rise angle β; they differ in how.

§4Comparing the laws

The counter-intuitive result: the law with the highest peak acceleration is the best for high-speed cams. Peak value is not the whole story — continuity is.

Uniform velocity looks ideal until the ends: to start and stop the follower instantly demands infinite acceleration, an impossible shock that hammers the mechanism, so it is used only with rounded corners or for slow, lightly-loaded motion. Parabolic motion gives the lowest finite peak acceleration (factor 4.0), attractive for the inertia force alone, but its acceleration jumps abruptly at the start, middle and end — steps that produce finite jerk spikes and vibration. Simple harmonic motion is smooth through the middle but still steps its acceleration at the two ends. Cycloidal motion has the highest peak (factor 6.28), yet its acceleration rises from zero and returns to zero at each end and is continuous throughout — so there is no sudden jerk anywhere. That smoothness makes cycloidal the standard choice for high-speed cams, where vibration and noise, not peak force, are the limiting problem. The rule of thumb: choose parabolic to minimise force at modest speed, cycloidal to minimise vibration at high speed, SHM as an easy middle ground.

§5Base circle and pressure angle

Two further choices decide whether the cam actually works smoothly: how big to make it, and how steeply the profile pushes the follower sideways.

The base circle is the smallest circle of the cam profile; every dimension grows from it. The pressure angle α is the angle between the direction the follower moves and the line along which the cam actually pushes it — the cam analogue of the gear pressure angle. A large pressure angle throws much of the force sideways across the follower stem, jamming it in its guide; keeping α below about 30° for a translating follower is the usual limit. The cure is a larger base circle: it flattens the profile’s slope for the same lift, dropping the pressure angle — so a jamming cam is very often simply too small, and enlarging it fixes the motion at the cost of size.

§6Worked rise

A single rise puts numbers on the three finite laws.

§7Quick reference

The working core of the page on one card rack.