A Cam Timing Diagram

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Constant Acceleration (Parabolic Displacement)
is also Unacceptable

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Simple Harmonic Motion (SHM)
(Also Unacceptable – Infinite Jerk

Cam motion is defined not by a single mathematical expression, but by a series of separate Piecewise functions

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When designing a cam, consider first the higher derivatives, e.g. the accelerations, then the velocities, THEN displacements and to a lesser extent the jerk.

Variables

t is time (sec)
q is the cam angle (deg or rad)
b is the angle over which the event occurs (deg or rad)
q/b is the normalized cam angle (unitless)
w is the camshaft angular velocity (rad/sec)
h is total displacement (length units)
S, s are follower displacement (length units)
V, v are follower velocity (length /sec), (length /rad)
A, a are follower accel. (length/sec^2), (length/rad^2)
J, j are follower jerk (length/sec^3), (length/rad^3)
P, p are follower ping (length/sec^4), (length/rad^4)

The Fundamental Law of Cam Design

The cam-follower function must have continuous velocity and acceleration across the entire interval, thus making the jerk finite.

Any cam designed for operation at other than very low speeds must be designed with the following constraints:

The cam function must be continuous through the first and second derivatives of displacement

across the entire interval (360 degrees). Must have 3rd order continuity. S, V and A must have no discontinuity in them.

corollary:

The jerk function must be finite across the entire interval (360 degrees).

Choosing Cam Functions

They must obey the fundamental law
Lower peak acceleration is better: F = ma
Lower peak velocity lowers KE = 0.5 mv²
Smoother jerk means lower vibrations
Magnitude of jerk is poorly controlled in manufacturing

Some Acceptable Double-Dwell Functions

Cycloidal
Modified Trapezoidal
Modified Sine

Cycloidal Motion

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Cycloidal Motion

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A Naïve and Poor Cam Design -Constant Velocity is Unacceptable

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The SCCA Family of Classic Double Dwell Functions

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Unacceptable Functions

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Constant Acceleration Problems

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Compare Mod Trap, Mod Sine, and Cycloidal Motion Programs

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Factors for Various Functions

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Comparison of 5 double-dwell cam functions 8.10.png

Rotary Indexers Use Ribbed Barrel Cams

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Unacceptable Double-Dwell Functions

pure constant velocity
constant acceleration (parabolic displacement)
cubic displacement
simple harmonic motion

Barrel Cam - Tracked

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Barrel Cam - Ribbed

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Copyrights

Created for "Design of Machinery" by R.L. Norton and " The Multimedia Handbook of Mechanical Devices" by S.Wang Copyright © The McGraw-Hill Education. Permission required for reproduction or display.