Constant-Acceleration and Constant-Deceleration Cam-Law, Motion-Law

A Traditional Motion-Law. It also has the name: Parabolic motion-law.

Segment-Editor AND Blend-Point Editor

CAN specify its:


The Start-Position usually flows from the End-Position of the Previous-Segment

CANNOT specify its:

Start-Velocity OR End-Velocity.
Start-Acceleration OR End-Acceleration.
Start-Jerk OR End-Jerk

Segment Editor only

Specify its Segment Range

Motion-Law ConstantAccelerationDeceleration

Motion-Law Coefficients

Cv = 2.000

Ca = ±4.000

Cj = ± ∞


It has the lowest nominal* peak acceleration.

* Nominal: the discontinuities in its acceleration, with infinite jerk, will incite vibrations, so that the real peak acceleration - in a real mechanical system - will be at least 2 times the nominal peak acceleration.

This Motion-Law is often used with servomotors. It is easy to program and for electrical engineers to understand - the poor things!
We do not recommend this motion-law if the speed and reflected inertia are 'high', and there is a low Period-Ratio.
To design a Trapezoidal Velocity segment, [and not the Triangular Velocity segment that this motion-law gives] use the Sine-Constant-Cosine Motion-Law.

Application Notes

This Motion-Law has been used frequently in the past because it has the lowest nominal acceleration of the Traditional Motion-Laws. However, it has infinite jerk at three points: the start, end, and at its cross-over. This makes it a very poor choice form a dynamic viewpoint.  Infinite-Jerk incites vibrations in any mechanical system.

Dynamic Performance

The actual acceleration of the load being driven by Constant-Acceleration motion will always be significantly higher than the nominal value, because of induced vibrations.

For this reason, this segment should only be used in applications where inertia effects are small or even insignificant.

Pressure Angle Considerations

This segment produces a relatively large pressure angle - and so might need a large cam for a given lift. The pressure angle for this segment varies quite severely throughout this Motion-Law indicating that it is unsuitable for roller follower applications because of the severe accelerations imposed on the roller that will tend to induce roller slip.

Drive Torques

This law performs badly in terms of drive torque considerations. All of the torque factor curves for this law exhibit a discontinuity, indicating shock loading and noise in operation. Particularly notable is the sudden reversal of the inertia torque factor, and hence of the torsional strain energy, at the cross-over of the motion segment. These reversals will contribute further to noise, shock loading and vibration during operation.

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd