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

It is a Traditional Motion-Law

It is also named the Parabolic Cam Law.


With the Segment-Editor and the Blend-Point Editor you ...

CAN specify the:

Position at the START of the segment.
Position at the END of the segment.

The Position motion-value usually flows from the Previous-Segment to the START of the segment.

CANNOT specify the

Velocity at the START or END of the segment.
Acceleration at the START or END of the segment.
Jerk at the START or END of the segment.

Segment Editor

You can edit its Segment Range.


Motion-Law ConstantAccelerationDeceleration

Motion-Law Coefficients

Cv = 2.000

Ca = ±4.000

Cj = ± ∞


Notes:

It has the lowest nominal peak acceleration.
This Motion-Law is often given to Servomotors, which we do not recommend if the speed and reflected inertia are 'high', and there is a low Period-Ratio.
Because it has discontinuities in acceleration, with infinite jerk, the actual peak acceleration - in a real mechanical system - will be at least 2 times the nominal peak acceleration.  The discontinuities in acceleration incite vibrations.
To design a Trapezoidal Velocity Segment, [and not a 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 maximum 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.

See Motion Coefficients

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.

Tutorial and Reference Help Files for MechDesigner and MotionDesigner 13.2 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd