Motion-Law: Constant-Acceleration and-Deceleration

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Motion-Law: Constant-Acceleration and-Deceleration

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

Motion Description

A Traditional Motion-Law.  Its name is often give Constant-Acceleration, or Triangular Velocity.

It has the lowest nominal maximum Constant Acceleration of the Dwell-Rise-Dwell type motion-laws. For this reason, historically, it was recommended for cam motion-design. It is still commonly used for Servo and Stepper motions.

However, it has three Acceleration Discontinuities (infinite Jerk). The middle acceleration discontinuity (Step change in value), when its acceleration reverses sign, is twice those at the start and end of the motion-law. These tend to induce vibrations in the mechanism it is driving.

Also, its peak Drive Torque is relatively high to others, and its Drive Torque reverses direction instantly at the crossover. The high peak torque can lead to drive shaft wind-up, and the instant reversal can lead to drive speed over-run in which the drive shaft increases its speed as it begins to decelerate the mechanism and payload.

It is not recommend for high-speed machinery, even if the motion is applied by Servo-motor or a Stepper-motor.


You CAN control the:

Start Position

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

End Position

You CANNOT control the:

Start Velocity & End Velocity

Start Acceleration & End Acceleration

Start Jerk & End Jerk

Segment Parameters




End- Range

0 ≤ Start-Range < End-Range ≤ 1

See also : MD-Globe-www-24 Tutorial 5: Edit the Start of a Traditional Motion-Law.

See also : MD-Globe-www-24 Tutorial 9: Asymmetrical Motions.

Constant-Acceleration - Constant-Deceleration Motion-Law - Parabolic Motion (Cam-Law)

Constant-Acceleration - Constant-Deceleration Motion-Law - Parabolic Motion (Cam-Law)

Motion-Law Coefficients

Velocity Coefficient :

Acceleration Coefficient :

Jerk Coefficient :

Jerk at Crossover :

Application Notes

This Motion-Law was used in the past because it has the lowest nominal acceleration of the Traditional Motion-Laws. However, it has infinite-jerk at three points: at its start, end, and at its crossover. This makes it a very poor choice form a dynamic viewpoint. Infinite-Jerk incites vibrations in any mechanical system. We do not recommend this motion-law if the Period-Ratio is less than 10, or even 20.

Dynamic Performance

The actual acceleration of the load being driven by Constant-Acceleration motion is significantly more 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 induce roller slip.


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 crossover of the motion segment. These reversals contribute to noise, shock loading, and vibration during operation.