﻿ 3-Harmonic-Zero-Jerk-at-Crossover Motion-Law

# 3-Harmonic-Zero-Jerk-at-Crossover Motion-Law

### Triple-Harmonic: 'Approximate Zero-Jerk at Crossover'

Crossover : the point at which the Acceleration changes to Deceleration.

When Jerk is Zero, the Acceleration changes slowly. When Jerk is zero, and the also the acceleration changes from a positive value to a negative value, we say the the Motion-Law has 'Zero Jerk at Crossover'.

[You will notice that the Jerk also changes slowly. Thus the Crossover is especially 'gentle'].

When acceleration changes slowly, and it is also near to zero, the velocity changes slowly.

If there is backlash in the mechanical transmission between the follower and the tool, then backlash is traversed as the force changes from a positive action to a negative action. Since the velocity happens to be changing slowly, the impact velocity should also be be small, with this motion-law.

[Note: the Force will change when the total force on the mechanical element changes sign. The force in the system is not only a function of the Motion-Law. The Force may also include: constant, spring, damping and other forces].

To use this Motion-Law:

 1 Select 'Triple Harmonic' in the Motion-Law Selector
 2 Edit the Segment Parameters to:
 • First Harmonic = 9*Π/4
 • Second harmonic = 0.0
 • Third Harmonic = -3*pi/4

MotionDesigner calculates the third harmonic, based on the fact that the segment always creates a D-R-D segment.

#### Summary

This law is continuous in position, velocity, acceleration and jerk.

The output motion is near to the traditional Modified Sinusoid Acceleration Cam Law. However, it has only three harmonics and, thus, it is a smoother function at the higher derivatives.

The maximum velocity is slightly lower and the nominal acceleration is higher than the traditional law.

Harmonic Settings that give an Acceleration with Zero Jerk at Crossover

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