﻿ Triple-Harmonic Motion-Law

# Triple-Harmonic Motion-Law

### Triple-Harmonic Motion-Law

Triple-Harmonic is a Traditional Motion-Law  has Segment-Parameters that can match other Traditional Motion-Laws.

Blend-Point Editor : edit its:

 • Start Position
 • End Position

To edit the Position at the end of this Segment you must select the Next-Segment.

Segment Editor :  edit the:

 • First Harmonic
 • Second harmonic

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

#### Segment Parameters.

 • First Harmonic
 • Second Harmonic
 • Third Harmonic

Notes:

You can only enter values of the First and Second Harmonic.

Notes:

 • The Start and End Velocity and Accelerations are zero.
 • The Start and End Jerk values are a consequence of the mathematical form of the segment.
 • The Segment is symmetrical about the mid-point.

This Motion-Law can approximate the Cycloidal, Modified-Trapezoidal, Modified Sine, Polynomial 3-4-5, Motion-Laws by using the harmonic settings indicated below.

To the Left, a 'Modified-Trapezoid' has been created by setting the first Harmonic to 6.025. The third harmonic recalculates itself. The second stays at zero, unless you edit it of course.

#### Cycloidal:

 • Parameter 1 (First Harmonic): 2*pi
 • Parameter 2 (Second Harmonic): 0.0
 • Parameter 3 (Third Harmonic): 0.0

#### Modified Trapezoidal:

 • Parameter 1 (First Harmonic): 6.04
 • Parameter 2 (Second Harmonic): 0.0
 • Parameter 3 (Third Harmonic): 0.73

#### Modified Sine:

 • Parameter 1 (First Harmonic): 5.1968
 • Parameter 2 (Second Harmonic): 1.769
 • Parameter 3 (Third Harmonic): 0.6057

#### Polynomial 3-4-5

 • Parameter 1 (First Harmonic): 5.9
 • Parameter 2 (Second Harmonic): 0.704
 • Parameter 3 (Third Harmonic): 0.9

It can also create other useful Segment Forms with these harmonic settings:

#### Zero-Jerk at Start, End and Cross-over

 • Parameter 1 (First Harmonic): 9*pi/4
 • Parameter 2 (Second Harmonic): 0.0
 • Parameter 3 (Third Harmonic): -3*pi/4

#### Zero-Jerk at Cross-over

 • Parameter 1 (First Harmonic): 4.9832
 • Parameter 2 (Second Harmonic): 2.6
 • Parameter 3 (Third Harmonic): 0.0

#### Zero-Jounce * at Start

 • Parameter 1 (First Harmonic): 7.79
 • Parameter 2 (Second Harmonic): -2.29
 • Parameter 3 (Third Harmonic): -1.08

*Jounce is a term used for rate-of-change of Jerk.

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