Triple-Harmonic Motion-Law

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Triple-Harmonic Motion-Law

Triple-Harmonic Motion-Law

A Traditional Motion-Law

Motion Description

The Triple-Harmonic Motion-Law can approximate the Cycloidal, Modified-Trapezoidal, Modified Sine, Polynomial 3-4-5 Motion-Laws by using the Segment-Parameters

Motion-Values

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 and End Velocity

Start Acceleration and End Acceleration

Start Jerk and End Jerk

Segment Parameters

MT-CamLaw-TripleHarmonic-SegParameters

Three Segment-Parameters:

Red-14-1 First Harmonic

Red-14-2 Second Harmonic

Red-14-3 Third Harmonic (calculated automatically from First Harmonic and Second Harmonic)

Segment-Range

Start-Range

End- Range

0 ≤ Start-Range < End-Range ≤ 1
TRIPLE HARMONIC 1st Harmonic = 4.983 ; 2nd Harmonic = 2.6 ; 3rd Harmonic = 0

TRIPLE HARMONIC
1st Harmonic = 4.983 ; 2nd Harmonic = 2.6 ; 3rd Harmonic = 0

Triple Harmonic as Approximate Motion-Laws

tog_minusCycloidal

Parameter 1 (First Harmonic):

Parameter 2 (Second Harmonic): 0.0

Parameter 3 (Third Harmonic): 0.0
tog_minusModified Trapezoidal

Parameter 1 (First Harmonic): 6.04

Parameter 2 (Second Harmonic): 0.0

Parameter 3 (Third Harmonic): 0.73
tog_minusModified Sine

Parameter 1 (First Harmonic): 5.1968

Parameter 2 (Second Harmonic): 1.769

Parameter 3 (Third Harmonic): 0.6057
tog_minusPolynomial 3-4-5

Parameter 1 (First Harmonic): 5.9

Parameter 2 (Second Harmonic): 0.704

Parameter 3 (Third Harmonic): 0.9

Triple Harmonic and other Motion-Laws

tog_minusZero-Jerk at Start, End and Cross-over

Parameter 1 (First Harmonic):

Parameter 2 (Second Harmonic): 0.0

Parameter 3 (Third Harmonic):

tog_minusZero-Jerk at Cross-over

Parameter 1 (First Harmonic): 4.9832

Parameter 2 (Second Harmonic): 2.6

Parameter 3 (Third Harmonic): 0.0
tog_minusZero-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.