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 specify the:

Position at the Start

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

Position at the End

You CANNOT specify the:

Start Velocity & End Velocity

Start Acceleration & End Acceleration

Start Jerk & 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 - remove the start of the Ramp Motion-Law

End- Range- remove the end of the Ramp Motion-Law

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): 2*pi

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): 9*pi/4

Parameter 2 (Second Harmonic): 0.0

Parameter 3 (Third Harmonic): -3*pi/4

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.