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# Sine-Constant-Cosine (SCCA) Motion-Law

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# Sine-Constant-Cosine (SCCA) Motion-Law

### Sine-Constant-Cosine Acceleration (SCCA) Cam-Law, Motion-Law - a Traditional Motion-Law

Motion Description

 The Segment-Parameters make this motion-law very flexible. It is possible to get many of the Traditional Motion-Laws that are based on Sine and Cosine harmonics.

#### Motion-Values

You CAN specify the:

 Position at the Start The Start-Position usually flows from the End-Position of the Position at the End

You CANNOT specify the:

 Start Velocity & End Velocity Start Acceleration & End Acceleration Start Jerk & End Jerk

Segment Parameters

 The SCCA motion-law is a defined by a sequence of trigonometric segments in acceleration motion-derivative. The motion-law is symmetrical, thus the sequence is: 0.0 ≤ X ≤ 0.5 a.Sine Fraction b.Constant Fraction c.Cosine Fraction: d.Zero Acceleration 0.5 ≤ X ≤ 1 a.Zero Acceleration b.Cosine Fraction c.Constant Fraction d.Sine Fraction Example Motion-Law - see image below a = 0.333 ; 33.3% : Total Sine Acceleration Fraction b = 0.333 ; 33.3% : Total Constant Acceleration Fraction c = 0.333 ; 33.3% : Total Cosine Acceleration Fraction ∴ d = 1 – a – b – c = 0.0 ; 0% : of the Zero Acceleration Fraction. Rules for the segment parameters: Segment-Parameters may be zero, but not all. No Segment-Parameter can be negative.

Segment-Range

 Start-Range End- Range 0 ≤ Start-Range < End-Range ≤ 1

An Example Sine Constant-Cosine Acceleration Law.

 Example motion with Sine-Constant-Cosine Motion Law with Segment Parameters: Sine Fraction a=0.333, Constant b=0.333, Cosine Fraction c=0.333

### Segment Parameters to give other Traditional Motion-Laws.

 MOTION-LAW: Coefficients Parameters Cv Ca a b c Modified Trapezoidal: 2 4.89 0.25 0.5 0.25 'Lazy' Modified Trapezoidal: 2 4.88 0.333 0.333 0.333 Modified-Sine: 1.760 5.5 0.25 0 0.75 Modified-Sine CV 20%: 1.528 5.999 0.2 0 0.6 Modified-Sine CV 33%: 1.404 6.616 0.1667 0 0.5 Modified-Sine CV 50%: 1.275 8.0127 0.125 0 0.375 Modified-Sine CV 66%: 1.168 11.009 0.0833 0 0.25 Cycloidal: 2 6.2832 0.5 0 0.5 Cycloidal CV 50%: 1.333 8.378 0.25 0 0.25 Constant Acceleration-Deceleration: 2 4 0 1 0 Trapezoidal Velocity CV33%: 1.5 4.5 0 0.6667 0