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.

See below: Segment-Parameters for Traditional Motion-Laws.

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-MotionLaw-SCCA-SegmentParameters

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:

From 0.0 ≤ X ≤ 0.5 of the Segment-Width

a.Sine Fraction

b.Constant Fraction

c.Cosine Fraction:

d.Zero Acceleration

From 0.5 ≤ X ≤ 1 of the Segment-Width

d.Zero Acceleration

c.Cosine Fraction

b.Constant Fraction

a.Sine Fraction

Example Motion-Law - see image below

a = 0.25 ; 25% : Total Sine Acceleration Fraction

b = 0.25 ; 25% : Total Constant Acceleration Fraction

c = 0.25 ; 25% : Total Cosine Acceleration Fraction

∴ d = 1 – a – b – c = 0.25 ; 25% Total Zero Acceleration Fraction

Rules for the segment parameters:

Segment-Parameters may be zero, but not all.

Segment-Parameters cannot 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=0.25, Constant b=0.25, Cosine Fraction c=0.25

Example motion with Sine-Constant-Cosine Motion Law with Segment Parameters: Sine Fraction a=0.25, Constant b=0.25, Cosine Fraction c=0.25

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