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

Sine-Constant-Cosine Acceleration : a Traditional Motion-Law

Segment-Parameters

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

See Segment-Parameters for Traditional Motion-Laws.


What motion-values can you specify?

You CAN specify the:

Position at the START of the segment.
Position at the END of the segment.

The Position motion-values most frequently flow from the Previous-Segment.

You CANNOT specify the

Velocity at the START or END of the segment.
Acceleration at the START or END of the segment.
Jerk at the START or END of the segment.

To specify motion-values with the Blend-Point Editor:

Start-Position:

1.Select the Sine-Constant-Cosine Acceleration segment [so that it becomes the Selected-Segment]

If No-Flow Control-Button is active, then:

2.Edit the Start-Position [of the SCCA Segment]

If Flow Control-Button is active, then:

2.Edit the End-Position [which will 'flow' to become the the Start-Position of the SCCA Segment]

End-Position

1.Select the next-segment that is after the SCCA segment [the SCCA segment becomes the Previous-Segment]
2.Edit the End Position [of the Previous-Segment, which is the End-Position of the SCCA segment]

To specify motion-values with the Segment Editor:

Start-Position

If No-Flow Control-Button is active

1.Select the SCCA segment [so that it becomes the Selected-Segment]
2.Edit the Start-Position [of the Selected-Segment]

If Flow Control-Button is active

3.Select the segment that is before the Sine-Squared segment [the Sine-Squared segment becomes the Next-Segment]
4.Edit the End-Position [which will flow to become the Start-Position of the Sine-Squared Segment]

End-Position

1.Select the SCCA segment [so that it becomes the Selected-Segment]
2.Edit the End-Position

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

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

About the SCCA Motion-Law:

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

d.Zero Acceleration
c.Cosine Fraction
b.Constant Fraction
a.Sine Fraction

Segment Parameters

a = Total Sine Acceleration Fraction [the acceleration at the start + deceleration at the end]

b = Total Constant Acceleration Fraction

c = Total Cosine Acceleration Fraction

a + b + c + d = 1

Enter only a, b, & c.

d = 1 – (a + b + c)

d = Total Zero Acceleration Fraction

 

Rules for the segment parameters:

Segment-Parameters may be zero, but not all.
No Segment-Parameter can be negative.

 

 

MT-MotionLaw-SCCA-SegmentParameters

Segment Parameters in the example Motion-Law - see images to left

a = 0.333 ; 33.3% : Sine Acceleration Fraction

b = 0.333 ; 33.3% : Constant Acceleration Fraction

c = 0.333 ; 33.3% : Cosine Acceleration Fraction

 ∴ d = 1 – a – b – c = 0.0 ; 0% : of the Zero Acceleration Fraction.

 

Sine-Constant-Cosine 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

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