We can compare Traditional MotionLaws with their 'Motion Law Coefficients DE: Kennwert'.
To obtain a Motion Law Coefficient, we must normalize the motions, whereby the the Xaxis has a range from 0 to 1, and the Yaxis position graph also has a range of 0 to 1. Then, the motionderivatives of the functions automatically become normalised values.
The three MotionLaw Coefficients, Cv , Ca , and Cj , are the maximum velocity, acceleration and jerk that a motionlaw has when the output has a stroke (or 'lift') of '1' [linear or angular unit] and the time taken is a period of '1' [second].
•  Velocity Coefficient, Cv = Maximum Velocity of a motionlaw when the output has a stroke and period of '1'. 
•  Acceleration Coefficient, Ca = Maximum Acceleration of a motionlaw when the output has a stroke and period of '1'. 
•  Jerk Coefficient, Cj = Maximum Jerk of a motionlaw when the output has a stroke and period of '1'. 
•  Dynamic Torque Coefficient, CT = Maximum of the Product of Velocity X Acceleration of a motionlaw when the output has a stroke and period of '1'. 
To calculate the actual velocity and acceleration when the stroke and period are not '1':
•  Actual Maximum Velocity = Cv × Actual Stroke ÷ Actual Period 
•  Actual Maximum Acceleration = Ca × Actual Stroke ÷ Actual Period 2 
•  Actual Maximum Jerk = Cj × Actual Stroke ÷ Actual Period 3 
The Input Torque Coefficient, Cc [also given as 'Q' in indexer catalogues. However, we use Q as the 'inertia ratio' [See the MechDesigner manual].
•  Input Torque Coefficient, Cc = max(vi × ai)/Ca 
Note: Like acceleration, it is not only the absolute maximum of the Torque given by the 'Input Torque Coefficient', but also how quickly the torque changes from a 'positive' to a 'negative' torque  'rate of change of Torque at crossover from Acceleration to Deceleration'. A positive Torque on the camshaft will tend to 'windup' [twist] the camshaft, and similarly, the camshaft will 'winddown' in the other direction during negative Torque on the camshaft. When the change in torque at the 'crossover' is rapid, then the winding of the shaft in one direction to the other. The motor is driving then it is suddenly driven by the load. It is here that there is a greater tendency for the input transmission to 'overrun', or increase its speed. If the camshaft speed, then the load also moves more quickly. 
When Torque and Angular Velocity are constant, then Power is:
P = τ × ω
Similarly, when Linear Force and Linear Velocity are constant, then Power is:
P = F × v
Clearly, when the Torque and Angular Velocity [or Force and Linear Velocity] both change continuously throughout the motion, the instantaneous Power also changes continuously.
Thus, if we use the suffix 'i' to indicate any instant in the motion, then the 'instantaneous' Power is:
Pi = τi × ωi,
or
Pi = Fi × vi
Torque and Force are found from instantaneous values of reflected inertia and acceleration.
•  Acceleration changes throughout the motion. 
•  Reflected Inertia is the inertia referred back to the Power Source [usually the Drive Motor or Servomotor]. This would vary for any mechanism that has a variable transmission ratio between the drive and payload. Again, in the general case, the reflected inertia varies throughout the motion. 
τi = Ii × αi,
or
Fi = mi × ai
When Reflected Inertia or Mass are not a function of the motion, the Power Coefficient is normalized by ignoring their values. We can use the instantaneous values of angular acceleration and linear acceleration. Thus:
MotionLaw Name 
Nondimensional Maximum Velocity Cv 
Nondimensional Maximum Acceleration Ca 
Nondimensional Input Torque Coefficient Cc 
Nondimensional Power Coefficient Pc 

Constant Acceleration, Parabolic 
2 
4 
2 
8 
Simple Harmonic 
1.570796 (π/2) 
4.934803 (π2/2) 
0.785 
3.8758 
Cycloidal 
2 
6.283185 
1.298 
8.1621 
Modified Trapezoid 
2 
4.888124 
1.655 
8.0894 
Polynomial 345 
1.875 
5.773503 
1.159 
6.6925 
Polynomial 4567 
2.1875 
7.5132 
1.431 
10.750 
Modified Sine 
1.759603 
5.527957 
0.987 
5.4575 
Edit the Segment Parameters (Fractions) of the SineConstantCosine Acceleration (SCCA) Motion Law to give many of the popular motion camlaws for industrial cams. The most common variations are symmetrical, with a zeroacceleration / constantvelocity in the middlesection of the motion. This tends to r Enter the SegmentParameters, indicated below, in the boxes in the Segment Editor. 


Motion Law Name 
Coefficients 
SCCA Parameters (Factors) 

Velocity Coefficient Cv 
Acceleration Coefficients Ca 
a 
b 
c 

ModifiedSine CV 0% 
1.760 
5.528 
0.25 
0 
0.75 
ModifiedSine 
1.528 
5.999 
0.2 
0 
0.6 
ModifiedSine 
1.404 
6.616 
0.1667 
0 
0.5 
ModifiedSine 
1.275 
8.0127 
0.125 
0 
0.375 
ModifiedSine 
1.168 
11.009 
0.0833 
0 
0.25 
Cycloidal 
1.333 
8.378 
0.25 
0 
0.25 
Trapezoidal Velocity CV 33% 
1.5 
4.5 
0 
0.6667 
0 
Edit the Segment Parameters of the Triple Harmonic Motion Law to give alternatives to some of the popular motionlaws. Enter the SegmentParameters for each Harmonic in the boxes in the Segment Editor. 


Motion Law Name 
Coefficients 
Harmonic 

Velocity Coefficient Cv 
Acceleration Coefficients Ca 
1st 
2nd 
3rd 

3Harmonic 
2.0 
5.16 
5.96 
0 
0.9696 
3Harmonic 
1.72 
6.07 
5.1968 
1.7690 
0.6057 
3Harmonic 
2.0 
9.42 
9*Π/4 
0 
3*Π/4 