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Use MotionLaw Coefficients DE: Kennwert to compare motions that you design with the Traditional MotionLaws.

Velocity Coefficient 

Acceleration Coefficient 

Jerk Coefficient 
The MotionLaw Coefficients are the maximum motionvalues for the motionderivative when the motion has a:
•Motion Period,
AND
•Output Displacement,
You can use the MotionLaw Coefficients to calculate the actual maximum motionvalues of each motionderivative if you know the Actual Displacement ( ) and the Actual Period ( ) of the Motion:
Actual Maximum Velocity = 


Actual Maximum Acceleration = 


Actual Maximum Jerk = 



Output Torque Coefficient  E.g. the torque rotating the swinging arm of a Follower 

Input Torque Coefficient  E.g. the torque at the output of a gearbox connected to the CamShaft 

Note on Input Torque Coefficient
The maximum torque of a motionlaw is important. Just as important is the rateofchange of torque at crossover from acceleration to deceleration.
A positive input torque on the camshaft windsup (twists) the camshaft. A negative torque windsdown (untwists) the camshaft. When the rateofchange of torque is rapid, the winding and unwinding of the camshaft is also rapid.
When the Torque changes from a positive to a negative value  at the crossover  backlash is traversed. The speed of the drivemotor may increase rapidly as the torque is released from it and then, after the Backlash has been traversed, becomes driven by the load. If the speed of the motor does increase, then the motionlaw is also distorted. The maximum deceleration increases when the drivingshaft momentarily increases its speed.

Power  constant Torque and constant Angular Velocity 

Power  constant Force and constant LinearVelocity 
Of course, Torque and Angular Velocity at the Follower continuously change throughout the motion. Thus, the Power at the output shaft also changes continuously.
Use the suffix to indicate an instant in the motion, then the Instantaneous Power, when calculated at the output is:

Instantaneous Power  varying Torque and Angular Velocity 

Instantaneous Power  varying Force and LinearVelocity 
Total Load Torque or Load Force are found from values of inertia, mass, and acceleration.
However, the:
•Acceleration continually changes throughout the motion  of course.
•Load Inertia and Mass, referred to the drivenshaft, can be constant (e.g. DialPlate) or can continually change (e.g. Toggle mechanism).
In the general case, the Load Inertia and Mass that is reflected to the CamFollower varies throughout the motion.
Use the suffix 'i' to indicate any instant in the motion, the instantaneous Load Torque and Load Force are:

Load Torque with changing Load Inertia and Angular Acceleration. 

Load Force with changing Load Mass and Linear Acceleration 
Also, the instantaneous Load Power is:

Load Power with changing Load Inertia, Angular Acceleration, and Angular Velocity. 

Load Power with changing Load Mass, Linear Acceleration, and Linear Velocity. 
When reflected Load Inertia is not a function of the motion, the PowerCoefficient is less complex.
The instantaneous Load Power, with constant reflected Load Inertia or Load Mass is:

Load Power with constant Load Inertia, Angular Acceleration, and Angular Velocity. 

Load Power with constant Load Mass, Linear Acceleration, and Linear Velocity. 
Power Coefficient 


MotionLaw Name 
Velocity Coefficient

Acceleration Coefficient

Torque Coefficient

Power Coefficient


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 (in the Segment Editor) of the SineConstantCosine Acceleration (SCCA) MotionLaw to give many of the popular motion camlaws for industrial cams.
MotionLaw Name 
Coefficients 
SCCA Parameters (Factors) 


Velocity Coefficient Cv 
Acceleration Coefficient 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 (in the Segment Editor) of the Triple Harmonic MotionLaw to give alternatives to some of the popular motionlaws.
MotionLaw Name

Coefficients 
Harmonic 


Velocity Coefficient Cv 
Acceleration Coefficient 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 

0 
