<< Click to Display Table of Contents >> Navigation: MotionDesigner Reference & User Interface > MotionLaw Coefficients 
We can use MotionLaw Coefficients DE: Kennwert to compare Traditional MotionLaws.

Velocity MotionCoefficient 

Acceleration MotionCoefficient 

Jerk MotionCoefficient 
Specifically, the MotionLaw Coefficients are the maximum values when the:
•Motion Period = 1 second
AND
•Output Displacement = 1 unit (Linear or Angular Unit)
You can quickly calculate the actual motionvalues for each motionderivative if you know the Actual Displacement and the Actual Period of the Motion
Actual Maximum Velocity = 

× Actual OutputDisplacement / Actual Period 
Actual Maximum Acceleration = 

× Actual OutputDisplacement / Actual Period2 
Actual Maximum Jerk = 

× Actual OutputDisplacement / Actual Period3 

Output Torque Coefficient 

Input Torque Coefficient 
 
Note on Input Torque Coefficient
Like acceleration, the maximum torque is important, and also how quickly the torque changes from a positive to a negative value  the rateofchange of Torque  particularly 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 (untwist) in the other direction with a negative Torque on the camshaft. When the change in torque is rapid, the unwinding of the shaft is also rapid.
At the crossover, if there is backlash will be traversed. The Drive Torque becomes zero for a short while and the motor may accelerate rapidly.
Also, the load on the motor will tend to drive the motor as the load torque becomes negative. This will tend also to increase the speed of the driving camshaft.
If the speed of the camshaft does increase, then the motionlaw is also distorted. The maximum deceleration increases when the drivingshaft momentarily increases its speed.

Power when Torque and Angular Velocity are constant. 

Power when LinearForce and LinearVelocity are constant. 
The Torque and the Angular Velocity (or Force and Linear Velocity) continuously change throughout the motion. Thus the instantaneous Power also changes continuously.
Thus, if we use the suffix 'i' to indicate any instant in the motion, then the Instantaneous Power, when calculated at the output is:

Power when load is rotating  e.g. a dial plate. 

Power when load is sliding  e.g. a punch tool. 
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 they can continually change (e.g. Toggle mechanism).
In the general case, the Load Inertia or Load Mass reflected to the CamFollower shaft varies throughout the motion.
Thus, if we use the suffix 'i' to indicate any instant in the motion, then 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 
 (i = equal increments; from 1 to n) 

MotionLaw Name 
Velocity Coefficient Cv 
Acceleration Coefficient Ca 
Torque Coefficient Cc 
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 (in the Segment Editor) of the SineConstantCosine Acceleration (SCCA) MotionLaw 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.
MotionLaw Name 
Coefficients 
SCCA Parameters (Factors) 


Velocity Coeff. Cv 
Acceleration Coeff. 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 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 