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<< Click to Display Table of Contents >> Navigation: MotionDesigner Reference & User Interface > Motion-Law Coefficients |
Use Motion-Law Coefficients DE: Kennwert to compare motions that you design with the Traditional Motion-Laws.
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Velocity Coefficient |
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Acceleration Coefficient |
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Jerk Coefficient |
The Motion-Law Coefficients are the maximum motion-values for the motion-derivative when the motion has a:
•Motion Time Period of
AND
•Output Displacement of
You can use the Motion-Law Coefficients to calculate the actual maximum motion-values of each motion-derivative if you know the Actual Displacement ( ) and the Actual Period ( ) of the Motion:
Actual Maximum Velocity = |
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Actual Maximum Acceleration = |
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Actual Maximum Jerk = |
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Output Torque Coefficient - E.g. the torque rotating the swinging arm of a Follower |
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Input Torque Coefficient - E.g. the torque at the output of a gearbox connected to the Cam-Shaft |
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Note on Input Torque Coefficient
The maximum torque of a motion-law is important. Just as important is the rate-of-change of torque at crossover from acceleration to deceleration.
A positive input torque on the cam-shaft winds-up (twists) the cam-shaft. A negative torque winds-down (untwists) the cam-shaft. When the rate-of-change of torque is rapid, the winding and unwinding of the cam-shaft is also rapid.
When the Torque changes from a positive to a negative value - at the crossover - backlash is traversed. The speed of the drive-motor 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 motion-law is also distorted. The maximum deceleration increases when the driving-shaft momentarily increases its speed.
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Power - constant Torque and constant Angular Velocity |
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Power - constant Force and constant Linear-Velocity |
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:
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Instantaneous Power - varying Torque and Angular Velocity |
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Instantaneous Power - varying Force and Linear-Velocity |
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 driven-shaft, can be constant (e.g. Dial-Plate) or can continually change (e.g. Toggle mechanism).
In the general case, the Load Inertia and Mass that reflect to the Follower varies throughout the motion.
Use the suffix 'i' to indicate any instant in the motion, the instantaneous Load Torque and Load Force are:
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Load Torque with changing Load Inertia and Angular Acceleration. |
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Load Force with changing Load Mass and Linear Acceleration |
Also, the instantaneous Load Power is:
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Load Power with changing Load Inertia, Angular Acceleration, and Angular Velocity. |
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Load Power with changing Load Mass, Linear Acceleration, and Linear Velocity. |
When reflected Load Inertia is not a function of the motion, the Power-Coefficient is less complex.
The instantaneous Load Power, with constant reflected Load Inertia or Load Mass is:
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Load Power with constant Load Inertia, Angular Acceleration, and Angular Velocity. |
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Load Power with constant Load Mass, Linear Acceleration, and Linear Velocity. |
Power Coefficient |
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Motion-Law Name |
Velocity Coefficient
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Acceleration Coefficient
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Torque Coefficient
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Power Coefficient
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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 3-4-5 |
1.875 |
5.773503 |
1.159 |
6.6925 |
Polynomial 4-5-6-7 |
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 Sine-Constant-Cosine Acceleration (SCCA) Motion-Law to give many of the popular motion cam-laws for industrial cams.
Motion-Law Name |
Coefficients |
SCCA Parameters (Factors) |
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Velocity Coefficient Cv |
Acceleration Coefficient Ca |
a |
b |
c |
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Modified-Sine CV 0% |
1.760 |
5.528 |
0.25 |
0 |
0.75 |
Modified-Sine |
1.528 |
5.999 |
0.2 |
0 |
0.6 |
Modified-Sine |
1.404 |
6.616 |
0.1667 |
0 |
0.5 |
Modified-Sine |
1.275 |
8.0127 |
0.125 |
0 |
0.375 |
Modified-Sine |
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 Motion-Law to give alternatives to some of the popular motion-laws.
Motion-Law Name
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Coefficients |
Harmonic |
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Velocity Coefficient Cv |
Acceleration Coefficient Ca |
1st |
2nd |
3rd |
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3-Harmonic |
2.0 |
5.16 |
5.96 |
0 |
0.9696 |
3-Harmonic |
1.72 |
6.07 |
5.1968 |
1.7690 |
0.6057 |
3-Harmonic |
2.0 |
9.42 |
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0 |
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