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<< Click to Display Table of Contents >> Navigation: MotionDesigner Reference & User Interface > Motion-Law Coefficients |
We can use Motion-Law Coefficients DE: Kennwert to compare Traditional Motion-Laws.
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Velocity Motion-Coefficient |
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Acceleration Motion-Coefficient |
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Jerk Motion-Coefficient |
Specifically, the Motion-Law 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 motion-values for each motion-derivative if you know the Actual Displacement and the Actual Period of the Motion
Actual Maximum Velocity = |
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× Actual Output-Displacement / Actual Period |
Actual Maximum Acceleration = |
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× Actual Output-Displacement / Actual Period2 |
Actual Maximum Jerk = |
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× Actual Output-Displacement / Actual Period3 |
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Output Torque Coefficient |
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Input Torque Coefficient |
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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 rate-of-change of Torque - particularly at crossover from Acceleration to Deceleration.
A positive Torque on the cam-shaft will tend to wind-up (twist) the cam-shaft, and similarly, the cam-shaft will wind-down (untwist) in the other direction with a negative Torque on the cam-shaft. 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 cam-shaft.
If the speed of the cam-shaft 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 when Torque and Angular Velocity are constant. |
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Power when Linear-Force and Linear-Velocity 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:
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Power when load is rotating - e.g. a dial plate. |
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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 driven-shaft, can be constant (e.g. Dial-Plate), or they can continually change (e.g. Toggle mechanism).
In the general case, the Load Inertia or Load Mass reflected to the Cam-Follower 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:
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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 |
| (i = equal increments; from 1 to n) |
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Motion-Law 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 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. The most common variations are symmetrical, with a zero-acceleration / constant-velocity in the middle-section of the motion.
Motion-Law Name |
Coefficients |
SCCA Parameters (Factors) |
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Velocity Coeff. Cv |
Acceleration Coeff. 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 Coefficients 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 |
9*Π/4 |
0 |
-3*Π/4 |