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We can use Motion-Law Coefficients DE: Kennwert to compare Traditional Motion-Laws.
The Motion-Law Coefficients are the maximum values of each motion-derivative when the:
•Input-period = 1 second
AND
•Displacement = 1 unit (Linear or Angular Unit).
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Velocity Motion-Coefficient |
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Acceleration Motion-Coefficient |
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Jerk Motion-Coefficient |
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Dynamic Torque-Coefficient |
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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Input Torque Coefficient |
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Note on Input Torque Coefficient
Like acceleration, it is not only the maximum of the torque that is important, but also how quickly the torque changes from a positive to a negative torque - 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 in the other direction during negative Torque on the cam-shaft. When the change in torque at the 'cross-over' is rapid, then the winding and unwinding of the shaft in one direction and then the other is also rapid. The load on the motor that drives the shaft reduces to zero, and , worse, the load then drives the motor to increase its speed. If the cam-shaft increases its speed, then the load also moves more quickly, and the torque fluctuation also increases. |
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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 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:
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Power when Torque and Angular Velocity are varying. |
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Power when Linear-Force and Linear-Velocity are varying |
Torque and Force are found from instantaneous values of reflected inertia, mass, and acceleration.
•Acceleration changes throughout the motion.
•Reflected Inertia and Mass is referred back to the Power Source (usually the Drive Motor or Servomotor). In the general case, the reflected inertia varies throughout the motion.
Thus, if we use the suffix 'i' to indicate any instant in the motion, then the instantaneous Power is:
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Torque with varying Reflected-Inertia and Angular-Acceleration. |
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Torque with varying Reflected-Mass and Linear-Acceleration |
When Reflected Inertia is 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:
Thus, if we use the suffix 'i' to indicate any instant in the motion, then the 'instantaneous' Power is:
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 |