MotionDesigner Reference & User Interface

MOTION-LAWS COEFFICIENTS

Use Motion-Law Coefficients DE: Kennwert to compare motions that you design with the Traditional Motion-Laws.

Motion-Law Coefficients

	Velocity Motion Coefficient
	Acceleration Motion Coefficient
	Jerk Motion Coefficient

The Motion-Law Coefficients are the maximum motion-values for the motion-derivative when the motion has a:

•Motion Period ( ) = 1 second

AND

•Output Displacement ( ) = 1 Linear or Angular Unit

Actual Velocity and Actual Acceleration

You can use the Motion-Law Coefficients to 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 =
Actual Maximum Acceleration =
Actual Maximum Jerk =

Torque Coefficients

	Output Torque Coefficient - E.g. the torque rotating the swinging arm of a Cam-Follower
	Input Torque Coefficient - E.g. the torque at the output of a gearbox connected to the Cam-Shaft

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. Similarly, a negative torque on the cam-shaft 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.

Power

Constant Power

	Power - constant Torque and Angular Velocity
	Power - constant Force and Linear-Velocity

Variable Power

Of course, the Torque and the Angular Velocity of the output shaft 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 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 is reflected to the Cam-Follower 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 Power-Coefficient 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

Power Coefficient	\| (i = equal increments; from 1 to n)

MOTION COEFFICIENTS OF THE TRADITIONAL MOTION-LAWS

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

SINE-CONSTANT-COSINE ACCELERATION (SCCA) with CONSTANT VELOCITY

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)
Motion-Law Name	Velocity Coefficient Cv	Acceleration Coefficient Ca	a	b	c
Modified-Sine CV 0%	1.760	5.528	0.25	0	0.75
Modified-Sine CV 20%	1.528	5.999	0.2	0	0.6
Modified-Sine CV 33%	1.404	6.616	0.1667	0	0.5
Modified-Sine CV 50%	1.275	8.0127	0.125	0	0.375
Modified-Sine CV 66%	1.168	11.009	0.0833	0	0.25
Cycloidal CV 50%	1.333	8.378	0.25	0	0.25
Trapezoidal Velocity CV 33%	1.5	4.5	0	0.6667	0

3-HARMONIC MOTION-LAWS

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	Coefficients		Harmonic
Motion-Law Name	Velocity Coefficient Cv	Acceleration Coefficient Ca	1st	2nd	3rd
3-Harmonic Modified Trapezoidal	2.0	5.16	5.96	0	0.9696
3-Harmonic Modified Sine	1.72	6.07	5.1968	1.7690	0.6057
3-Harmonic Zero-Jerk at Crossover	2.0	9.42		0