MotionDesigner Reference & User Interface > Motion-Law Coefficients / Characteristic Values

MOTION-LAW CHARACTERISTIC VALUES

You can use the Motion-Law Characteristic Values DE: Kennwert to compare Traditional Motion-Laws.

Motion-Law Characteristic Values.

Label	Normalized Characteristic Values	Nominal Relevance
	Velocity	A measure of the maximum Pressure Angle.
	Acceleration	A measure of the maximum force on a follower from the inertia of the following-system.
	Effective Acceleration	A measure of RMS inertia load on a follower over a machine-cycle.
	Jerk	A measure of the risk of the motion exciting a vibration in the follower-system.
	Torque (cam-system)	A measure of the maximum torque to rotate a camshaft, when the following system is an inertia load.
	Power (servo-system)	A measure of the maximum Power required from a Servomotor to directly drive a linear inertia load.

The Normalized Characteristic Values are equal to the maximum motion-values when the motion has a:

•period: and

•displacement: (linear or angular).

To calculate the actual maximum motion-values you need to know the:

•motion-law

•maximum displacement,

•motion period,

Actual Maximum Velocity =

Note: If you reduce the motion-period, , by about 10% the :

•maximum velocity increases by ~10%,

•maximum acceleration increases by ~20%

•maximum jerk increases by ~40%

Actual Maximum Acceleration =

Actual Maximum Jerk =

Drive Torque Characteristic Values or Factors

Usually, it is desirable that the speed of the cam-shaft is constant. However, a force-closed follower system imposes three torque components on the cam-shaft, each of which tends to decrease or increase its speed.

Label	Torque Factor		Nominal Relevance
	Constant Load		The component of drive torque required to overcome a static or constant load of the follower-system, for example, due to gravity or friction. It is identical to the normalized Velocity, . Usually the least significant Torque Factor.
	Inertia Load		The component of drive torque required to accelerate the inertia load of a follower-system. Usually the most dominant. It disregards Spring Force. It is also an indication of the Power required from a servo-system to drive an inertia load.
	Spring Load		The component of drive torque required to overcome the linear increase in force as a spring is compressed in the follower-system. It disregards the inertia force.
where		= normalized displacement (0 1)
		= non-dimensional velocity
		= non-dimensional acceleration

Note on Input Torque

The maximum torque that is needed to drive a Cam is important. However, the rate-of-change of torque, especially at crossover, as it changes from positive to negative torque is also important, if not more important than the maximum torque.

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 Torque changes from a positive to a negative value, at the crossover, backlash in the drive shaft system, and the following-system begins to be traversed, and the Torque at the input suddenly reduces to only the “friction torque”. The speed of the drive-motor and cam-shaft may increase rapidly. Therefore the impact shock after the backlash is traversed is also increased beyond the impact that would be the case had the speed remains constant. If the speed of the motor does increase, the motion-law of the cam is distorted and the maximum values of velocity and deceleration also increase, sometimes substantially.

When percentage increase to the speed at crossover is called the percentage Overrun.

Power

Constant Power

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

Variable Power

Of course, Torque and Angular Velocity at the Follower continuously change throughout the motion. Thus, the Power at the output shaft also changes continuously. We can use to indicate any step in the motion.

	Instantaneous Power - varying Torque and Angular Velocity
	Instantaneous Power - varying Force and Linear-Velocity

Torque and Force are found from the product of inertia and angular-acceleration, and from mass and linear-acceleration, respectively.

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 reflected Load Inertia and Mass vary throughout the motion.

	Load Torque with changing Load Inertia and Angular Acceleration.
	Load Force with changing Load Mass and Linear Acceleration

Therefore, the instantaneous Power is:

	Power with changing Load Inertia, Angular Acceleration, and Angular Velocity.
	Power with changing Load Mass, Linear Acceleration, and Linear Velocity.

Characteristic Values of the Traditional Motion-Laws

Motion-Law Name	Velocity Coefficient	Acceleration Coefficient	Torque Coefficient	Power Coefficient
Constant Acc & Dec or Parabolic	2	4	2	8
Simple Harmonic	π/2	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	Characteristic Values		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	Characteristic Values		Harmonic (Segment Parameters)
Motion-Law Name	Velocity Cv	Acceleration 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