Velocity Coefficient

A measure of the Pressure Angle

Acceleration Coefficient

A measure of the Inertia Force at the output shaft

Jerk Coefficient

A measure of the risk of vibration excitation

Actual Maximum Velocity =

Actual Maximum Acceleration =

Actual Maximum Jerk =

Output Torque Coefficient - E.g. the torque that rotates the swinging arm of a follower.

The Output Torque Coefficient considers the dynamic-response of an inertial load. It is the ratio between the maximum acceleration of the dynamic-response and the maximum acceleration of the command.

Input Torque Coefficient - E.g. the torque needed by Motor to drive the Cam-Shaft.

Also termed: (VDI - German Standards).

Also (e.g. Sankyo, Heinz):

Note on Input Torque Coefficient

The maximum torque of a motion-law at the Follower is important. However, the rate-of-change of torque at crossover from acceleration to deceleration is as, if not more, important.

A positive input torque on the cam-shaft winds-up (twists) the cam-shaft. A negative torque winds-down (untwists) the cam-shaft.

The Torque changes from a positive to a negative value at the crossover. As backlash is traversed at crossover, the Torque reduces to only the 'friction torque'. The result is the speed of the drive-motor and cam-shaft may increase rapidly. Also, after backlash has been traversed, the drive becomes driven by the load. If the speed of the motor does increase, then the motion-law at the output is distorted. The maximum deceleration increases when the cam-shaft momentarily increases its speed.

Power - constant Torque and constant Angular Velocity

Power - constant Force and constant Linear-Velocity

Instantaneous Power - varying Torque and Angular Velocity

Instantaneous Power - varying Force and Linear-Velocity

Instantaneous Load Torque with changing Load Mass Moment of Inertia and/or Angular Acceleration.

Instantaneous Load Force with changing Load Mass and/or Linear Acceleration

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

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

Load Power with constant Load Mass Moment of Inertia, Angular Acceleration, and Angular Velocity.

Load Power with constant Load Mass, Linear Acceleration, and Linear Velocity.

Power Coefficient :

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

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
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

Parabolic

5

1

2

1

1

1

1

Simple Harmonic

3

1

4

4

5

2

1

Modified Trapezoid

3

3

2

2

2

3

3

Modified Sinusoid

2

4

3

4

4

4

4

Cycloidal

1

5

2

3

3

4

5

Peak Acceleration

This merit rating applies to the nominal maximum output acceleration during the motion period, calculated by the motion-law equation.

Output Vibration

Output vibration is superimposed on the nominal output acceleration, thereby increasing the nominal peak value. The vibration severity depends on the elasticity and operating speed of the mechanism. The merit rating applies to mechanisms of average rigidity running at fairly high speed.

Peak Velocity

Peak Velocity is the nominal maximum output velocity during the motion period, calculated by the motion-law equation. Its value is also increased by superimposed vibration.

Impact / Backlash

Impact forces occur at the locations of backlash in the mechanism when the changeover from acceleration to deceleration occurs. The severity of the impact depends on how gradually the changeover takes place. That is, how low the jerk is at point of impact. Strictly speaking, it is the changeover from positive to negative force or torque that matters, but in most high speed systems, that almost coincides with the acceleration changeover.

Input Torque

The nominal input torque of a mechanism varies throughout the motion period and is a function of the output load profile, and the velocity pattern. The peak acceleration and the peak velocity do not coincide and neither coincides with the peak input torque. Motion-Laws with good, that is low, acceleration do not necessarily have good input torque.

Input Vibration

The elasticity and backlash of the input transmission can cause serious over-run and input-vibration. This is when the sudden reversal of the input torque when the load crosses over from acceleration to deceleration - or load - causes the cam to jump forwards before it can transmit a decelerating force to the output. The more gradual that the nominal input torque changes sign, the less severe is the overrun and its consequences.

Residual Vibration

Residual Vibration takes place in the dwell period immediately following the motion period in high speed or elastic systems. Its amplitude depends on the vibration generated during the motion period, and the degree of damping present in the output transmission. It is very difficult to add sufficient damping to high speed mechanisms to eliminate residual vibration, so the choice of a motion-law is vital in some cases.