Introducing Motion-Laws.

A motion is made from at least one segment, but usually more. You select th motion-law for each segment with the Motion-Law Selector.

A common question is 'Which motion-law is best?'

When the motion is complex, possibly with many segments, and it must satisfy many different position, velocity and acceleration requirements, it is almost impossible to answer the question 'Which motion-law is best?'.

However, when the motion is simple, when the segments are arranged for a 'Dwell-Rise-Return-Dwell' motion, then it is easier to select a motion-law that is best for the mechanical system.

Which Motion-Law?

You will see that, with many of the motion-laws, especially the 'Traditional Motion-Laws', you can only specify the position at the start and end of the segment.  When you give the same position at the start and the same position at the end of the segment , then the displacement plot of each Traditional Motion-Law is almost the same!

Surely, if you want to move the part, then why worry as to which motion-law you select for the segment?

The question is 'Why are there so many different motion-laws when each provides nearly the same result?'.

Actually, it is the shape of the acceleration plot, and not the displacement plot, that become more important as machine-speed is increased.

Although there is little difference between the Motion-Laws' Displacement plots, there is more difference between their Velocity plots, and a large difference between their Acceleration plots. The shape of the Acceleration plot has a significant influence on the dynamic response of the part.

For this reason, it is the shape of the acceleration plot that gives the name to a Traditional Motion-Law, and not the shape of the displacement plot.

When the motion is simple, it is easier to explore the advantages and disadvantages of each motion-law.


See Also: Design of Cam Mechanical Systems


Initial Selection

We can give relative ratings to the most common 'Traditional Motion-Laws'. You can use the ratings to help you select a law at the initial stage of a machine design. The ratings range from1 (bad) to 5 (excellent). The ratings apply to Dwell-Rise Dwell type motions.

Of the laws listed, that the Modified Sine(MS) is the best for general purposes. Its particular merit is that it is very tolerant of a bad input drive and transmission (elasticity, backlash, wear, low inertia). It is frequently the first choice of cam designers and is almost always used by commercial manufacturers of cam-operated indexing and oscillating mechanisms.

Additionally, you can look at the Motion-Law Coefficients of the common cam motion-laws. These indicate the relative values of their Velocity Coefficient and Acceleration Coefficient.

Cam Law Designation

Peak Acceleration

Output Vibration

Peak Velocity

Impact

Input Torque

Input Vibration

Residual Vibration

Const Acc, Const Decel

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

Explanatory Notes

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'. This is when the sudden reversal of the input torque at the changeover 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 over, 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 the choice of a motion-law is vital in some cases.

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