﻿ Motion-Laws and Cam-Laws

# Motion-Laws

## Motion-Laws [also called 'Cam-Laws'].

A Motion-Law specifies, with a mathematical expression, how an 'output variable' changes as a function of an 'input variable'.

The mathematical expression calculates displacement, velocity, acceleration and jerk values. The calculations are not 'numerical' techniques. Rather, all motion-derivatives are calculated with an algebraic expression to give the motion-values for each motion-derivative exactly.

In the Motion-Law Selector, we list the Motion-Laws alphabetically [English Language]

Here, we can separate the motion-laws into three broad groups.

Traditional Motion-Laws [sometime named Standard Motion-Laws] have been used for many years in cam mechanisms as 'Rise' and 'Return' segments, usually between two 'Dwell' Segments.

Their main disadvantage is that you cannot usually edit their velocity, acceleration and jerk values at their start and end.

The Traditional Motion-Laws are based on function that are:

 • Trigonometric / Harmonic

or

 • Polynomial

 1 Constant-Acceleration & Deceleration - Polynomial Function
 2 - Polynomial Function
 3 - Polynomial Function
 4 Trigonometric Function
 5 Cycloidal Constant-Velocity 50% -Trigonometric Function
 6 - Polynomial Function
 7 Trigonometric Function
 8 Trigonometric Function
 9 - Polynomial Function
 10 - Polynomial Function
 11 - Polynomial Function
 12 Polynomial Low Impact Crossover - construct with two Flexible-Polynomial segments
 13 - Polynomial Function
 14 Ramp - Trigonometric Function
 15 Trigonometric Function
 16 Sine-Constant-Cosine + SCCA with Constant-Velocity 20%, 33%, 50%, 66%.... - Trigonometric Function
 17 Trigonometric Function
 18 Trigonometric Function
 19 Triple-Harmonic (also called Three Harmonic) - Trigonometric Function

Also, use the 'Triple Harmonic' Controls in the Segment-Editor to give:

 20 Trigonometric Function
 21 Trigonometric Function
 22 Trigonometric Function

Throw Motion Laws* [Symmetrical & Asymmetrical]

* A Throw motion-law is a 'Rise' segment followed immediately by a 'Return' Segment - no dwell between. It can be imagined to be similar to the vertical 'rise and fall[return]' motion when you 'throw' a ball up in the air. Also, the swing of a pendulum.

We construct Throw motion-laws with two Flexible Polynomial segments. Each segment can have the same or different motion-periods [time-duration]

The Throw is a Quick-Return motion when the acceleration tends towards the return motion during the later part of the rise.

The transition from 'rise' to 'return' is quicker than two adjacent [concatenated] Traditional Motion-Laws that have zero-acceleration at their transition.

 22 Quick-Return 1: Finite Jerk @ Start / End - construct with two Flexible-Polynomial segments
 23 Quick-Return 2: Zero Jerk @ Start / End - construct with two Flexible-Polynomial segments
 24 Rapid-Return 1: Finite-Jerk @ Start/End/Mid-Point - construct with two Flexible-Polynomial segments
 25 Rapid-Return 1: Zero Jerk @ Start/End, Finite Jerk @ Mid-Point - construct with two Flexible-Polynomial segments

The 'Crossover Jerk' of 25 is greater than other motion laws. This means that backlash is traversed quickly to give a large velocity impact.

### Special Motion-Laws

These meet the needs of specific applications.

 26 Y–Inverse-Sinusoid : when applied to a the motion of a 'crank', it gives a constant linear velocity at the tip of a crank. Limited to one segment per crank rotation.
 27 Crank-Constant-Velocity : an enhancement of Y-Inverse-Sinusoid, this motion-law can be applied more than one segment in a motion.
 28 Flexible-Polynomial - a VERY important motion law .
 29 Ramp - a VERY useful motion law.

### Imported Motion Data

When you select these 'Motion-Laws', you can import your own motion-values.

The Z-Raw-Data is the easiest to use, as it imports your data values directly.

The Position-List scales all of the values you import. The scale is in proportion to the difference between the start and end positions that you specify with the Blend-Point Editor - it is compatible with Camlinks.

 30 Position-List
 31
 32 Z-Raw-Data

### When to use the Flexible Polynomial OR a Traditional Motion-Law?

The Flexible Polynomial is the 'default' motion-law. It is very powerful tool. We strongly recommend that you learn how to use it effectively and efficiently.

Traditional Motion-Laws have advantages in some circumstances, especially for simple Rise-Dwell-Return motions.

Thus, we recommend, that you make the segments:

 • All Flexible-Polynomials - most powerful and flexible motion design possibilities

- or -

 • All Traditional Motion-Laws - 'standard' motion-design requirements

- or -

 • A mixture of Flexible-Polynomial and Traditional Motion-Laws - least preferred.
 The Motion-Laws available in MotionDesigner exceed the German Technical VDI-guidelines 2143 Papers (Part) 1 and 2. Also bare in mind, that the motion at a cam-follower or servomotor is usually found by MechDesigner with Inverse-Kinematics. In this case, the motion at the cam-follower or servomotor will not be the same as the motion of the Motion-Part.

Tutorial and Reference Help Files for MechDesigner and MotionDesigner 13.2 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd