﻿ Motion-Laws and Cam-Laws

Motion-Laws

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

A Motion-Law defines, with a mathematical expression, how an output variable changes as a function of an input variable. The output variable is either a linear [m, cm, mm, inch] or an angular [degrees, radians] value. The input variable is usually machine-angle [ degrees, radians, cycles] or time [ msecs, seconds].

The mathematical expression is defined as a displacement, velocity or acceleration function.

The mathematical expression is differentiated or integrated to obtain displacement, velocity, acceleration and jerk. The calculus does not use 'numerical' techniques. Rather, we solve the equations for each motion-derivative to give the motion-values for each motion-derivative exactly.

We list the Motion-Laws alphabetically [English] in the Motion-Law Selector.

We can separate the motion-laws into three broad groups.

Traditional Motion-Laws are those that have been used for many years as 'Rise' or 'Return' segments, usually between two Dwell Segments.

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

 • Trigonometric / Harmonic

or

 • Polynomial

In English alphabetical order, the Traditional Motion-Laws are:

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

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

 19 Trigonometric Function
 20 Trigonometric Function
 21 Trigonometric Function

Throw Motion Laws*

Construct a 'Throw' motion with two Flexible Polynomial segments. The two segments can be thought to be a Rise and Return motion, without a Dwell segment between them.

The motion is named 'Throw' because it is similar to the vertical motion of a ball when it is 'thrown' up in the air. For convenience, they are called 'Quick-Return'. However they are actually a 'quick-transition' from the Rise segment to the Return segment.

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

The 'Crossover Jerk' of motion 26 is high compared to the other motion laws. This means that backlash is traversed quickly to give a large velocity impact.

Asymmetrical Throw Motion

We construct the Throw motion-laws with two segments. Thus, they do not need to have the same duration, nor actually the same displacement.

Special Motion-Laws

These meet the needs of specific applications.

 27 Y–Inverse-Sinusoid
 28 Crank-Constant-Velocity
 29 Flexible-Polynomial - see below.
 30 Ramp

Motion-Laws from Imported Data

When you select these 'Motion-Law', 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 used to compatible with Camlinks.

 31 Position-List
 32
 33 Z-Raw-Data

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

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

Thus, we recommend, 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.

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