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 output is either a linear [m, cm, mm, inch] or an angular [degrees, radians] value. The input is usually machine-angle [ degrees, radians, cycles] or time [ msecs, seconds].

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.


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

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

Traditional Motion-Laws

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

Traditional Motion-Laws:

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

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

20.Triple Harmonic - Modified Trapezoidal - Trigonometric Function
21.Triple Harmonic - Modified Sine - Trigonometric Function
22.Triple Harmonic - Zero Jerk at Crossover - 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 periods.

The 'throw' is a 'Quick-Return motion' when its acceleration is not zero as its 'rise' segment becomes its 'return'.

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, it can be applied more than one time to 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.


'Flexible Polynomial' OR 'Traditional' Motion-Laws?

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