Motion-Laws

<< Click to Display Table of Contents >>

Navigation:  MotionDesigner Reference & User Interface >

Motion-Laws

Motion-Laws - also called Cam-Laws.

Each segment is assigned a Motion-Law by the user.

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. All motion-derivatives are exact, evaluated motion-values. The user does not need to know any mathematics. We plot the motion-laws.

The user needs to specify various parameters that may relate to the Motion-Law.


In the Motion-Law Selector, we list the Motion-Laws alphabetically (English Language).

In this topic, we can separate the motion-laws into three groups.

Traditional Motion-Laws

Traditional Motion-Laws (also named Standard Motion-Laws) have been used for many years in cam mechanisms for motions that have Rise and Return segments separated with Dwell segments.

The Traditional Motion-Laws are based on:

Trigonometric Functions

Polynomials Functions


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 Functions

8.Modified-Trapezoidal - Trigonometric Functions

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 Functions

16.Sine-Constant-Cosine + SCCA with Constant-Velocity 20%, 33%, 50%, 66%.... - Trigonometric Functions

17.Sine-Squared - Trigonometric Functions

18.Sinusoidal - Trigonometric Functions

19.Triple-Harmonic (also called Three Harmonic) - Trigonometric Functions

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

a.Triple Harmonic - Modified Trapezoidal - Trigonometric Functions

b.Triple Harmonic - Modified Sine - Trigonometric Functions

c.Triple Harmonic - Zero Jerk at Crossover - Trigonometric Functions


Throw Motion-Laws (Symmetrical & Asymmetrical)

A Throw motion-law is a rise segment followed immediately with a return segment.

We call it a Throw because the motion is similar to a ball that is thrown up in the air. The transition of the ball from its Rise to Return (at its maximum-displacement) has zero-velocity, but has finite deceleration.

In general, the shape of the Throw motion from Rise to Return is defined by the acceleration and jerk values at the transition.

We design the Rise and Return parts of the Throw motion-law with two Flexible Polynomial segments. Thus, we can also edit the Segment-Width of the two segments that will also influence the shape of the Throw segments.

22.Quick-Return 1: Finite Jerk @ Start / End

23.Quick-Return 2: Zero Jerk @ Start / End

24.Rapid-Return 1: Finite-Jerk @ Start/End/Mid-Point

25.Rapid-Return 1: Zero Jerk @ Start/End, Finite Jerk @ Mid-Point

The 'Crossover Jerk' of 25 is greater than other motion-laws. This means that any 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 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 to more than one segment in a motion.

28.Flexible-Polynomial - a VERY important and useful motion-law.

29.Ramp - a useful motion-law.

List Segment-Types

You can import your own motion-values to a List Segment-Type:

30.Position-List

31.Acceleration-List

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. We recommend that you learn how to use it effectively and efficiently.

Traditional Motion-Laws have advantages in some circumstances.

We recommend that the segments are:

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

- or -

All Traditional Motion-Laws - easiest motion-design

- or -

A mixture of Flexible-Polynomial and Traditional Motion-Laws - most difficult motion-design but may offer advantages

The Motion-Laws available in MotionDesigner exceed the German Technical VDI-guidelines 2143 Papers (Part) 1 and 2. Also bear 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.