Motion-Laws for Segments

 

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Motion-Laws for Segments

 

Motion-Laws - also called Cam-Laws.

Select the Motion-Law for each segment with the Motion-Law Selector or the Segment-Editor.

Each Motion-Law is a mathematical expression that defines how an output variable changes as a function of an input variable.

The mathematical expressions evaluate exactly the displacement, velocity, acceleration, and jerk motion-values. You do not need to know any mathematics.

For convenience, we can separate the motion-laws into three groups.

Note: We list the motion-laws for you in the Motion-Law Selector alphabetically (English spelling).

Traditional Motion-Laws

The 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.

The Traditional Motion-Laws are based on:

•Trigonometric Functions, and/or

•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 Acceleration + SCCA with Constant-Velocity 20%, 33%, 50%, 66%.... - Trigonometric Functions

17.Sine-Squared - Trigonometric Functions

18.Sinusoidal - Trigonometric Functions

19.Triple-Harmonic - Trigonometric Functions

You can edit the Segment Parameters in the Segment Editor to get a motion-law similar to:

a.Triple Harmonic - Modified Trapezoidal

b.Triple Harmonic - Modified Sine

c.Triple Harmonic - Zero Jerk at Crossover

20.Flexible Polynomial - it can be used for different motion-laws - see also Special Motion-Laws Flexible-Polynomial, below.

Throw: a motion-law is a rise segment followed immediately by a return segment.

You must design these different Throw motion-laws with two Flexible Polynomial segments. They have different continuity, and shape as they rise and return from the maximum displacement.

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

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

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

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

Low Impact at Crossover uses two Flexible-Polynomial segments to give one Rise motion-law. The Jerk is zero when the Acceleration changes to Deceleration.

e.Low Impact at Crossover

Special Motion-Laws

These meet the needs of specific applications.

25.Y–Inverse-Sinusoid : when applied to the motion of a crank, it gives a constant linear velocity at the tip of a crank. Maximum of one Y-Inverse-Sinusoid segment per crank rotation.

26.CV Inverse Crank : similar to the Y-Inverse-Sinusoid, Not limited to one Crank-Constant-Velocity segment per motion.

27.Flexible-Polynomial - a VERY important and useful motion-law - see also Motion-Laws 20 - 24

28.Ramp - also a useful motion-law - see also Motion-Law 5, Cycloidal CV50

List Segment-Types

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

29.Position-List

30.Acceleration-List

31.Z-Raw-Data

When to use the Flexible Polynomial OR a Traditional, or the both Motion-Laws?

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 you use:

•All Flexible-Polynomials - to give powerful and flexible motion-design possibilities

or

•All Traditional Motion-Laws - usually the easiest to design a Rise and Return type motion.

or

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

The Motion-Laws available in MotionDesigner exceed the German Technical VDI-guidelines 2143 Papers (Part) 1 and 2. Also bear in mind, that a motion at a cam-follower or servomotor is usually found by MechDesigner with Inverse-Kinematics. When this is the case, the motion at the cam-follower or servomotor is not the same as the motion-design that is given to the tooling, or Motion-Part.