Motion-Laws

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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. All motion-derivatives are exact, evaluated motion-values.

The user does not need to know any mathematics. We plot the motion-laws.


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 [sometime named Standard Motion-Laws] have been used for many years in cam mechanisms as Rise and Return segments, traditionally 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 functions that are:

Trigonometric / Harmonic

or

Polynomials


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 - and no dwell.

The Throw rise and return can be imagined as the motion at the high-point of a ball thrown up in the air or the swing of a pendulum. This makes the throw a so-called Quick Return.

We provide the Throw motion-law with two Flexible Polynomial segments. This gives is a lot of flexibility to the shape of the motion at the transition.

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 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 to more than one segment in a motion.

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

29.Ramp - a VERY useful motion law.

List segment types

You can import your own motion-values to a List type segment.

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

Traditional Motion-Laws have advantages in some circumstances.

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.