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