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
Traditional Motion-Laws:
| 3. | Cubic - Polynomial Function |
| 6. | Dwell - Polynomial Function |
| 14. | Ramp - Trigonometric Function |
| 16. | Sine-Constant-Cosine + SCCA with Constant-Velocity 20%, 33%, 50%, 66%.... - Trigonometric Function |
Also, use the 'Triple Harmonic' Controls in the Segment-Editor to give:
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.
The 'Crossover Jerk' of 25 is greater than other motion laws. This means that backlash is traversed quickly to give a large velocity impact.
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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. |
| 29. | Ramp - a VERY useful motion law. |
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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.
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'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.
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