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January 31st, 2018, 05:15 PM  #1 
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Join Date: Dec 2005
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Cams and polynomials
Concerning cams in a motion controller that represent slave position related to master position, I would like to ask if my statements are wright, concerning the internally used polynomial :
1)slave start velocity = 0, slave end velocity = master velocity, slave start and end accelerations and jerks = 0 > polynomial 6. 2)slave start velocity = master velocity, slave end velocity = master velocity, slave start and end accelerations and jerks = 0 > polynomial 7. 3)if for start and end point, velocities and jerks are known as parameters, I suppose the polynomial order will never get higher then 7? 
January 31st, 2018, 10:18 PM  #2 
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Normally a 7th order polynomial is used to specify the jerks at the beginning and end of a motion segment. The starting position, velocity, acceleration and jerk determine the first four coefficients of the 7th order polynomial. The final position, velocity, acceleration and jerk are used as well as the initial position, velocity, acceleration and jerk to determine the higher order coefficients.
There was a thread about this topic years ago. Norm Dzeidic was computed the coefficients for a 7th order polynomial that moved from point to point. 7th order polynomials are very good when there is plenty of distance or time to ramp up or down like in an elevator or high speed train. However the peak acceleration of a 7th order polynomial is 1.875 times the average accelerations compared to 1.5 for a 5th order polynomial or 1.57 for using cosine ramps. The peak acceleration may not be obtainable. Also, the math gets messy. Cam tables usually use a series of 3rd order polynomials. It is possible to implement 5th order polynomials but they aren't widely used in motion but they are in graphical design.
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February 8th, 2018, 02:27 PM  #3 
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March 19th, 2018, 03:21 PM  #4 
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I should want to create a profile where for start and end point position, velocity, acceleration and jerk are specified.
In my controller I can only implement polynomials of degree six. It should be possible to compose the profile I want by two polynomials of max degree six. However I don't know to define the intermediary point (endpoint first curve, startpoint second curve). Anyone has advices? 
March 19th, 2018, 06:19 PM  #5 
Member

You are asking for trade secrets. If it was easy your current controller would be able to do it.
Even calculating the time the first and last point is a ***** if there are limits on velocity, acceleration and jerk.
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