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Acceleration from commanded position equation

I have a simple equation that defines actual pos (mm) using counts. It looks something like this

P= 100*sin((P5-10000)/P117)+100

Where P5 is counts and P117 is a constant.

My problem is: Theoretically I should be able to differentiate this position formula to get Velocity, and then again to get acceleration; but there is now time variable in this equation to differentiate with. Im trying to find the max accel that the robot arm sees through this motion. What am I missing here (other than time)?

If I understand you correctly, you have one position (P) that is a function of another position (P5). You want to be able to take derivatives of P with respect to time to get expressions for its velocity and acceleration. To do this, you will need to know (or at least assume) how P5 varies with time.

Mathematically speaking, we employ the "chain rule":

dP/dt = dP/d(P5) * d(P5)/dt

The first term is the derivative term of your expression. The second term is the rate of change (velocity) of the P5 position. You may take this to be a constant velocity, but you must specify the velocity of P5 somehow before you can take the time derivatives of P.

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