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JayD

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**S-Curve Equations??**

Hi All,

Am new to this but here goes.

I am trying to model a 7 segement S-Curve Motion Profile (see http://en.wikipedia.org/wiki/File:Third-order_motion_profile.svg" ) with VBA. I am wanting to use a linear encoder value to determine the switching points between the segments.

I am using the following equations:

A = A + J * t

V = V + (A * t) + (0.5 * J * t ^ 2)

X = X + (V * t) + ((A / 2) * (t ^ 2)) + ((J / 6) * (t ^ 3))

x = displacement

v = velocity

a = acceleration

j = jerk

t = time interval

I am struggling with the final change over from segment 6 to 7 (constant negative acc to non constant negative acceleration) as I want to use distance to Target (X_Target - X) as a trigger.

The constraints I have are:

- current velocity (V)
- final velocity (V_f =0)
- current acceleration (A)
- final acceleration (A_f =0)
- current displacement (X)
- final displacement (X_f =X_Target)

The variables are:

- Time (t)
- Jerk (J)

Hope this makes sense.

Any suggestions/help would be appreciated.

Cheers

JD

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