Modified sine curve motion

[aand74]

I already succeeded in programming a function to find parameters of fifth order polynomial, in the runtime of a motion controller.
To use if at runtime the cam has to be calculated.
Next to polynomials there also exist sine curves for cam profiles.
More in specific, when should I use the modified sine curve?
When does it have an advantage to a polynomial?
I suppose a modified sine curve is a sine curve where the first and last part are not a pure sine, but the middle part is.
If I should write a function to be executed at runtime in the controller, to calculate a modified sine curve, based on start and end position and velocity,
how should I start? What function should be used in the first and last part?
For the sine part, how to calculate amplitude, phase and period?

[Peter Nachtwey]

When you say sine curve do you mean s-curve?
s-curves start and end a ramp with the acceleration at 0.
This can be done with half a sine wave but it is not clear what you are trying to do.

A sine is generated using a polynomial. Usually the order is very high.
A fifth order polynomial will execute faster than a sine function. The motion profiles are similar. The peak acceleration using a sine function is 1.57 or PI/2 times the average acceleration. The peak acceleration using a 5th order polynomial is 1.5 times the average acceleration. You can see there isn't much difference.

I do not know what you mean by modified sine curve.

To do what you want to do requires calculus. The motion controller should have these functions built into firmware. You should not need to write them.