# How to distort a sigmoid / logistic function?

Please help. I need to move an object such that its distance / time profile resembles a sigmoid curve but in a non-symmetrical manner.

1- Let's say that I need to move 800cm in 3 seconds. How do I distort a sigmoid curve whilst still crossing the axes at the same points, eg: In the above diagram, y is the distance left to travel (800cm) and t is time, starting at 0 and going to 3s.

2- How do I make sure that the acceleration of the curve doesn't exceed some value a, eg 1.5m/s^2?

• It is not clear what you want. "distort the curve" how? How do you need the distorted curve to differ from the original curve? What sort of "non-symmetric" behavior are you after? – Paul Sinclair Apr 4 at 23:58
• Thanks for your message @Paul Sinclair. Normally with a sigmoid curve such as the one in the diagram I posted, we would fall to a/2 within b/2. I want a faster initial acceleration and slower deceleration so that I reach a/2 at say, b/10 and then a smooth deceleration to b. Even better, I'd like to set a maximum acceleration. – the_ether Apr 6 at 0:42