How to couple two pistons to a rotating shaft so that the piston heads move like this?

Question

Assume two vertical pistons with their flat head facing upward.

Is it possible to couple them to one rotating shaft in a way that the position vs. time diagram gets like this? (This is one complete cycle)

Each color being representing a piston.

The equations are:

Red: $$2 left|cos(pi t)right| - frac12$$

Blue: $$2 left|sin(pi t)right| - frac12$$ (The first with a phase difference of $pi over 2$)

I think because of the Absolute values, this can not be a simple crankshaft.

Can anyone help?

EDIT:

Actually I want to get as close as possible to this diagram of motion, which is the ideal theoretical case. Maybe this can help you for a better approximation.

Patstep · Answer

You can (come close to) this motion profile with two cams on one shaft. the tops being the dwell portion of the cams, and the bottom being the peak between two accelerations. As some one else mentioned since the bottom of your motion profile is an instantaneous acceleration change, you will never achieve it perfectly. this can be minimized by reducing mass, speed, and stroke length. This is going to be the closest mechanical way to do this.

Answered by Patstep on September 1, 2021

How to couple two pistons to a rotating shaft so that the piston heads move like this?

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