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

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. • That instantaneous velocity direction change is a killer. would require infinite acceleration. – joojaa Jan 19 '17 at 16:59
• @joojaa Then we could soften the edge so that it becomes seamless. Would $\sin^2(\pi t)$ be fine enough? Is sin squared motion possible to be achieved using mechanical structures? – AHB Jan 19 '17 at 17:55
• How exact do you need to be with any of this? A little insight as to why they have to have that position profile could help. – JMac Jan 19 '17 at 18:09
• @JMac I added what you want. – AHB Jan 19 '17 at 18:32
• You can do a lot with 4-bar linkages. Note that the vertical movement of the feet (ignoring the horizontal movement) is very close to the profile you're looking for. – Dave Tweed Jan 20 '17 at 13:29