[Tristan Lall]

A lot of these sorts of mechanisms will have sinusoidal motion—the path can be anything, but the timing between points is sinusoidal. So, in general, are there any timing requirements? (This also doesn't account for the actual behaviour of the actuator, since it also needs time to accelerate; this assumes that the thing is operating without regard to dynamic effects.)

Also, what's following the arc; can you put a pivot at the centre of the arc, for example?

One simple example of this kind of motion would be a flexible rod attached to a piston and a pulley. Start with the rod wrapped around the pulley, and pull it to go one way. Push on it (so you can't use chain or string) to go the other way.

If you don't mind pivoting the piston, and don't mind rather uneven forces, you can also just attach an arm from the rod of the piston to the centre of the arc, and pin the tail of the piston in place. When the rod extends, the change in length causes the centre joint to move along an arc determined by the arm length.

Another idea would be to take a section of a gear, and a piece of rack. Just design it so that one extension of the piston corresponds to 90° of rotation. (Are the given direction arrows critical? Because if so, you'd need to actually reverse the piston output as part of the linkage—that seems like a waste.)

Lots more possibilities exist; a better idea of the application would help. Are you trying to move the drive modules with this, and if so, why only 90°? Also, what level of complexity and cost do you want?