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I would like to be able to tilt a platform (the green cuboid below, pivoting around the red point) from a single solenoid (one of the blue cylinders below). The solenoid cannot move (other than the shaft) and can only push (or pull).

enter image description here

I need something that will connect the solenoid to the platform so that one pulse of the solenoid will tilt the platform one way and an identical pulse would tilt the platform the other way. The platform can also be manually moved, so the solenoid must be able to cope with the platform being in a different position than expected.

Any ideas would be really well received! If I can clarify in any way, please let me know.

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Sounds like the mechansim in a "clicky-top" ballpoint pen. You'll need a rotating cylindrical ratchet mechanism; the solenoid plunger moves inside this cylinder.

Here's a drawing from quora.com

enter image description here

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There is another mechanism I once found on a ballpoint pen which I made a simple sketch of:

different ballpoint pen mechanism

Once you press the bolt on the left side, the wedge is released from the top wall hook and pushed against the bottom wall. When you move the bolt far enough against the spring, the wedge will link with the hook on the bottom wall. Upon releasing the bolt, the spring on the right side will push the wedge forward, causing it to tilt.

In the ballpoint pen, the two hooks on upper and lower wall are not at the same location, but one is further left than the other. This causes the wedge to rest at two different positions, which is what you want in a ballpoint pen. But this is probably not important for your application.

Probably you can adapt this mechanism to your problem.

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