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I'm rather new to the field of gear systems, and to the field of RC models to which this case applies. I'm trying to design a system where a single variable speed engine would drive two different propulsion systems (in this case, rows of oars on a model galley). I want to be able to steer the galley by means of differential rowing.

I could use a double differential like in a tank, but it seems unnecessarily complicated, as I don't need to vary the turning radius continuously, in fact I only need three fixed configurations, RC-ed by a selector switch: both sides rowing, left only (turning right), right only (turning left). It could be go up to five if adding neutral turns left and right (the two sides rowing in opposite directions).

A major additional difficulty is the need for synchronization: although it would only minimally affect performance, visually it's quite important to have both sides rowing together when going forward - this is also a point where a double differential would fail, in my understanding.

Can anyone think of a relatively simple gear system to solve this problem?

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I'm not sure if "simple" fits into this possible solution, but run this through the gray matter:

Your motor has an output gear which is connected to the left drive gear and the right drive gear. This results in those two gears turning in the same direction and if sized the same, at the same rate.

Those gears are connected in a convenient manner to a set of planetary gear sets, one for each side.

Typically, planetary gears will provide reduction in a relatively small space, but they also allow for reversal using a braking mechanism. This will require some research on your part, but it's an easily observable action.

When you attach the drive to the sun gear and lock the ring gear from rotating, the planet gears turn in one direction with a specific gear ratio, the calculation of which is left as an exercise to the reader. Those planet gears are often attached to a planet gear carrier, allowing you to direct the output in the manner desired.

Additionally, if you attach the drive to the sun gear and lock the planet carrier from rotating, you will get a different ratio (not necessarily) but you will get a reversed rotation.

From your description, you'd take the outputs from the rim to create a reciprocating motion, but that's a general assumption, because reciprocating motion isn't restricted by direction of rotation, but it's a good way to avoid top-dead-center complications.

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