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The two motors are mounted in parallel as you can see in the picture and each one of them is connected to a gearbox through an elastic coupling. My question is : how do they operate together ? is one of them supposed to be off ? if you have any book or any website that discuss such transmissions I'd be thankful.
Three gears (and gearhousing body) in that configuration is a differential. Differentials work in both directions, connected this way they simply add the outputs together to one shaft. That is simply one of the uses of the differential. Although the reverse of this is more commonly known and is used in cars to spread the forces of one shaft to two.
Mathematically a differential works as follows:
A + B = C
Since you have motors connected to A and B their combined input is the output C. Also note this means the other motor can be not running it still works perfectly fine (since A + 0 = A = C).
And yes, before you ask, differentials can be used to do mechanical arithmetical calculations of adding or subtracting. It was used in all kinds of targetting devices in WW2.
Although I'm sure there are exceptions, I think it is common for the two motors to share the load 50-50. Adding the gearbox adds cost and complexity to the system (versus just one motor), so you are only going to do it if you get a big benefit from the second motor. If it's a 90-10 split, you might as well get just rid of the second motor and save yourself the cost.
In practice, the split may deviate from 50-50 due to slight differences between the two motors. In this case a master-slave arrangement might be used to get an exactly even split. E.g. run one motor on speed control, measure the output torque, and the run the other motor on torque control. For a dc motor, volarge is proportional to speed and current is proportional to torque. So you run one motor on a constant voltage and then match the other motor to the same current.
Elastic couplings are going to eliminate/reduce shock loading in the gear train.
How does it work? Either the second motor is for redundancy/backup and/or additional power/torque. It's the same concept as adding more cylinders to an internal combustion engine. They apply more power to the crank shaft.
