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how to produce 2 different speed by using only a motor when the motor is running?
The easiest way is to use a bipolar engine, for example 4/8 pole or 2/4. The result is two speeds more or less a double.
you can use a gear system as the easiest way.
motor is connected to a shaft with a gear installed on it. this shaft is connected to another shaft with another gear. so each shaft has different speed.
instead of a gear system you can use chain or belt-pulley system.
my application is which the motor will be mounted at the bottom. on top of the motor, there are 2 layers, both layer rotate in same direction but with different speed. so any idea?
well using gear is possible if you wanna the same direction, then you should use an idler gear too. or using belt or chain depending on situation.
how about if the top layer needs to rotate in 20 degree rather than in a straight form?
i can't imagine your model this way. I should see your system. if you could upload a cad model, it's easier to answer.
up-vote if you find the answer useful and upload a cad model.