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Power is everything...
Power is the thing that you should be thinking about when you choose a motor for a particular job.
Given that you want to lift an arm and ball of weight X a distance Y in time T, you know how much power you are requiring.
If your motor cannot provide that much power you have to choose another or relax your requirements.
Once you know what motor, then you can pick your gear ratio such that your expected load reflected back to the motor gives you a torque between 20-50% of your stall torque of the motor.
If you do this, your motor will be happy, your robot will be happy, and your fans will be happy.
This is obviously a much condensed answer, but the basic idea is sound.
Joe J.
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