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enter image description hereHello everybody. For my robot design, I would like to utilize the most optimal gear ratio that I can use. For that I want to utilize the torque of my motor which is a linear function of rpm. This task proved to be difficult as I have no idea to turn my acceleration function which is dependent on the rpm to a time variable function. Any help is appreciated. The image attached is the torque vs rpm curve. Rpm of the motor is capped at 6400 ish.

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I think there is information missing to analyze the problem. If that's an rpm-torque graph the fast answer is to search the largest combination of torque*rpm... And for the reduction ratio, 1:1 is the most efficient if you don't have any constraints 😅.

But optimal will always depend on the application. And if you want motor efficiency you need to look at nominal values (for continuous use) of rpm and torque. Here you will have the best performance.

Hope that this also helps How high of a gear ratio can a motor have?

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