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Another key relationship to note is that at the same instantaneous power, speed and torque are inversely proportional. As speed increases, torque decreases and vice versa. 

What Gear Ratios do we Need?

This is a very important question to ask, but at the same time is a very difficult question to answer. I won't be able to provide any answers in this page but I will list the things that must be considered before properly answering this question.

• How many linkages does our arm have, and how long are the linkages?
• How much does each linkages weigh, and where is it's center of mass?
• What is the rated torque of the motor driving the joint in question?
• What kind of drive are you using (gear drive, belt drive, cycloid drive, etc.)
• How many stages of reduction are you using in your drive? 
• How heavy of a load do you need to manipulate?
• What safety factor are you applying?

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