Hi. I am new to robotics and I plan to create a robot arm on a human scale.

I have a problem with the calculation of the motor that I need. That is, I cannot find the correct formula to calculate:

1- Engine torque

2- Electricity consumption

3- Electric power

4- Reduction with gears

In other words, I want to know how many W my motor must have to move X kg, how much electricity it consumes, how much force can be increased with a reducer X.

I have found many formulas, and I honestly don't know which one to trust and if they are correct:

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### TORQUE

W = M (Nm) x w (rad / s)

W = mechanical power

M = torque / torque

w = angular velocity

W = M * w

M = W / w

(Gearless at 3000 RPM)

w = RPM * 2 * pi / 60

w = 3000 * 2 * pi / 60 = 315 rad / s

M = 500 W / 315 rad / s = 1.5Nm

**I don't know if that last one works, because it doesn't have the diameter. Because the force is not the same if the gear measures 0.3 m as if it measures 0.1 m, as you know.**

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### ELECTRICAL CONSUMPTION

P = F * d / t

P = 196.13 N * d / t

P = 196.13 N * 0.1 m / s

P = 19.613 W

**I don't know if it's correct, because I saw another formula for the same and it gave me something different:**

Ec = ½ * m * v²

Ec = 0.5 * 20 kg * 0.1 m / s²

Ec = 1 J

W = Ec / T

W = 1 J / 10 s = 0.1 Watt

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Can you help me?

Regards.