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I am designing a robotic manipulator. The basic design is shown below. I am trying to calculate the torques around each joint to choose servo motors. I have made an attempt to find the torque around the two pitch joints for the two links (although I'm not fully sure that this is correct).

However I do not know how to find the torque required for the base rotation joint. How would this be calculated?

Basic design of robotic manipulator

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I recently built a robotic arm using 5 servos.Here is my thought process-

Torque can be thought as angular force. As we know W = mg.Ignoring friction the minimum force required to move an object in the z direction(vertically), at least force greater than weight is needed.Let's say an object weighing w is placed on a friction-less surface. In that case any amount force can move it, the acceleration will vary.(F= ma,applied force /mass = resulting acceleration )

In case of the first revolute joint ,in theory any torque should do.But if the moment of inertia is very high it might burn the motor.

but for the second revolute joint minimum torque required = (mass of the first link * half of the length of first link) + (weight of the third servomotor * length of the first link) + (mass of the second link * (length of first link + half of the length of second link)) + (weight at the end-effector * (length of first link + length of second link)).

And for the thrid revolute joint minimum torque required = (mass of the second link * half of the length of second link) + (weight at the end-effector * ( length of second link)).

use S.I. units in all cases.

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