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Suppose I have a Robot Arm with 3 joint(revolute)( 3 DOF) as shown below , and I'm given

-The ranges of each joint q1,q2,q3

-The lengths of each link L1,L2,L3

-Load on the end effector [Fx Fy M]

how can I calculate the max torque at each joint of the robot ?

*image below describes the robot configuration.

If I missed any details , mention it in a comment and I will add it . Thanks in advance

enter image description here

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Torque is pretty easy to calculate for a single static arm configuration. Torque is just the length of the moment arm * the perpendicular force. And it is easy to decompose the problem into X and Y components, then sum. So in your example you would have the torque about joint 1 to be:

$$ T_1 = a * F_y + b * F_x $$

(Assuming $F_x$ and $F_y$ are in the global frame). You don't list the masses of the links, (which is typically not negligible), but you would want to add those in too. You should check out this arm torque calculator. The robot arm tutorial on that same site also has lots of helpful info.

For very complicated arms or dynamic situations, you might want the help of some code. See my answers to these other similar questions for pointers.

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