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enter image description here

In the picture above you can see a SCARA robot, with its end effector (the point x,y). The torques c_a and c_b are the ones of the motors in the joints, while f is an external force. My teacher has written the virtual work principle equation (for the static case) without considering the opposite c_b torque acting on the first link (the red one, which I drew). My question is why? They are internal torques but are on two different links that also have different virtual angular displacement, so I think we have to consider it.

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Work done is related to motion, which usually results in change of positions. In your picture the rotation of the arms produces positive work, if a counter C_b is added, it means partial work is negated, since C_B + (-C_b) = 0.

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  • $\begingroup$ You're saying the teacher was incorrect to neglect the counter-torque? Is there an approximation in which that might be reasonable? $\endgroup$ – electronpusher Mar 1 at 13:40
  • $\begingroup$ I stated that your teacher is correct. There works are done by the two arms in motion only. $\endgroup$ – r13 Mar 1 at 16:18
  • $\begingroup$ The word "counter" in my response was a mistake, as the c_b in red rotates in the same direction as the c_b in black. If it is included in the calculation, it means the total work equals to c_a + 2c_b, which does not make sense, unless the upper arm has changed position twice. $\endgroup$ – r13 Mar 1 at 17:03

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