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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.


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.

  • $\begingroup$ 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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