# Why this torque is not considered into the virtual work principle equation?

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.

## 1 Answer

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.

• You're saying the teacher was incorrect to neglect the counter-torque? Is there an approximation in which that might be reasonable? Commented Mar 1, 2021 at 13:40
• I stated that your teacher is correct. There works are done by the two arms in motion only.
– r13
Commented Mar 1, 2021 at 16:18
• 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.
– r13
Commented Mar 1, 2021 at 17:03