# How to calculate the mechanical advantage of torque reaction arms (or balanced articulated arms)?

So, I was trying to figure out how to figure out how much force I would need to apply to these articulated arms in order to make them extend or "contract", but I can't figure out. I tried to search on google, but I couldn't find any information/formulas on the subject, only product lists and ads selling said articulated arm.

To be honest, what made me interested on knowing the answer to this was the megabots mech that uses a similar mechanism for its legs, but the question isn't about it, I'm just wondering. • did you try force diagrams? Mar 13 at 21:41
• @TigerGuy yes, I couldn't find anything Mar 13 at 21:43
• Usually designed so the force needed is just enough to exceed the friction and springs. ie designed so the user thinks they are "weightless". If you don't believe test it. Mar 14 at 8:28

In each joint, The moments are the weight of the load plus the weight of the lift arm(s) multiplied by the distance to the joint.

setting the moments sum about the joint equal to zero will give equilibrium. An increase in the spring tension, F, or hydraulic actuator force will lift the arm or vice versa.

$$\Sigma M_{joint}=0 \quad P*D-sin(\theta)*F_{spring}*C=0$$

The wider the distance K the less power is needed to lift the load.

I used a drafting light but the concept is the same.

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