# 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? Commented Mar 13, 2023 at 21:41
• @TigerGuy yes, I couldn't find anything Commented Mar 13, 2023 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. Commented Mar 14, 2023 at 8:28

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