6.15 : Machines

Machines are complex structures consisting of movable, pin-connected multi-force members that work together to transmit forces. One example of a machine is the cutting plier, which is used to cut wires by applying forces to its handles. When equal and opposite forces are exerted on the handles of the cutting plier, they cause the cutting edges to come together and apply equal and opposite reaction forces on the wire, which are greater than the applied forces.

A free-body diagram of the components of the cutting plier is considered to determine the magnitude of the forces acting on the wire due to the applied forces.

Analyzing the moment about the pivot pin that holds the plier together can help establish a direct relationship between the applied force F and the reaction force P, with respect to their respective distances from the pivot pin.

Additionally, by creating a free-body diagram for the pivot pin, it is possible to determine the components of the internal force at the pivot point. Applying the horizontal force equilibrium condition, the internal force O_x is zero. Similarly, applying the vertical force equilibrium condition, the internal force O_y equals the sum of the applied force F and the reaction force P.