How is the ideal mechanical advantage of a vise calculated?

The ideal mechanical advantage of a vise is calculated by considering the relationship between the input lever arm (the length of the handle) and the output distance moved by the load (which relates to the pitch of the threads in the screw mechanism of the vise).

In this calculation, the circumference of the circular path that the handle traces as it rotates is represented by (2 \times \pi \times \text{length of handle}). This value reflects the distance traveled by the handle for one complete turn. The pitch of the thread defines how far the screw moves the load with each complete turn, or how much linear distance is gained on the load for every rotation around the screw. Therefore, the ideal mechanical advantage is determined by the ratio of the distance input through the handle to the distance output moved by the threads.

Thus, the formula for the ideal mechanical advantage can be expressed as (distance moved by the handle)/(distance moved by the load) or in this context, (2 × π × length of handle)/(pitch of thread). This precisely captures how the input lever arm’s movement translates into mechanical advantage when using the vise.