# How to do linkage analysis for a two-arm lever?

I am not a mechanical engineer and am hoping someone can explain in simple terms how to do a linkage analysis for a two-armed lever. An example of such a linkage is shown below in the illustration of a tailstock driving lever for a Potter lathe:

The goal of the linkage analysis is to compute the mechanical advantage or disadvantage as a function of the critical dimensions of the parts of the machine. So, in other words, if a force is exerted on the handle of the tailstock lever (or is it a torque?), then what would be the resulting force on the tailstock as a ratio?

• Name of this mechanism is the four bar mechanism. This is a special case though Jul 9, 2022 at 12:58

The mechanism consists of four members, and can be modelled using three revolute joints at $$A$$, $$B$$ and $$C$$ and one prismatic joint at $$D$$. However, to get the ratio between stock force and handle force, we only need to consider a static moment analysis, e.g. about the point $$B$$, turning the problem into a lever problem: $$M_B=F_sd_s-F_hd_h=0\hspace{0.5cm}\Rightarrow\hspace{0.5cm}F_s=F_h\left(\frac{d_h}{d_s}\right)$$ Note that this expression is exact only when the forces have lines of attack perpendicular to the axis of the handle. The right figure shows the forces when this is not the case, in which the stock force is the component aligned with the axis of the prismatic joint: $$F_s=F_h\cos(\theta)\left(\frac{d_h}{d_s}\right)$$
Note that some percentage of the force $$F_s$$ will be counteracted by friction in the prismatic joint, but the mechanical advantage is nevertheless the same ratio.