A scissor lift jack mechanism is a 
mechanical device used to lift up or down an upper platform. The term “Scissor” comes from the mechanical configuration, which is based on linked, folding supports disposed as a crisscross ‘X’ pattern. The platform displacement motion is achieved applying a force to one of the supports, resulting in an extension of the crossing pattern.
The force applied to extend the scissor mechanism may be hydraulic, pneumatic or mechanical (via a lead screw or rack and pinion system). It can be applied at the bottom of the mechanical structure or at its center pin.
Design Equations for Scissor Lift, with force applied at Center Pin:
For a scissor lift that has equal-length arms, it is possible to compute the relationship between the actuation force F and the load force W acting on the mobile platform. This relationship depends on the geometrical parameters of the mechanical structure. Starting from the notes published on this website, I made my own computations trying to fix some sign errors and better explain some notations. Just click on the two images below to open them in their original size. I hope it could sound interesting to somebody facing with such kind of problem 🙂
andreacollo 