  Scissor lifts, a staple of mechanical design, especially in competitive
robotics, are a type of linkage that can be used to raise a load to some
height, when acted upon by some force, usually exerted by an actuator. The
position of this actuator, however, can affect the mechanical advantage and
velocity ratio of the system. Hence, there needs to be a concrete way to
analytically compare different actuator positions. However, all current
research into the analysis of scissor lifts either focusses only on the screw
jack configuration, or derives separate force expressions for different
actuator positions. This, once again, leaves the decision between different
actuator positions to trial and error, since the expression to test the potency
of the position can only be derived once the position is chosen. This paper
proposes a derivation for a general force expression, in terms of a few
carefully chosen position variables, which can be used to generate the force
expression for any actuator position. Hence, this expression illustrates
exactly how each of the position variables (called a, b and i in this paper, as
defined later) affect the force output, and hence can be used to pick an
appropriate actuator position, by choosing values for the position variables
that give the desired result.
