Deriving a Generalized, Actuator Position-Independent Expression for the Force Output of a Scissor Lift

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.