Solutions to systems of non-linear equations that arise in the kinematic synthesis of spatial mechanisms - Sandor, George N. (Philippine Engineering Journal)
Determining the key dimensions of a mechanism for a prescribed performance is called the "synthesis" of the mechanism. The prescribed performance is given by specifying position or motion specifications at "precision points." These specifications lead to a system of equations whose solutions give the desired key dimensions of the mechanism. Synthesis for two or three positions generally results in a linear system of equations. Synthesis for more than three positions leads to a non-linear system. Different types of mechanisms give different forms of synthesis equations. In this paper, two spatial mechanisms-a three link mechanism with an intermediate higher pair for function generation and a five-link motion generator mechanism are considered.