Synthesis of spatial parallel mechanisms with initial conditions using line geometry

In this paper we describe a coordinate-independent method for synthesis of a spatial parallel mechanism. The mechanism consists of a platform, a base, and five legs connecting the base and platform with spherical joints. The objective is to find the positions of the base anchor points and leg lengths for two arbitrary platform positions and their desired instantaneous motions. A unique solution will be presented that applies the linear line complex, a tool from line geometry. Potential applications that may benefit from this research include a five-link independent suspension system (wheel multilink suspension system for automobiles) and spatial mechanisms used in manufacturing. The algorithm and a numerical example will be discussed.