Synthesis of Spatial Chains with Reachable Surfaces

In this chapter, we consider the design of spatial serial chains that guide a body such that a point in the body moves on a specific algebraic surface. The problem originates with Schoenflies [113], who sought points that remained in a given configuration for a given set of spatial displacements. Burmester [7] applied this idea to planar mechanism design by seeking the points in a planar moving body that remain on a circle. Chen and Roth [10] generalized this problem to find points and lines in a moving body that take positions on surfaces associated with the articulated chains used to build robot manipulators.