Planar generalized Stewart platforms and their direct kinematics

In this paper, we introduce the concept of planar generalized Stewart platform (GSP) consisting of two rigid bodies connected with three constraints between three pairs of geometric primitives in the two rigid bodies respectively. This problem can be treated as a special but important class of geometric constraint solving problems. We show that there exist sixteen forms of planar GSPs. We also obtain the closed-form solutions of the direct kinematics for the planar GSPs, For a class of GSPs with two distance and one angular constraints, we may give pure geometric solutions based on ruler and compass constructions.