Solving the Forward Kinematics of a Planar Three-Legged Platform With Holonomic Higher Pairs

Abstract

A practical solution procedure for the forward kinematics problem of a fully-parallel planar three-legged platform with holonomic higher pairs is presented. Kinematic mapping is used to represent distinct planar displacements of the end-effector as discrete points in a three dimensional image space. Separate motions of each leg trace skew hyperboloids of one sheet in this space. Therefore, points of intersection of the three hyperboloids represent solutions to the forward kinematics problem. This reduces the problem to solving three simultaneous quadratics. Applications of the platform are discussed and an illustrative numerical example is given.