Kinematic Synthesis of Planar Platforms with RPR, PRR, and RRR Chains

Abstract

This paper presents a method for determining the fixed and outermost moving joint locations of three-legged planar platforms composed of RPR, PTCR, and RRR chains. We seek three of these chains such that, when assembled into a platform, they reach an arbitrary set of displacements and orientations called positions. In addition, an acceptable platform design must satisfy joint limit constraints and potentially be able to move between the positions without crossing singularities. The methodology presented addresses nine of the ten possible topologies defined by these three chain types. The design problem is addressed through the use of constraint manifolds, the platform's workspace defined in terms of planar quaternion coordinates, hn example shows the synthesis of a platform via this methodology.