Dimensional Synthesis of Parallel Robots with a Guaranteed Given Accuracy over a Specific Workspace

We are considering a n d.o.f. parallel robot that has to move within a given workspace and whose geometry is defined by a set of parameters. The motion of active joints of the manipulator are measured with sensors with a known accuracy ±Δρ. These errors together with bounded manufacturing errors on the parameters describing the geometry of the robot induces a positioning errors ΔX of the platform. We present an algorithm that allows one to determine geometries of the robot ensuring that these positioning errors will lie within pre-specified limits for any pose of the robot in its workspace even if the physical realization of the robot differs from the theoretical model while staying within the given manufacturing errors bounds. A by-product variant of this algorithm allows one to compute the maximal positioning errors of a given robot up to a predefined accuracy.

I. Introduction

It is well known that the performances of parallel robots are very sensitive to their geometry. In this paper we will consider a Gough platform (but the approach may be extended to any type of parallel robot as soon as its inverse jacobian has an analytic form) and we intend to determine the geometries of this type of robot such that the errors in the positioning of the platform lie within prescribed intervals.