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.