The Isotropic Conditions of Parallel Manipulators of Delta Topology

Abstract

This paper proposes a necessary and sufficient number of 24 geometric parameters allowing to describe the design manifold of the Delta topological class, i.e., all geometries of manipulators having the same topology and mobility of the end-effector as the Delta parallel manipulator. Two isotropic conditions are then applied on this manifold in order to define the constraint manifold of isotropic designs, i.e., those having an isotropic Jacobian matrix. These constraints would facilitates the design of isotropic manipulators in this topological class.