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Kinematic Modelling and Isotropic Conditions of a Family of Translational Parallel Manipulators

This paper presents a unified kinematic model of a family of four different topologies of translational parallel manipulators of general geometry. With this unified model, it becomes possible to implement kinematic synthesis algorithms that can take both geometrical and topological parameters as design variables. Using this model, we derive a single set of algebraic equations representing the necessary and sufficient geometrical conditions to obtain isotropic translational parallel manipulators. An isotropic configuration allows the best mechanical transmission of the motion from the actuators to the end-effector.