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On the Kinematic Design of Spherical Three-Degree-of- Freedom Parallel Manipulators

This article studies the kinematic design of different types of spherical three-degree-of-freedom parallel manipulators. The mechanical architectures presented have been introduced elsewhere. However designs having at least one isotropic configuration are suggested here for the first time. Isotropic configurations are defined, in turn, as those configurations in which the Jacobian matrix, mapping the angular velocity vec tor of the effector into the joint velocities, is proportional to an orthogonal matrix. First, a review of the direct and inverse kinematics of spherical three-degree-of-freedom parallel ma nipulators is outlined, and a general form for the Jacobian matrix is given. Parallel manipulators with revolute or pris matic actuators are discussed. Then, the concept of kinematic conditioning is recalled and used as a performance index for the optimization of the manipulators. It is shown that this leads to designs having at least one isotropic configuration. Finally, a few examples of such designs are presented.