Numerical Methods
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This paper considers the kinematic optimization of a parallel manipulator actuated in redundant form, using a numeric conditioning of the Jacobian matrix. The kinematic model proposed by Zanganeh and Angeles (1994) consists of nine prismatic in-parallel actuators, i.e., three actuators, called external legs, connect the moving platform directly to the base platform by spherical joints, and the six actuators, termed the upper internal and the lower internal legs, are coupled in pairs by three concentric spherical joints at the internal point. First, the end effector velocity problem is solved, and then the identification of a neutral configuration of manipulator is developed. Finally, the platform geometry parameters of the manipulator are formulated, and solved as an optimization problem.