A study of the kinematic characteristics of a three degree-of-freedom (dof) parallel mechanism is presented. The architecture of the mechanism is comprised of a mobile platform attached to a base through three identical prismatic-revolute-spherical jointed serial linkages. The prismatic joints are considered to be actuated. These prismatic actuators lie on a common plane and have radial directions of action. The mechanism's inverse displacement solution is obtained. Since the mechanism has only 3 dof, constraint equations describing the inter-relationship between the six motion coordinates are derived. These constraints allow the definition of parasitic motions, i.e., motions in the three unspecified motion coordinates. Architecture optimization of the device is undertaken demonstrating that specific values of design variables allow minimization of parasitic motion.

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Stewart platform configurations (architectures and poses) optimizing local dexterity are investigated. The condition number of the Jacobian matrix is used to quantify the dexterity of the manipulator. For a platform-centered Jacobian reference location and a given characteristic length for scaling purposes, a two-parameter family of optimal configurations is shown to exist. Two suitable architectural parameters defining the family are identified and properties of the optimal configurations are discussed. The optimization results are shown to be easily extended for other Jacobian reference locations and for other singular value-based local dexterity measures. It is suggested that the existence of a two-parameter family of optimal local configurations could be exploited to aid in the resolution of optimal architectures for global measures. 0

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