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

Parallel manipulators consisting of serial branches acting in parallel on a common end effector are examined. All nonredundant, six DOF manipulators corresponding to this in-parallel class of structures are enumerated. A specific in-parallel structure, three branches with two actuated joints per branch (3–2,2,2), is chosen as most promising based upon performance considerations. A class of kimematically simple (KS) serial-chain branch joint layouts suitable for the chosen in-parallel structure is defined. Arguments based upon kinematic equivalency of the branches and mobility of the assembled in-parallel manipulator chain are used to show that there exist only five unique branch joint-layouts belonging to the KS class. It is demonstrated that the solution to the inverse displacement problem for in-parallel manipulators based on the KS branches can be expressed in a closed form. Furthermore, the 3–2,2,2 in-parallel manipulators are shown to belong to a family of manipulators whose forward displacement solutions can be resolved through roots of a 16th order polynomial.

Hybrid-chain manipulators consisting of serial branches acting in parallel on a common end effector are examined. All non-redundant, six DOF hybrid manipulator structures are enumerated and a specific hybrid-chain structure is chosen as most promising based upon performance considerations. A class of kinematically simple (KS) serial-chain branches suitable for the chosen hybrid structure is defined. Arguments based upon kinematic equivalency of the branches and mobility of the assembled hybrid chain are used to show that there exist only five unique branch structures belonging to the KS class. It is demonstrated that the solution to the inverse displacement problem for hybrid structures based on the KS branches can be expressed in a closed form. Furthermore, the KS based hybrid-chains are shown to belong to a family of manipulator structures whose forward displacement solutions can be resolved through roots of a 16th order polynomial.