THESIS
2007

xv, 162 leaves : ill. ; 30 cm

**Abstract**
Parallel manipulators potentially possess some superior properties over their serial counterparts. In general, the design of a parallel manipulator involves interactively solving two tightly coupled problems: (i) mechanism synthesis and (ii) dimensional optimization. Nowadays, mechanism synthesis is mostly dependent on the designer's experience and intuition and is difficult to automate. This work starts with a development of a rigorous and precise geometric theory for synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group SE(3), we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using...[

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Parallel manipulators potentially possess some superior properties over their serial counterparts. In general, the design of a parallel manipulator involves interactively solving two tightly coupled problems: (i) mechanism synthesis and (ii) dimensional optimization. Nowadays, mechanism synthesis is mostly dependent on the designer's experience and intuition and is difficult to automate. This work starts with a development of a rigorous and precise geometric theory for synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group SE(3), we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using conjugacy classes. Then, we introduce a new structure for subchains of parallel manipulators using the product of two subgroups of SE(3) and discuss its realization in terms of the primitive joints. We propose the notion of quotient manipulators that substantially enriches the topologies of serial manipulators. Finally, we present a general procedure for specifying the subchain structures given the desired motion type of a parallel manipulator. The parallel mechanism synthesis problem is thus solved using the realization techniques developed for serial manipulators. Generality of the theory is demonstrated by systematically generating a large class of feasible topologies for (parallel or serial) mechanisms with a desired motion type of either a Lie subgroup or a submanifold.

A parallel manipulator is said to be overconstrained if the associated set of loop constraints is linearly dependent. Overconstrained parallel manipulators usually have simpler and stiffer structures over their non-overconstrained counterparts, and are built with less number of joints and links. Overconstrained parallel manipulators are synthesized in theory using ideal lower pairs, and built in practice using clearance-free preloaded joints to improve precision. This dissertation also intends to present a geometric theory for analyzing such parallel manipulators. We show that a parallel manipulator is non-overconstrained if and only if the intersection of the constituting subchains' configuration spaces is transversal, and overconstrained, otherwise. As non-transversal intersections are not stable, we conclude that an overconstrained parallel manipulator in practice becomes non-overconstrained because of inevitable manufacturing and assembly errors. As such, it will either lose degree of freedom (DoF) motions, or become impossible to assemble. Joint clearance must be introduced for correct functioning and assembly of these manipulators.

Because of the joint clearance, parallel manipulators exhibit some position and orientation (pose) errors at the end-effector. In this dissertation, we also propose a novel and efficient method to evaluate the maximal pose error of a manipulator's end-effector . We show that for both overconstrained and non-overconstrained parallel manipulators, the pose error analysis of the end-effector can be formulated into a standard convex optimization problem. We then incorporate this error evaluation algorithm into an optimal design of a parallel manipulator with precision and performance requirements. The resultant manipulator not only is well-conditioned with respect to some performance index, but also possesses a satisfactory position accuracy within the desired workspace.

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