Geometric Optimization of Serial Chain Manipulator Structures for Working Volume and Dexterity

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Abstract
Broadly speaking, the regional structure of a manipulator, which consists of the three inboard joints and their associated members, determines the workspace shape and volume. The orientation structure, which for a six-degrees-of-free dom manipulator consists of the three outboardjoints and members, determines the geometric dexterity or orientation potential of the manipulator. It is possible to determine the optimal dimensions of the regional structure for a given total length, using straightforward geometric arguments. By the use of the spherical counterpart of Grashof's theorem formu lated by Freudenstein (1964-65), it is also possible to show that there is an optimum geometry of the orientation structure. Two methods of characterizing geometric dexterity are utilized in this paper. The first is the concept of a dexterous workspace, which is a portion of the workspace within which the hand may assume any orientation. Although the dex terous workspace is a very useful concept for theoretical purposes, it is of limited practical utility because mechanical joint motion limits usually preclude its existence in real industrial robot structures. The second method of character izing geometric dexterity is to trace the portion of the work space within which the hand can assume a specified orienta tion. In this paper, the geometric conditions for the existence of a dexterous workspace are formulated for geometrically optimum, six-revolute manipulator structures. The optimiza tion criteria used include,freedom from geometric singular ities. We show that for an optimal geometry, singular posi tions can be completely excluded with small reductions of the joint motion ranges. These reductions have a negligible effect on the geometric performance of the system.

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