An optimization approach to the determination of manipulator workspaces

Abstract

The main objective of this study is to propose and develop a general numerical technique by means of which the workspaces of mechanical manipulators may be determined with relative ease.The emphasis is on parallel or so-called Stewart platforms.Stewart platforms have many advantages over the traditional serial manipulators.These advantages include high accuracy, high stiffness, high load-to-weight ratio and most importantly, low cost.According to the literature, it is strongly felt that the use of parallel manipulators in many robotic tasks is so necessary that they will become indispensable in the near future.In spite of the advantages of these mechanisms, the use of Stewart platforms is still mainly in an experimental stage.This is because there seems to be a lack of rational synthesis tools for the design of practically useful platform manipulators.In particular, the problems of the forward kinematics and workspace determination remain to be satisfactorily solved.This study addresses the latter problem.It is believed that if the workspace is understood, and its characterization properly done, then many design problems will easily be solved.In this study a novel optimization approach to solving the workspace problem is introduced.An attempt is made to demonstrate that this approach is general in the sense that it is applicable to different kinds of manipulators, and may also easily be implemented to determine various types of accessible workspaces.In particular, the generality of the method is illustrated by the fact that the optimization approach was successfully implemented for a redundantly controlled planar serial manipulator, a planar Stewart ABSTRACT platform as well as a spatial 6-3 Stewart platform.The optimization method is also successful in assisting in the characterization of the workspace by, for example, identifying interior curves connecting bifurcation points.This is of great potential importance with regard to the control of a manipulator within its workspace.The description of the behavior of the planar manipulators, led to a new notation for labeling the workspaces.This notation arises in a natural way from the optimization approach, is generally applicable and easy to understand.Using this notation, the complete workspace may be described in terms of the behavior of the manipulator.Of great practical importance is the treatment of dexterity requirements imposed on a Stewart platform.The optimization approach successfully determines different specified dextrous workspaces of the planar Stewart platform.An example of a dextrous workspace of the 6-3 Stewart platform was also successfully mapped.This is very significant, because as far as the author is aware, such a mapping has not previously been performed for the spatial case.It is hoped that this study will lie the foundation for the development of a general and rational synthesis design tool for parallel manipulators.Further research that will be addressed in the near future, and stems from the work done here, is the determination of the feasible workspace for parallel manipulators subject to various additional prescribed mechanical constraints.This study has important potential impact for the manufacturing industry of South Africa and other developing countries.The implementation of this technology lies in retrofitting existing non-CNC milling equipment to increase their capability at a lower cost than that of the alternative of purchasing traditional 5-axis machining centers.