Methodologies for the optimal design of parallel manipulators

Abstract

SUMMARYIn this paper the problem of determining a manipulator design so that its workspace corresponds to a prescribed workspace is considered. Two di erent strategies, resulting in two di erent types of optimization problem are considered. The ÿrst strategy attempts to obtain a good overall approximation to the prescribed workspace and results in an unconstrained optimization problem. The second strategy entails designing a manipulator so that its workspace fully encloses the prescribed workspace and results in a constrained optimization problem. Two speciÿc formulations of the constrained problem are proposed. The ÿrst constrained problem simply aims to ÿt the manipulator workspace as exactly as possible to the prescribed workspace, while still ensuring that the prescribed workspace is fully enclosed. The second constrained optimization formulation is used to design a manipulator, the workspace of which fully encloses the prescribed workspace, but which is also well-conditioned throughout the workspace with respect to some performance measure. The particular manipulator used to illustrate and evaluate these formulations is a simple 2-dof planar parallel manipulator, and the ÿnal formulation is also applied to a 3-dof planar parallel manipulator. Although the manipulators studied here are simple, the objective of this study is to obtain a robust numerical methodology which can be extended to more practical and complex manipulators.

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