A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators

A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators

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Article ID: iaor20061279
Country: Germany
Volume: 30
Issue: 6
Start Page Number: 422
End Page Number: 427
Publication Date: Dec 2005
Journal: Structural and Multidisciplinary Optimization
Authors: ,
Abstract:

A numerical multi-level optimization methodology is proposed for determining dextrous workspaces of 3-degree-of-freedom (3-dof) planar parallel manipulators, in which it is required that at any point within the workspace, the manipulator is able to assume any orientation in a specified range. The method starts by finding a single initial point on the boundary of the dextrous workspace. This first stage requires the successive solution of three separate optimization sub-problems, where the evaluation of the objective function for the second problem and the constraint functions in the third problem are determined by the solution of appropriate optimization problems at a lower level. Once the boundary point is identified, further successive points along the dextrous workspace boundary are traced by the application of the so-called chord method. In the latter procedure, the determination of each successive boundary point is also obtained via a constrained optimization problem, where the constraint functions are again evaluated via the solution of an optimization problem at a lower level. The proposed method is illustrated by its successful application to three different manipulator design geometries, and for various ranges of dexterity.

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