Excursion-limits at the third joint of a three-hinged planar robot are incorporated into a new systematic formulation for path-placement in which the three-dimensional solution-space is decomposed into a two-dimensional space of variables that strongly control the placement of the path and a one-dimensional space that is much less critical. The new formulation determines all acceptable positions for the first joint of the robot relative to the workpiece. All possible acceptable designs appear in a graphical form that can be readily visualized and be directly measured in a Cartesian frame of reference in the workcell. The method is extended to closed tool-paths, and the method is illustrated with practical examples.

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Soman
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A Two-Dimensional Formulation for Path-Placement in the Workcells of Planar 3-R Robots
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