A new method is used for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar RPR robots that can provide dexterous workspace. All three joints of the robot have excursion-limits that bound their displacement. For the purposes of this paper, the third joint, a revolute, permits exactly one full turn. Successful locations for the workpiece are those places where the rotations at each task-axis and the third joint are synchronized. For a fixed mounting angle of the tool, the radial location and orientation of the workpiece are determined by just two 2π-rotations of the tool. When the mounting-angle of the tool is also a variable, the tool can be rotated a full turn at three locations on the workpiece. The method is particularly well suited to applications in which the task requires large rotations of the end-effector. The results are presented as coordinates of points in a two-dimensional Cartesian reference frame attached to the workcell. Consequently, a technician or an engineer can determine the location for the workpiece by laying out these coordinates directly in the workcell. Example problems illustrate the method. Practical applications include welding and deposition of adhesives.

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