A new method is developed 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. The method is an analytical representation of the geometry of the robot and the task, and is particularly well suited to applications in which the task requires large rotations of the end-effector. It is determined that, when the task requires that the end-effector rotate a full turn at just two locations and when the first or third joint in the robot is rotatable by one turn, then the radial location of the workpiece is fixed in the workcell but its angular location is not fixed. When the mounting-angle of the tool is also a variable, the method accommodates tasks in which the tool must rotate a full turn at three locations on the workpiece. 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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