A new method is developed for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar 3-R robots that can provide dexterous workspace. The method is an adaptation of traditional techniques of linkage synthesis, and it is particularly well-suited to applications in which the motion-trajectory requires large rotations of the end-effector. It is determined that, when the trajectory requires that the end-effector rotate a full turn at just two locations and when the critical 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 trajectories in which the tool must rotate a full turn at three locations on the workpiece. The method can be applied not only to planar robots with three hinge-joints, but also to spatial robots, each with a planar 3-R module, when the principal attitudinal excursions of the trajectory are all about a set of parallel axes. Variables are identified, for both the motion-trajectory and the workpiece itself, which strongly affect the design of the workcell and the time for it to complete a motion-trajectory. Example problems illustrate the method. The new method is suggested as an alternative to the existing methods of computer science for motion-planning.

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