An interactive graphics-based computer scheme was developed that determines suitable locations for a workpiece, and its associated task-motion, in the dexterous workspace of a three-hinged planar robotic workcell. It determines all acceptable positions for the first joint of the robot relative to the workpiece; therefore, all solutions are represented as an area in two dimensions, unlike existing methods of motion-planning that present them as a volume in a three-dimensional joint-space for the same planar robot. This simplifies the solution-space by reducing its dimension from three to two. The method differentiates between the constraints that singular configurations, workspace boundaries, the excursion-range of one full turn at the third rotary joint, and physical obstacles impose on the design of a planar robotic workcell, thus giving a better understanding of the global properties and physical limitations of the workcell. 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 can be applied to either open or closed motion trajectories. Applications include the design of robotic workcells that are used for fusion welding and for deposition of adhesives, where, in each case, the attitude of the end-effector is as important to the task as is the path that a point on the tool follows.