A general formulation for calculating where a kinematic structure must be positioned (and oriented) is presented. This study is applicable to both humans; to place a human in a working environment while minimizing stress on extremity joints, or for robot manipulators. In recent years, there has been focused interest on ergonomics and ergonomic design with emphasis on the disposition of a worker while performing tasks at prolonged periods of time and where repetitive motions are exerted. To a great extent, the effect of stress on a joint is major factor leading to potential injuries. We believe there is a unique opportunity for the mechanical engineering community to make a significant contribution to this field. Furthermore, because the ergonomic design process encompasses many parameters, it is evident that it must be formulated using optimization methods where the best possible solution is calculated from an infinite number of solutions. This study presents a rigorous formulation for placement of a worker based on minimizing the torque (as a cost function) induced at a joint, whereby satisfying constraints imposed by the given task. The reverse of this problem is the calculation of the coordinates of a number of target points in the reachable space of a fixed kinematic structure, which is also addressed. Both problems are mathematically formulated and numerically solved. Examples are illustrated.

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