Force applicability of robotic mechanisms

In this paper, the statics of robotic mechanisms is discussed considering the constraints between the end effectors and the environment. In order that the end effector applies the desired force to the environment, the required joint torque of the robotic mechanism has been computed by multiplying the transposed Jacobian matrix to the desired force. However, to generate this torque is only a necessary condition and does not guarantee that it does apply the force to the environment. This paper shows a necessary and sufficient condition for the force applicability of robotic mechanisms and proves it. The necessary and sufficient condition works even for redundant manipulators and manipulators at singular states.