The kinematics and statics of manipulators

As the kinematics and statics play a very important role in determining the actuating inputs and the effective loads that the end-effector sustains, this article focuses on this issue and proposes an analytical process to study the forward and inverse kinematics and statics of spatial manipulators. As series manipulators and parallel manipulators show different features in kinematics and statics, this article discusses them separately. First, the forward and inverse velocity problems of the manipulator linkages are investigated with reciprocal screw theory. Then, the static balance conditions together with forward and inverse statics of the manipulator linkages are established through virtual power theory. In the kinematics analysis, the primary conditions for feasible motions of an end-effector are addressed through velocity screws. Illustrative examples indicate that the method proposed in this article can be used to guide the singularity identification, path planning, and feasible motion determination.