Chapter 8 – Kinematics and Statics of Manipulators

Based on Chapter 4, the forward and inverse kinematics and statics of spatial manipulators are investigated. The primary conditions for feasible motions of an end effector are firstly addressed by analyzing its velocity screws. The forward and inverse velocity problems are discussed both for series and for parallel manipulators. Then, the static balance conditions together with forward and inverse statics of series and parallel manipulators are exploited by using virtual power theory. Both the forward and the inverse velocity models of the manipulators provide explicit relationship between the possible joint velocities and the end effector velocities. Similarly, the forward and the inverse statics of the manipulators represent the relationship between the affordable forces of the end effectors and driving forces of the joints. This method is particularly useful in singularity identification, path planning, and the controllability determination of series manipulators as well as parallel manipulators.