Kinematic Analysis for a Planar Redundant Serial Manipulator

A planar serial manipulator with three rotational joints (planar 3R) can be seen to be a kinematically redundant system if only the position of the end-effector is taken into account. Configuration sets of serial manipulators of planar 3R will be considered in this work in detail. The configuration set is the solution set of all rotational joint angles (actually, we use the tangent of the half-angle) fulfilling the kinematic mapping. Then the configuration set will be an algebraic set if we fix the end-effector or the end-effector follows algebraic motions (for instance, algebraic curves in the special Euclidean group). We show the characteristic of configuration curves among the workspace in terms of the number of real connected components. The configuration curve has either one connected component or two connected components. Furthermore, we also studied the torque variation among the real connected components of the configuration set.