Admissible motions of special manipulators

Special manipulators are those manipulators whose inverse kinematics can be solved through equations of degree two. In this paper, it is shown that each C sheet of a special manipulator contains only one inverse kinematic solution continuation. The joint space of such manipulators can be completely described using concepts of conjugate and neighboring C sheets. It is also shown that all inverse kinematic solution branches of the special manipulators can be distinctly separated and identified inside the work space and related to the C sheets in the joint space. In the paper, a theory is developed for determining admissibility of inverse kinematics dependent paths of special manipulators with or without joint motion limitations. Examples of trajectory planning of special manipulators are provided for illustration