Instantaneous kinematics and singularity analysis of three-legged parallel manipulators

Instantaneous kinematics and singularity analysis of a class of three-legged, 6-DOF parallel manipulators are addressed in this paper. A generic method of derivation of reciprocal screw and consequently, the instantaneous kinematics model is presented. The advantage of this formulation is that the instantaneous kinematics model possesses well-defined geometric meaning and algebraic structure. Singularity analysis is performed under three categories, namely forward, inverse and combined singularities. A new concept of Passive Joint Plane is introduced to correlate the physical structure of the manipulator and these geometric conditions. In the inverse kinematic analysis, a new approach is introduced. At each leg end point a characteristic parallelepiped is defined whose sides are the linear velocity components from three main joints of the leg. An inverse singularity occurs when the volume of this parallelepiped becomes zero. Examples are demonstrated using RRRS and RPRS-type parallel manipulators.