Identification of principal screws of 3-DOF parallel manipulators by quadric degeneration

This paper presents a new method for identifying the principal screws of the spatial 3-DOF parallel manipulators and discusses its kinematic characteristics using the principal screws. Firstly, the quadric equation describing all twist axes of the spatial 3-DOF parallel manipulators is established. Its principal screws are identified by using the quadric degenerating theory. Three principal axes and a center point of hyperboloid of one sheet are found out. Furthermore, the principal screws of the 3-DOF 3-RPS parallel pyramid manipulator are evaluated using this method under three different configurations of this mechanism. The planar conics representing the relations between the pitches of the output twists and the three linear inputs are described, and the three-dimensional distribution of the axes of all the twists with the same pitch is illustrated under each of the configurations. Finally, we recognize that the motions of this mechanism belong to a general third-order screw system under a general configuration. The method presented in this paper has great significance for studies of the kinematic properties of the other 3-DOF mechanisms.