Motion generators of quadric surfaces

Abstract

This paper presents research work on synthesis of the mechanisms that generate translations on circular, cylindrical, and conical surfaces. As these three kinds of surfaces are all basic quadrics, the synthesized mechanisms are called motion generators of quadric surfaces. Firstly, the characteristics of these quadrics are analyzed, which result in an easy way to express them. Secondly, the motion sets of one-degree-of-freedom (one-DoF) joints are described by finite screws, leading to a simple and non-redundant manner for mechanisms’ motion description. Based upon this, the motion generators of circular, cylindrical, and conical surfaces are respectively synthesized, and all the serial kinematic chains that generate these quadrics are obtained. The results are verified through simulations in MATLAB software. Finally, as an application of the motion generators of quadrics, closed-loop linkages constituted by the generators of cylindrical and circular surfaces with specific geometric conditions are synthesized, which purely generate one-DOF translations along ellipse curves. Some new serial kinematic chains and closed-loop linkages are invented in this paper. These new mechanisms have simple mechanical structures, and they have potential applications in design of robots used in machining and manufacturing of complex surfaces and curves.