Type synthesis of closed-loop robots for machining and manufacturing of complex quadric surfaces

Abstract This paper presents a general approach to synthesizing closed-loop robots for machining and manufacturing of complex quadric surfaces, such as toruses, helicoids, and helical tubes. The proposed approach begins by employing finite screw theory to describe the motion sets generated by prismatic, rotational, and helical joints. Subsequently, generatrices and generating lines are put forward and combined for type synthesis of serial kinematic limbs capable of generating single-DoF translations along spatial curves and two-DoF translations on complex quadric surfaces. Following this manner, the two-DoF translational motion patterns on these complex quadric surfaces are algebraically defined and expressed as finite screw sets. Type synthesis of close-loop robots having the newly defined motion patterns can thus be carried out based upon analytical computations of finite screws. As application of the presented approach, closed-loop robots for machining toruses are synthesized, resulting in four-DoF and five-DoF standard and derived limbs together with their corresponding assembly conditions. Additionally, brief descriptions of robots for machining helicoids and helical tubes are provided, along with a comprehensive list of all the feasible limbs for these kinds of robots. The robots synthesized in this paper have promised applications in machining and manufacturing of spatial curves and surfaces, enabling precise control of machining trajectories ensured by mechanism structures and achieving high precision with low cost.