A novel 5-DoF Interconnected-Chains PKM for manufacturing of revolute surfaces

The paper presents the novel architecture of a 5-DoF parallel kinematics mechanism, purposely conceived for accurate machining of conical revolute surfaces. The industrial interest of this kind of operation is remarkable, e.g. for production of optical equipments. The proposed architecture belongs to the class of Interconnected-Chains Parallel Kinematics Machines, IC-PKMs, since the moving platform is connected to the fixed base not by independent serial chains, but by interconnected chains. The end-effector behaves like a spindle; its mobility consists of three rotational freedoms around a spherical center of rotation (one is the rotation about the spindle axis) and two translational freedoms in a plane of the pencil of planes defined by a fixed axis (revolute axis) through the spherical center of rotation. While one actuator commands the location of the spherical center of rotation along the revolute axis and one actuator provides the rotation about the spindle axis, the three other actuators command the orientation of the spindle and its heave along the spindle axis. The revolute axis also represents the revolution axis of the machined surface. For Hybrid Chain Manipulators the inverse position analysis is relatively trivial, while the direct position analysis is much more difficult; on the contrary, for IC-PKMs both direct and inverse position analyses are expressed by coupled systems of algebraic equations. The paper discusses the architecture of the mechanism and the possible approaches to direct and inverse kinematics. Two different possible mechanism layouts are proposed. The end-effector mobility and the Jacobian operator are provided and analyzed by means of the screw theory.