CCUP based on precession polishing process is a novel polishing

http://dx.doi.org/10.1016/j.rcim.2016.08.003 0736-5845/& 2016Published by Elsevier Ltd.

method proposed and developed by Walker et al. [13,14]. Unlike traditional CCP technology, the precession polishing process makes use of compliant tooling controlled by air pressure. Due to the compliance of the tool, the fitproblembetweenthe tooling and the workpiece in the traditional CCP polishing method can be solved. The position and orientation of tooling in space is orche- strated by a machine tool with an open kinematic chain and se- rially connected links. Zeeko Ltd. has developed a series of In- telligent Robotic Polishers (IRP) for this process. However, the constructions of these machines are based on serial manipulators. The motions of the actuators require high accuracy because of the cumulative error effect of the serial manipulator. Furthermore, to minimize processing time, the machine needs to achieve max- imum linear traverse speed, which imposes stringent require- ments on the machine dynamics.

A parallel manipulator is one in which there exist two or more closed kinematic chains linking the base to the end effector. The parallel manipulator has some favorable characteristics compared to the serial manipulator, such as higher stiffness, higher dynamic performance, superior accuracy, low mobile masses and greater load-to-weight ratio, allowing a wide range of applications as an industrial robot and machine tool [15–20]. The most notable shortcoming of parallel manipulators is their relatively small workspaces compared with their serial counterparts. However, in an ultra-precision polishing machine in which accuracy, stiffness and dynamic performance are more important than the size of the workspace, a parallel manipulator is an alternative to a serial manipulator.

A hybrid manipulator can be a combination of a parallel ma- nipulator and a serial manipulator or a sequence of parallel ma- nipulators [21–24]. A hybrid manipulator can provide the features and possess the advantages of both serial and parallel manip- ulators. In this study, a new polishing machining structure is proposed with the precession polishing process. It is a hybrid manipulator combining a three DOF parallel module and a two DOF serial module. It is believed that a machine with the proposed hybrid structure can enhance accuracy and stiffness compared to a multi-axisserial structure.

Kinematics analysis is a common basis for mechanical design and control system development. Generally, CAM systems gen- erate tool paths by indicating the tool tip coordinates and the tool axis orientation vectors in the workpiece coordinate system. These data are transformed into position commands for the linear and rotary actuators in the machine coordinate system by the kine- matics model of the machine tool [25]. As a result, the kinematic model of the machine is the key to solving the trajectory control problem. The feed rate control, precision control, and geometric error compensation also have to use the kinematic model of the machine.

The remainder of the paper is organized as follows. The prin- ciple of the precession polishing process is introduced in Section 2, and the novel polishing machine with a hybrid manipulator is presented in Section 3. Section 4 addresses the kinematics pro- blems of the parallel module, and the kinematics problems of the serial module are resolved in Section 5. Section 6 gives an example of the movement of the actuators in the proposed hybrid manip- ulator with respect to a saddle surface. Section 7 presents some conclusions.

2. Precessionpolishing process

During the polishing process, the polishing tool is rotated about its axis as shown in Fig. 1. In the traditional polishing process, the polishing tool is vertical to the surface. As a result, the velocity profilehas azero point at thecenter ofthecontactareabetween