528 KSME International Journal, Vol. 17 No. 4, pp. 528~537, 2003 Kinematic Analysis and Optimal Design of 3-PPR Planar Parallel Manipulator Kee-Bong Choi* Robot & Control Group, Intelligence & Precision Machine Dept., Korea Institute of Machinery and Materials 171, Jang-Dong, Yuseong-Gu, Daejeon, 305-343, Korea This paper proposes a 3-PPR planar parallel manipulator, which consists of three active prismatic joints, three passive prismatic joints, and three passive rotational joints. The analysis of the kinematics and the optimal design of the manipulator are also discussed. The proposed manipulator has the advantages of the closed type of direct kinematics and a void-free workspace with a convex type of borderline. For the kinematic analysis of the proposed manipulator, the direct kinematics, the inverse kinematics, and the inverse Jacobian of the manipulator are derived. Alter the rotational limits and the workspaces of the manipulator are investigated, the workspace of the manipulator is simulated. In addition, for the optimal design of the manipulator, the performance indices of the manipulator are investigated, and then an optimal design procedure is carried out using Min-Max theory. Finally, one example using the optimal design is presented. Key Words: Planar Parallel Manipulator, Kinematics, Jacobian, Workspace, Optimal Design, Min Max I. Introduction Parallel manipulators consisting of closed-loop mechanisms have many advantages compared to serial manipulators in terms of payload, accuracy, and stiffness. It is well known that parallel mani- pulators have a higher payload to-weight ratio, higher accuracy, and higher structural rigidity than serial manipulators (Ben-Horin et al., 1998). Recently some machine-tools (Kim el al., 2001 : Wang et al., 2001) have been developed utilizing these advantages. A manipulator tbr fine motion (Ryu et al., 1997) also adopted the parallel mec- hanism rather than the serial one, since the par- allel mechanism can be manufactured monolithic- ally. * E-mail : kbchoi @kimmre.kr TEL: +82 42 868 7132:FAX: +82-42 868-7135 Robot & Control Group, Intelligence & Precision Ma- chine Dept., Korea Institute of Machinery and Materials 171. Jang Dong, Yuseong-Gu, Daejeon. 305 343. Ko- rea. (Manuscript Received May 22, 2002;Revised De- cember 13, 2002) Copyright (C) 2003 NuriMedia Co., Ltd. Among the parallel manipulators, the planar parallel manipulator is a manipulator for plane motion. Planar parallel manipulators have two degree-of-freedom (DOF) motion; that is two translations, or 3-DOF motion, consisting of two translations and one rotation. It is well known that (23- 1) variations of 3-DOF planar parallel manipulators exist, which are RRR, RRP, RPR, RPP, PRR, PRP, and PPR, depending on the combinations of prismatic joints and rotational joints, excluding a PPP combination, where the prismatic and rotational joints are represented by P and R (Merlet, 1996 and 2000). The solutions of the direct kinematics lbr possible architectures of the planar parallel manipulators were also already proposed (Merlet, 1996), but more con- crete solutions and kinematic analyses of the architectures are stil! required. Most 3-DOF planar parallel manipulators have disadvantages that the manipulators have polynomial types of complex direct kinematics and small workspaces with useless voids as well as concave types of borderlines. As the order of