Abstract

In recent years, the progress in the development of parallel manipulators has been accelerated since parallel manipulators possess many advantages over their serial counterparts in terms of high accuracy, velocity, stiffness, and payload capacity, therefore allowing their wide range of applications as industrial robots, flight simulators, parallel machine tools, and micro-manipulators, etc. Generally, a parallel manipulator consists of a mobile platform that is connected to a fixed base by several limbs or legs in parallel as its name implies (Merlet, 2000). Up to now, most 6-DOF parallel manipulators are based on the Gough-Stewart platform architecture due to the aforementioned advantages. However, six DOF is not always required in many situations. Besides, a general 6-DOF parallel manipulator has such additional disadvantages as complicated forward kinematics and excessive singularities within a relatively small size of workspace. On the contrary, limited-DOF parallel manipulators with fewer than six DOF which not only maintain the inherent advantages of parallel mechanisms, but also possess several other advantages including the reduction of total cost of the device and control, are attracting attentions of various researchers. Many parallel manipulators with two to five DOF have been designed and investigated for pertinent applications. According to the properties of their output motion, the limited-DOF parallel manipulators can be classified into three categories in terms of translational, spherical, and mixed parallel manipulators. The first type allows the mobile platform a purely translational motion, which is useful as a machine tool, a positioner of an automatic assembly line, and so on. The second one enables the output platform only perform a rotational motion around a fixed point, and can be used in such situations as a telescope, an antenna, an end-effector of a robot, etc. And the last one allows the platform to both translate and rotate, and can be employed as a motion simulator, a mixed orientating/positioning tool, and others. Particularly, due to the application requirements of translational motion, translational parallel manipulators (TPMs) become the focus of a great number of researches. The most well-known TPM is the Delta robot (Clavel, 1988) whose concept then has been realized in several different configurations (Tsai et al., 1996; Li & Xu, 2005), and many other structures have been also proposed in the literature. For example, the 3-UPU, 3-RUU and 3-PUU mechanisms (Tsai & Joshi, 2002), 3-RRC structure (Zhao & Huang, 2000), 3-RPC architecture (Callegari & Tarantini, 2003), 3-CRR manipulator (Kong & Gosselin, 2002; Kim & Tsai, 2003),

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