Kinematic Parameters Auto-Calibration of Redundant Planar 2-DOF Parallel Manipulator

Parallel manipulators have the advantage of high speed and high precision in the theory of mechanisms. This has opened up broad possibilities for the use of parallel manipulators in many fields. But in real applications, due to the inevitable manufacturing tolerances and assembling errors, the actual kinematic parameters of parallel manipulators are always unequal to the nominal values and calibration procedures have to be implemented to compensate the kinematic parameter errors between them. According to the metrology devices adopted, calibration methods of parallel manipulators can be classified into two categories, the external calibration methods and the autocalibration methods. External calibration methods rely on the precise external 3D measuring devices, such as laser tracking systems (Koseki et al., 1998; Vincze et al., 1994), mechanical devices (Jeong et al., 1999) and camera systems (Zou & Notash, 2001; Renaud et al., 2006). With these external devices, one can measure the end-effector position of parallel manipulators and calibrate the kinematic parameters by minimizing either the errors between the measured end-effector positions and the estimated end-effector positions (Masory et al., 1993), or the errors between the measured joint positions and the estimated joint positions (Zhuang et al., 1995; Zhuang et al., 1998). The auto-calibration methods rely on the redundant joint sensors of parallel manipulators, which can be achieved by adding extra sensors to the uninstrumented joints (Baron & Angeles, 1998; Zhuang, 1997; Wampler et al., 1995; Patel & Ehmann, 2000), or by constraining the motion of end-effector or some joints (Khalil & Besnard, 1999; Wang & Masory, 1993). With the redundant joint sensors, extra information can be obtained for the sampled configurations without employing any external measuring devices (Hollerbach & Wampler, 1996; Yiu et al., 2003c; Chiu & Perng, 2004), and the auto-calibration procedure is usually implemented by minimizing a function of closed-loop constraint errors. Obviously, it is more convenient to measure the sampled configurations by the redundant joint sensors than the external 3D measuring devices. especially for the parallel manipulator with inherent redundant joint sensors. But it is