Accuracy Analysis of a 3-DOF Mechanism with Joint Clearances Under Different Working Modes
This paper presents an analytical investigation on the positioning accuracy of a planar 3DOF 3-R RR parallel mechanism with multiply joint clearances, in which eight working modes of the mechanism are included. The joint clearance is treated as a mass-les
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Abstract This paper presents an analytical investigation on the positioning accuracy of a planar 3DOF 3-RRR parallel mechanism with multiply joint clearances, in which eight working modes of the mechanism are included. The joint clearance is treated as a mass-less virtual link in the analysis. Assuming that the clearance size is much smaller than the geometric size of the mechanism, a simplified expression of the output errors is obtained by the kinematic analysis of the planar 3-RRR parallel mechanism. The error boundary for a given position of the mechanism and the maximum error distribution in the whole workspace is plotted out. The results show that the proposed method is an efficient way to predicate the positioning error of the 3-RRR mechanism with joint clearances under different working modes. Keywords 3-RRR mechanism modes
Joint clearance Accuracy analysis Working
1 Introduction Parallel robots are increasingly used for precision positioning, in which accuracy is of great importance in such application. The pose errors of a parallel mechanism are due to many factors [1–4]: manufacturing and assembling tolerances, flexibility of the links, input uncertainties and the clearances between the joint components. The manufacturing and assembly errors are considered predictable and can be compensated by calibration; the flexibility can be eliminated by adopting more rigid X. Zhang (&) School of Design, South China University of Technology, Guangzhou 510006, China e-mail: [email protected] X. Zhang Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, South China University of Technology, Guangzhou 510640, China e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 X. Zhang et al. (eds.), Mechanism and Machine Science, Lecture Notes in Electrical Engineering 408, DOI 10.1007/978-981-10-2875-5_96
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structures; the input uncertainties are determined by the actuators; while the influence of joint clearances are stochastic and unavoidable. In this paper, we address the problem of computing the accuracy of a planar parallel mechanism in the presence of joint clearances. Several methods have been developed to evaluate the accuracy of serial and parallel mechanisms. Yu et al. [5] showed a simple geometric approach to compute the exact local maximum position and orientation error caused by actuator inaccuracies, this method only works for special planar parallel mechanisms. Briot and Bonev [6, 7] presented an interval analysis method which is based on a detailed error analysis of the parallel robots, in which the Hessian matrix is used. In these two studies, only the input error is taken into consideration. For the purpose of predicting the influences of the joint clearance on the output errors, Innocenti [8] and Parenti-Castelli and Venanzi [9, 10] used the virtual work method to determine the position of the end-effector when a given external load is applied. After that, Venanzi and Parenti-Castelli [11–13] presented a general
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