Abstract
Error modeling is the foundation of a kinematic calibration which is a main approach to assure the accuracy of parallel manipulators. This article investigates the influence of error model on the kinematic calibration of parallel manipulators. Based on the coupling analysis between error parameters, an identifiability index for evaluating the error model is proposed. Taking a 3PRS parallel manipulator as an example, three error models with different values of identifiability index are given. With the same parameter identification, measurement, and compensation method, the computer simulations and prototype experiments of the kinematic calibration with each error model are performed. The simulation and experiment results show that the kinematic calibration using the error model with a bigger value of identifiability index can lead to a better accuracy of the manipulator. Then, an approach of error modeling is proposed to obtain a bigger value of identifiability index. The study of this article is useful for error modeling in kinematic calibration of other parallel manipulators.
Highlights
A parallel manipulator has become a research hot spot and attracting more and more attentions from both academia and industry after the parallel machine tool Hexapod was proposed in 1994.1 Compared with a serial manipulator, a parallel manipulator shows the characteristics of high stiffness–weight ratio,[2] high adaptability to circumstance,[3] high-response rate,[4] and high-speed motions[5,6] because of its structure feature
The simulation and experiment results show that the maximum output error after calibrated by error models (EMs) 3 with 3 1⁄4 92 % is smaller than the one after calibrated by EM 2 with 2 1⁄4 75 %, and the maximum output error after calibrated by EM 2 with 2 1⁄4 75 % is smaller than the one after calibrated by EM 1 with 1 1⁄4 50 %
One may see that a kinematic calibration adopting the EM with a bigger value improves the accuracy of parallel manipulators more significantly, which proves the validity of the proposed identifiability index
Summary
A parallel manipulator has become a research hot spot and attracting more and more attentions from both academia and industry after the parallel machine tool Hexapod was proposed in 1994.1 Compared with a serial manipulator, a parallel manipulator shows the characteristics of high stiffness–weight ratio,[2] high adaptability to circumstance,[3] high-response rate,[4] and high-speed motions[5,6] because of its structure feature. A plenty of scholars[11,12,13,14] all adopted LSM to solve geometrical error parameters in the kinematic calibrations of different parallel manipulators. Three basic formats of single error vector for describing one link are proposed These three basic formats are developed on every link vector for establishing an EM and the maximum total number of identification error parameters in an EM is determined. Single error vector of one link is developed on every link vectors of the parallel manipulator and the maximum total number of identification error parameters is determined. The maximum total number of identification error parameters above mentioned can be obtained if a parallel manipulator is given. The EM including output error parameters and geomecos’ À sin’ 0 cos 3 sin trical error parameters is obtained in the following
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