Parallel manipulators have broad application prospects on hybrid machine tools. The accuracy of parallel manipulators is very important for developing its high performance. Kinematic error modelling and identification are two key processes to improve the accuracy of parallel manipulators. The traditional kinematic error modelling adopts the method of partial differentiation of the ideal kinematic model. However, the partial differentiation is pure mathematical calculation, which ignores physical meaning of error terms in each link. In the process of error identification, the Jacobian matrix obtained from the partial differentiation is usually ill-conditioned, which leads to non-convergence of the identification process. In order to solve the above problems, this paper proposes a new kinematic error modelling method and an error identification model.

Owing to the machining errors and assembly errors of parts, it is inevitable that the practical pose, including position and orientation of a single link, can not coincide with the nominal pose of the link. The basic error terms in a single link, including translational errors and rotational errors, are analyzed firstly. Based on the basic error terms in a single link, this study proposed a new kinematic error modelling method: considering the practical connection point of two adjacent links, the practical terminal point (PTP) of the former link is the practical initial point (PIP) of latter link. Each link is expressed with translational and rotational errors to obtain the practical pose of it first. Then, add the PTP of former link and the practical pose of latter link up to obtain the PTP of the latter link. Repeat the process for all the links, the kinematic error model based on the physical meaning of error terms is obtained. Next, a new error identification model based on the polynomial equations is derived from the kinematic error model. By setting all the error terms zero, the kinematic error model becomes the ideal kinematic model. Subtracting the ideal kinematic model from the kinematic error model and ignoring the high order items of error terms, the nonlinear equation between the error terms of links and the pose errors of moving platform is obtained. Expanding the nonlinear equation and replacing the error terms by polynomial equations, the proposed error identification model is obtained. Finally, after the practical pose errors are measured, the error terms of links are obtained with the inverse solution of the error identification model.

As a study case, a 3-DOF parallel tool head is adopted to verify the effectiveness of the proposed method. The 3-DOF parallel tool head is composed of a base platform, a moving platform and three chains. There are thirty-nine error terms in the kinematic error model. The quadratic polynomial is selected to establish the error identification model. With the measurement data of pose errors of moving platform, thirty-nine error terms are identified. The identified results by the proposed method are more accurate than the published truncated singular value decomposition method. After compensation, the maximum position errors in *x*, *y* and *z* directions decrease from 5.752 mm, -3.493 mm and -3.726 mm to 0.063 mm, 0.038 mm and 0.077 mm, respectively. The maximum straight-line positioning error decreases from 7.561 mm to 0.104 mm. The numerical results show that the proposed error identification model is effective and the accuracy of the 3-DOF parallel tool head improves significantly. This proposed method takes a specified parallel tool head as the study object and can be also applied to other parallel manipulators.


A New Kinematic Error Modelling and Identification Method of the Parallel Manipulator

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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