Abstract
The fixture layout is well known as an important factor that influen-ces the localization accuracy of the workpiece in mass production. Meanwhile, due to the existence of the uncertain errors that originated from assembly and manufacture process, the positional variability which depends on the tolerance allocation has statistical features. In this work, we propose an uncertainty approach of optimizing the fixture layout to improve overall product quality. Firstly, we analyze the deterministic localization model and static equilibrium condition by introducing related uncertainty errors. Then, using the Monte Carlo Method (MCM), we randomly assign the fixture parameters from corresponding probability distributions. Further, we compute the norm of position error of critical point according to the principles of minimum potential energy and the Nonlinear Least Square Method (NLSM). After we sequentially search the minimal mean and variance of the position error in discrete point set domain, the optimal solution of the fixture layout is obtained. Finally, a numerical example is illustrated and compared with the result of FEA simulation.
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References
Ramesh, R.M., Mannan, A., Poo, A.N.: Error compensation in machine tools — a review. Part I: Geometric, cutting-force induced and fixture-dependent errors. International Journal of Machine Tools and Manufacture 40(9), 1235–1256 (2000)
Asada, H., By, A.B.: Kinematic analysis of workpart fixturing for flexible assembly with automatically reconfigurable fixtures. IEEE Trans. Robot. Autom. 1(2), 86–93 (1985)
Wang, M.Y.: Characterizations of positioning accuracy of deterministic localization of fixtures. IEEE Trans. Robot. Autom. 18(6), 976–981 (2002)
Liu, Y.H.: Qualitative test and force optimization of 3-D frictional formclosure grasps using linear programming. IEEE Trans. Robot. Autom. 15, 163–173 (1999)
Zhu, X.Y., Ding, H.: Optimality Criteria for Fixture Layout Design A Comparative Study. IEEE Trans. Robot. Autom. 6(4), 658–669 (2009)
Yu, Z., Chew, C.M.: Efficient Procedures for Form-Clousure Grasp Planning and Fixture Layout Design. ASME J. Manuf. Sci. Eng. 131, 041010:1–11 (2009)
Xiong, Y.L., Xiong, X.R.: Algebraic structure and geometric interpretation of rigid complex fixture systems. IEEE Trans. Robot. Autom. 4(2), 252–264 (2007)
Cai, W., Hu, S.J., Yuan, J.X.: Deformable sheet metal fixturing: Principles, algorithms, and simulation. ASME J. Manuf. Sci. Eng. 118, 318–324 (1996)
Malluck, J.A., Melkote, S.N.: Modeling of deformation of ring shaped workpieces due to chucking and cutting forces. ASME J. Manuf. Sci. Eng. 126, 141–147 (2004)
Johnson, K.L.: Contact Mechanics. Cambridge Univ. Press, Cambridge (1985)
Xiong, C.H., Ding, H., Xiong, Y.L.: On Clamping Planning in Workpiece-Fixture Systems. IEEE Trans. Robot. Autom. 5(3), 407–419 (2008)
Kulankara, K., Satyanarayana, S., Melkote, S.N.: Iterative fixture layout and clamping force optimization using the Genetic Algorithm. ASME J. Manuf. Sci. Eng. 124, 119–125 (2002)
Goldberg, K.Y., Mason, M.T., Requicha, A.: Geometric Uncertainty in Motion Planning: Summary Report and Bibliography, Catalina Island, CA, June 15-17 (1992)
Xiao, J., Zhang, L.: Towards obtaining all possible contacts — growing a polyhedron by its location uncertainty. IEEE Transactions on Robotics and Automation 12(4), 553–565 (1996)
Cheah, C.C., Han, H.Y., Sawamura, S., Arimoto, S.: Grasping and position control for multi-fingered robot hands with uncertainty Jacobian Matrices. In: Proceeding of the IEEE International Conference on Robotics and Automation, pp. 2403–2408 (1998)
Wang, M.Y.: An optimal design for 3D fixture synthesis in a point-set domain. IEEE Trans. Robot. Autom. 16(6), 839–846 (2000)
Zheng, Y., Qian, W.H.: Coping with uncertainties in Force-closure analysis. International Journal of Robotics Research 24(4), 311–327 (2005)
Sanchez, H.T., Estrems, M., Faura, F.: Determination of Key workpiece product characteristics in a machining fixture using uncertainty analysis and loss cost function implementations. International Journal of Advanced Manufacturing Technology 41, 452–460 (2009)
Slocum, A.H.: Precision Machine Design. Prentice-Hall International Inc., Englewood Cliffs (1992)
Barlow, R.E., Proschan, F.: Mathmetical Theory of Reliability. Society for Industrial and Applied Mathematics (1987)
Tripp, J.: Hertian Contact in two and three Dimension. Paper NASA Tech. 2473 (1985)
Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. The Macgraw-Hill Companys Inc., New York (1970)
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Zhang, X., Yang, W., Li, M. (2010). An Uncertainty Approach for Fixture Layout Optimization Using Monte Carlo Method. In: Liu, H., Ding, H., Xiong, Z., Zhu, X. (eds) Intelligent Robotics and Applications. ICIRA 2010. Lecture Notes in Computer Science(), vol 6425. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16587-0_2
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DOI: https://doi.org/10.1007/978-3-642-16587-0_2
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