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Optimal Design of the Three-Degree-of-Freedom Parallel Manipulator in a Spray-Painting Equipment

  • Guang Yu (a1) (a2), Jun Wu (a1) (a2), Liping Wang (a1) (a2) and Ying Gao (a1) (a2)


Spray-painting equipments are important for the automatic spraying of long conical objects such as rocket fairing. This paper proposes a spray-painting equipment that consists of a feed worktable, a gantry frame and two serial–parallel mechanisms and investigates the optimal design of PRR–PRR parallel manipulator in serial–parallel mechanisms. Based on the kinematic model of the parallel manipulator, the conditioning performance, workspace and accuracy performance indices are defined. The dynamic model is derived using virtual work principle and dynamic evaluation index is defined. The conditioning performance, workspace, accuracy performance and dynamic performance are involved in multi-objective optimization design to determine the optimal geometrical parameters of the parallel manipulator. Furthermore, the geometrical parameters of the gantry frame are optimized. An example is given to show how to determine these parameters by taking a long object with conical surface as painted object.


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[1]Yu, Y. Q., Du, Z. C., Yang, J. X. and Li, Y, “An experimental study on the dynamics of a 3-RRR flexible parallel robot,” IEEE Trans. Rob. 27(5), 992997 (2011).
[2]Wu, J, Chen, X. L. and Wang, L. P., “Design and dynamics of a novel solar tracker with parallel mechanism,” IEEE-ASME Trans. Mechatr. 21(1), 8897 (2016).
[3]Gosselin, C and Angeles, J, “The optimal kinematic design of a planar three-degree-of-freedom parallel manipulator,” J. Mech. Transm. Autom. Des. 110(1), 3541 (1988).
[4]Yu, G, Wu, J and Wang, L, “Stiffness model of a 3-DOF parallel manipulator with two additional legs,” Int. J. Adv. Rob. Syst. 11(10), 173 (2014).
[5]Yu, G, Wang, L, Wu, J, Wang, D and Hu, C, “Stiffness modeling approach for a 3-DOF parallel manipulator with consideration of nonlinear joint stiffness,” Mech. Mach. Theory 123, 137152 (2018).
[6]Wang, L, Yu, G and Wu, J, “A comparison study on the stiffness and natural frequency of a redundant parallel conveyor and its nonredundant counterpart,” Adv. Mech. Eng. 9(11), 1687814017733690 (2017).
[7]Wu, J, Wang, J, Wang, L and Li, T, “Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy,” Mech. Mach. Theory 44(4), 835849 (2009).
[8]Daniali, H. R. M., Zsombormurray, P. J. and Angeles, J, “Singularity analysis of planar parallel manipulators,” Mech. Mach. Theory 30(5), 665678 (1995).
[9]Bonev, I. A., Zlatanov, D and Gosselin, C. M., “Singularity analysis of 3-DOF planar parallel mechanisms via screw theory,” Trans. ASME J. Mech. Des. 125(3), 573581 (2003).
[10]Ji, Z. M., “Study of planar three-degree-of-freedom 2-RRR parallel manipulators,” Mech. Mach. Theory 38(5), 409416 (2003).
[11]Ider, S. K., “Singularity robust inverse dynamics of planar 2-RPR parallel manipulators,” Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 218(7), 721730 (2004).
[12]Huang, T, Li, M, Li, Z, Chetwynd, D. G. and Whitehouse, D. J., “Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index,” IEEE Trans. Rob. Autom. 20(3), 538543 (2004).
[13]Shao, Z. F., Tang, X. Q., Wang, L. P. and Sun, D. F., “Atlas based kinematic optimum design of the Stewart parallel manipulator,” Chin. J. Mech. Eng. 28(1), 2028 (2015).
[14]Kelaiaia, R, Zaatri, A and Company, O, “Multiobjective optimization of 6-dof UPS parallel manipulators,” Adv. Rob. 26(16), 18851913 (2012).
[15]Huang, T, Li, Z. X., Li, M, Chetwynd, D. G. and Gosselin, C. M., “Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations,” J. Mech. Des. 126(3), 449455 (2004).
[16]Xu, Q and Li, Y, “Design and analysis of a new singularity-free three-prismatic-revolute-cylindrical translational parallel manipulator,” Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 221(5), 565577 (2007).
[17]Hao, F and Merlet, J. P., “Multi-criteria optimal design of parallel manipulators based on interval analysis,” Mech. Mach. Theory 40(2), 157171 (2005).
[18]Liu, X. J., Li, J and Zhou, Y. H., “Kinematic optimal design of a 2-degree-of-freedom 3-parallelogram planar parallel manipulator,” Mech. Mach. Theory 87, 117 (2015).
[19]Kelaiaia, R, Company, O and Zaatri, A, “Multiobjective optimization of a linear delta parallel robot,” Mech. Mach. Theory 50, 159178 (2012).
[20]Wu, J, Chen, X. L., Wang, L. P. and Liu, X. J., “Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor,” Nonlinear Dynam. 78(1), 241250 (2014).
[21]Zhao, J. S., Chu, F. L. and Feng, Z. J., “Singularities within the workspace of spatial parallel mechanisms with symmetric structure,” Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 224(2), 459472 (2010).
[22]Merlet, J. P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” Trans. ASME J. Mech. Des. 128(1), 199206 (2006).
[23]Wu, C, Liu, X. J., Wang, L and Wang, J, “Optimal design of spherical 5R parallel manipulators considering the motion/force transmissibility,” J. Mech. Des. 132(3), 3100231010 (2010).
[24]Liu, X. J., Wang, J and Pritschow, G, “On the optimal kinematic design of the PRRRP 2-DoF parallel mechanism,” Mech. Mach. Theory 41(9), 11111130 (2006).
[25]Ma, O and Angeles, J, “Optimum Architecture Design of Plat-Form Manipulators,” Fifth International Conference on IEEE Robots in Unstructured Environments, ICAR, Pisa (1991) pp. 11301135.
[26]Xu, Q and Li, Y, “Error analysis and optimal design of a class of translational parallel kinematic machine using particle swarm optimization,” Robotica 27(1), 6778 (2009).
[27]Ider, S. K., “Singularity robust inverse dynamics of planar 2-RPR parallel manipulators,” Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 218(7), 721730 (2004).
[28]Wu, J, Gao, Y, Zhang, B and Wang, L, “Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment,” Rob. Comput. Integr. Manuf. 44, 199207 (2017).
[29]Tyapin, I and Hovland, G, “Kinematic and elastostatic design optimisation of the 3-DOF Gantry-Tau parallel kinematic manipulator,” Model. Identif. Control 30(2), 3956 (2009).
[30]Stamper, R. E., Tsai, L. W. and Walsh, G. C., “Optimization of a Three DOF Translational Platform for Well-Conditioned Workspace,” Proceedings of International Conference Robotics and Automation New Mexico, vol. 4 (1997) pp. 32503255
[31]Zhao, J. S., Liu, X, Feng, Z. J. and Dai, J. S., “Design of an Ackermann type steering mechanism,” Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 227(11), 25492562 (2013).


Optimal Design of the Three-Degree-of-Freedom Parallel Manipulator in a Spray-Painting Equipment

  • Guang Yu (a1) (a2), Jun Wu (a1) (a2), Liping Wang (a1) (a2) and Ying Gao (a1) (a2)


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