The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F & C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.
The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F & C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.
[1] K E Zanganeh, J Angeles. Instantaneous kinematics and design of a novel redundant parallel manipulator. Proceedings of IEEE International Conference on Robotics and Automation, 1994, 4: 3043-3048.
[2] H W Kim, J H Lee, H Suh, et al. Comparative study and experimental verification of singular-free algorithms for a 6 DOF parallel haptic device. Machatronics, 2005, 15(4): 403-422.
[3] H T Liu, T Huang, A Kecskeméthy, et al. Force/motion transmissibility analyses of redundantly actuated and overconstrained parallelmanipulators. Mech. Mach. Theory, 2017, 109: 126-138.
[4] J Kim, J C Hwang, J S Kim, et al. Eclipse Ⅱ: a new parallel mechanism enabling continuous 360-degree spinning plus three-axis translational motions. Robotics & Automation IEEE Transactions on, 2001, 17(4): 423-434.
[5] B J Yi. Geometric analysis of antagonistic stiffness in redundantly actuated parallel mechanisms. Journal of Robotic Systems, 1993, 10(5): 581-603.
[6] S H Lee, J H Lee, B J Yi, et al. Optimization and experimental verification for the antagonistic stiffness in redundantly actuated mechanisms: a five-bar example. Mechatronics, 2005, 15(2): 213-238.
[7] M A Adli, H Hanafusa. Effect of internal forces on stiffness of closed mechanisms. Journal of the Robotics Society of Japan, 1992, 10(1): 845-850.
[8] M A Adli, H Hanafusa. Contribution of internal forces to the dynamics of closed chain mechanisms. Robotica, 1995, 13(5): 507-514.
[9] JZ Guo, D Wang, R Fan, et al. Stiffness characteristic distribution of redundant drive parallel mechanism of 3PRS/UPS. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(4): 500-506.
[10] L Cheng, Y F Zhao, Y S Zhao. Motion control algorithm of a 5-DOF parallel machine tool. Proceedings of IEEE International Conference on Robotics and Biomimetics, Sanya, China, Dec. 15-18, 2007: 2194-2199.
[11] Y S Zhao, K J Zheng, Q C Li, et al. Kinematic analysis of 5-UPS / PRPU 5-DOF parallel machine tool. Journal of Mechanical Engineering, 2004, 40(2): 12-16. (in Chinese)
[12] D Q Kong, J Wu, T M Li, et al. Control of a 4-DOF parallel kinematic machine with actuation redundancy. Journal of Mechanical Engineering, 2009, 45(9): 152-157. (in Chinese)
[13] J Wu, J S Wang, L P Wang, et al. Dynamics and control of a planar 3-DOF parallel manipulator with actuated redundancy. Mech. Mach. Theory, 2009, 44(4): 835-849.
[14] X G Han, W Y Chen. Study on the kinematics of a new redundant actuated PKMS. 7th International Conference on Progress of Machining Technology, China, Beijing, China, 2004: 424-429.
[15] G Gogu. T1R3-type redundantly-actuated parallel manipulators. Recent Progress in Robotics: Viable Robotic Service to Human, Lecture Notes in Control and Information Sciences, 2008, 370: 79-90.
[16] G Gogu. Fully-isotropic redundantly-actuated parallel wrists with three degrees of freedom. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2007: 943-950.
[17] H B Qu. Type synthesis and parasitic motion avoidance of redundant actuated parallel mechanisms. Beijing: Beijing Jiaotong University, 2013. (in Chinese)
[18] H B Qu, Y H Liang, Y F Fang, et al. Statics and stiffness analysis of 4-RRS redundant spherical parallel mechanism. Journal of Mechanical Engineering, 2015, 51(11): 8-15. (in Chinese)
[19] S H Li, H L Cui, Y M Liu. The synthesis of eliminating redundant driving branches of internal singular three-translational parallel mechanisms. Journal of Mechanical Engineering, 2014, 50(23): 36-41. (in Chinese)
[20] F G Xie, X J Liu, T M Li. Type synthesis and typical application of 1T2R type parallel robotic mechanisms. Mathematical Problems in Engineering, 2013, 2013: 1-12.
[21] F G Xie, X J Liu, Y Zheng, et al. Type synthesis of 2T1R-type parallel kinematic mechanisms and the application in manufacturing. Robotics and Computer-Integrated Manufacturing, 2014, 30(1): 1-10.
[22] F G Xie, T M Li, X J Liu. Type synthesis of 4-DOF parallel kinematic mechanisms based on Grassmann line geometry and atlas method. Chinese Journal of Mechanical Engineering, 2013, 26(6): 1073-1081.
[23] Y Q Li, Y Zhang, Y Guo, et al. New method for type synthesis of 2R1T redundant driven parallel mechanisms. Journal of Mechanical Engineering, 2019, 55(23): 25-37. (in Chinese)
[24] Z Huang, Q C Li. Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method. Int. J. Robot. , 2003, 22(1): 59-79.
[25] Y D Xu, D S Zhang, J T Yao, et al. Type synthesis of the 2R1T parallel mechanism with two continuous rotational axes and study on the principle of its motion decoupling. Mech. Mach. Theory, 2017, 108: 27-40.
[26] M X Wang, T Huang. Type synthesis of 1T2R 3-DOF parallel mechanism. Journal of Mechanical Engineering, 2015, 51(17): 1-7.
[27] Q C Li, J M Hervé. 1T2R parallel mechanisms without parasitic motion. IEEE Trans. Rob. , 2010, 26(3): 401-410.
[28] T Sun, S F Yang, T Huang, et al. A way of relating instantaneous and finite screws based on the screw triangle product. Mech. Mach. Theory, 2017, 108: 75-82.
[29] T Sun, X M Hu. Type synthesis of 1T2R parallel mechanisms with parasitic motions. Mech. Mach. Theory, 2018, 128: 412-428.
[30] J Wei, J S Dai. Reconfiguration-aimed and manifold-operation based type synthesis of metamorphic parallel mechanisms with motion between 1R2T and 2R1T. Mech. Mach. Theory, 2019, 139: 66-80.
[31] B Monsarrat, C M Gosselin. Singularity analysis of a three-leg six-degree-of-freedom parallel platform mechanism based on Grassmann line geometry. Int. J. Robot Res. , 2001, 20(4): 312-326.
[32] S Z Li, J J Yu, G H Zong. Configuration synthesis and principal degree of freedom analysis of parallel flexible mechanisms based on screw theory. Journal of Mechanical Engineering, 2010, 46(13): 54-60. (in Chinese)
[33] J J Yu, X Pei, G H Zong. Graphical approach to creative design of mechanical devices. Beijing: Beijing Science Press, 2014. (in Chinese)
