Configuration Design of Single-Loop Non-overconstrained Mechanism with Inactive Joints

Jiali Liu1, Yong Xu1, Yong Liu1, Haoran Shi1, Xinyang Jiang1
1School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, China

Tóm tắt

In order to weaken the strict geometric constraint relationship between the axes of joints so as to reduce manufacturing/assembling errors of overconstrained mechanism, a configuration design methodology for single-loop non-overconstrained mechanism with inactive joints is proposed in this paper based on the screw theory. After completing analysis of degrees of freedom, the design principle and corresponding process of single-loop non-overconstrained mechanism with inactive joints are presented. By introducing two inactive R (R: single-degree-of-freedom revolute joint) joints to an active R joint of Goldberg overconstrained mechanism, the corresponding Goldberg non-overconstrained mechanism is obtained. It is verified that the velocities of two inactive joints in the Goldberg non-overconstrained mechanism are zero via investigating motion screws of branches. By further solving input and output kinematic parameters of Goldberg non-overconstrained mechanism, it is discovered that the overconstrained mechanism and corresponding non-overconstrained mechanism have the identical input–output relationship. Above results confirm that the overconstrained mechanism and its non-overconstrained counterpart with inactive joints are completely equivalent kinematically, which thereby demonstrate fully correctness of the configuration design principle and method of single-loop non-overconstrained mechanism proposed in this paper.

Tài liệu tham khảo

Abadi BNR, Mahzoon M, Farid M (2019) Singularity-free trajectory planning of a 3-(RP)under-barRR planar kinematically redundant parallel mechanism for minimum actuating effort. Iran J Sci Technol Trans Mech Eng 43:739–751 An P, Huang M (2002) Research on self-adjustment of planar linkage mechanism and its tolerance. China Mech Eng 23:66–75 Blanding D (2017) Precision mechanical design: principles and practice of kinematics design. Mechanical Industry Press, Beijing Chen J, Xu Y, Liu W (2019) Scale optimization of linear actuated parallel mechanism based on effective workspace ratio. Mech Des Res 35(01): 42–46 + 52 Chen CC, Li TJ, Tang YQ (2019b) Configuration synthesis of generalized mechanism based on screw theory. Iran J Sci Technol Trans Mech Eng 43:1013–1021 Craig JJ (2006) Introduction to robotics, 3rd edn. Mechanical Industry Press, Beijing Huang Z, Liu J, Li Y (2011) On the freedom of the mechanisms. Science Press, Beijing Huang Z, Zhao Y, Zhao T (2014) Advance spatial mechanism, 2nd edn. Higher Education Press, Beijing Hunt KH (1978) Kinematic geometry of mechanisms. Clarendon Press, Oxford Kong X, Gosselin C (2013) Type synthesis of parallel mechanisms. Int Adv Mech Eng Technol Lee CC, Jacques MH (2009) Uncoupled actuation of overconstrained 3T1R hybrid parallel manipulators. Robotica 27(1):103–117 Lin R, Guo W, Gao F (2015) Type synthesis of a family of novel 4-AND5- and 6-DOF Sea Lion ball mechanisms with three limbs. J Mech Robot 8(2):021023 Lv Y, Xu Y, Chen J (2019) Optimal design of kinematic performance for a novel 2R1T parallel mechanism with pantograph units. J Braz Soc Mech Sci Eng 41(8):279 Ma Z (2018) Optimization design of crank and rocker shearing mechanism. Mech Des 35(7):57–61 Raism IA, Gokhan K, Baris B (2014) Function synthesis of Bennett 6R mechanisms using Chebyshev approximation. Mech Mach Theory 81:62–78 Tingli Yang (1996) Basic theory of mechanical systems, structure, kinematics, dynamics. Mechanical Industry Press, Beijing Varshovi-Jaghargh P, Masouleh MT, Naderi D (2019) Forward kinematic analysis of parallel mechanisms in seven-dimensional kinematic space by considering limitation of passive joints motion. Iran J Sci Technol Trans Mech Eng 43:315–329 Wohlhart K (1991) Merging two general goldberg 5R linkages to obtain a new 6R space mechanism. Mech Mach Theory 26(7):659–668 Xianwen Kong (2014) Type synthesis of single-loop overconstrained 6R spatial mechanisms for circular translation. J Mech Robot 6:1–8 Xu Y, Liang Z, Liu J (2020) A new metamorphic parallel leg mechanism with reconfigurable moving platform. Math Probl Eng 2020:3234969 Yan Chen (2011) A spatial 6R linkage derived from subtractive Goldberg 5R linkages. Mech Mach Theory 46:1097–1106 Yang F (2017) Truss method for kinematic analysis of 3D overconstrained linkages and design of transformable polyhedrons. Ph.D. thesis, Tianjin University, Tianjin Yang F, Chen Y, Kang R et al (2016) Truss transformation method to obtain the non-overconstrained forms of 3D overconstrained linkages. Mech Mach Theory 102:149–166 Yu F, Gao F, Ge H (2008) Discrimination and introduction method of inactive degree of freedom. J Shanghai Jiaotong Univ 04:540–543 Zhang C, Lu Y, Geng M (2019) The kinematics analysis of a 5 degree of freedom parallel mechanism with composite spherical pair is presented. Mech Des 36(04):32–39 Zhen Huang, Ping Xia, Huafeng Ding (2004) Screws analysis of the degree of freedom of Bennett mechanism. J Yanshan Univ 03:189–191