| Citation: | NIE Liangyi, DING Huafeng, WANG Jun, et al. Branch graph method for crank judgement of complex multi-loop linkage[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(10): 1863-1874. doi: 10.13700/j.bh.1001-5965.2021.0152(in Chinese)
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Crank judgement is an important link in kinematic analysis of mechanisms, which determines the motion state of the mechanism. The existing Grashof theorem and N-bar rotation theorem can well solve the problem of crank judgement of single closed-loop linkage with only R joints, but there is no general and effective solution for crank judgement of complex multi-loop linkage widely used in aerospace. A branch graph identification method for determining the crank of complex multi-loop linkage is proposed. This method first determines the first sufficient condition for the existence of the crank through the inequality of the link relationship of each loop in the complex multi-loop linkage, and then determines the second sufficient condition for the existence of the crank by combining the branch graph of the linkage with the rotation range of the movable joint. On the basis of summing up the sufficient conditions, this method is used to analyze the planar 4R and 5R linkages, and the outcomes are compared with the existing recognized results, verifing the effectiveness of this method. Finally, the crank judgment is carried out on a complex multi-loop Stephenson six-bar linkage with only rotating pairs, which proves the feasibility of the method.
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