复杂多环路连杆机构曲柄判定的分支图识别法

曲柄是连杆机构运动学分析的一个重要环节，其决定着机构的运动状态。现有的Grashof定理、N杆旋转定理可以很好地解决只含有转动副单闭环连杆机构的曲柄判定问题，但对于广泛应用于航空航天的复杂多环路连杆机构的曲柄判定，至今没有通用有效的解决手段。基于此，提出了复杂多环路连杆机构曲柄判定的分支图识别法。通过复杂多环路连杆机构内各个环路的杆件关系不等式，确定了其曲柄存在的第一个充分条件；结合连杆机构的运动分支识别图活动关节旋转范围确定了曲柄存在的第二个充分条件。在归纳了曲柄存在充分条件基础上，利用所提方法在平面4R、5R连杆机构做了实例分析，并与现有公认结果进行对比，验证了方法的有效性。在仅含转动副复杂多环路Stephenson六杆机构上进行了曲柄判定，证明了方法的可行性。 

Branch graph method for crank judgement of complex multi-loop linkage

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.