并联式球面变胞机构及其完整雅可比矩阵

Parallel Spherical Metamorphic Mechanism and Its Complete Jacobian Matrix

提出了一种球面变胞机构。该机构采用并联连接方式,由动平台、静平台、3个环形支链和1个中间变胞支链组成,通过变胞支链提供不同约束,机构可演变为正常构态和变胞构态两种机构形式。正常构态时,动平台相对静平台具有3个转动自由度,等效于3自由度球面机构;变胞构态时,动平台具有一个额外的径向移动自由度。以螺旋理论为基础,首先分析机构的自由度数目和性质;其次,构建机构的运动子矩阵和约束子矩阵,并将约束子矩阵和运动子矩阵联立,建立完整的6×6雅可比矩阵;最后,分析雅可比矩阵的秩,得到机构产生奇异位形的条件,研究奇异位形的类型,提出避免发生奇异的方法,为机构设计提供理论依据。

A spherical metamorphic mechanism with parallel structure was proposed. It consisted of a moving platform, a base plate and four connecting legs between moving platform and base plate. Three of these legs had the same structure named circle legs and the other one named middle leg. Spherical metamorphic mechanism could transform to normal configuration and metamorphic configuration respectively with the change of constraint applied by middle leg. The moving platform was in possession of three revolute degrees of freedom which equivalent to spherical joint and extra translational freedom in the direction of radius. Based on screw theory, the mobility of this mechanism was analyzed firstly. Secondly, the constraint sub-matrix and actuation sub-matrix were obtained and the complete Jacobian matrix was established by integrating these two sub-matrices. In the end, the singular conditions of spherical metamorphic mechanism were analyzed by investigating the ranks of the complete Jacobian matrix and methods used to avoid the occurrence of singularities were given which were propitious to mechanical design.