利用分形理论的3T1R混联机构型综合
Type Synthesis of 3T1R Hybrid Mechanisms Based on Fractal Theory

为综合得到三移动一转动(3T1R)混联机构,利用分形理论和机构拓扑图,提出了一种全新有效的混联机构型综合方法,主要思想是将混联构型转化为连杆机构,机构拓扑图作为连杆机构的主体,运动副作为杆件的组成元素。根据分形理论,对机构拓扑图进行有序分形,并通过输出位移子集的排列组合和适配运动副,实现了混联机构构型的多样化。提出了可用于求解复杂机构拓扑图的多路径输出的路径法则,并且规定了用于推导运动副位移子集的串并联计算方法。根据机构拓扑图和分形方式,将混联机构按有、无横向支链分为2种类型。建立了分形与混联机构的关系模型,在数理逻辑关系上使机构设计与分形理论得到了统一。采用Matlab编程的形式综合出了3T1R四自由度混联机构,实现了其中一个混联机构的构型设计,并验证了构型设计方法的正确性。
To obtain the type synthesis of three？？translational and one？？rotational (3T1R) hybrid mechanisms, an efficient synthesis methodology is proposed based on fractal theory and topological graph. The major concept of this method is to transform the hybrid mechanism into linkage mechanism, whose main frame is determined by topological graph and whose links are composed of the assignment of kinematic pairs. Fractal theory is applied to the topological graph, and the permutation and combination of output displacement set and selecting suitable kinematic pairs are conducted to achieve the configuration diversity of hybrid mechanisms. The route rule for dealing with the topological graph is proposed, and the calculation rule of union？？intersection？？preserving for deriving the kinematic pair’s output is presented. According to fractal theory and topological graph, the hybrid mechanism is classified into two types. Thereafter, a relationship model of hybrid mechanism and fractal theory is established, so the mechanical design and fractal theory are unified in mathematics and logic. Matlab is utilized in type synthesis of 3T1R hybrid mechanism, and one of the configurations is achieved, demonstrating the validity of the proposed methodology