This study is on the enumeration of spatial robotic manipulators, which is an essential basis for a companion study on dimensional synthesis, both of which together present a wider utility in manipulator synthesis. The enumeration of manipulators is done by using adjacency matrix concept. In this paper, a novel way of applying adjacency matrix to spatial manipulators with four types of joints, namely revolute, prismatic, cylindrical and spherical joints, is presented. The limitations of the applicability of the concept to 3D manipulators are discussed. 1-DOF (Degree Of Freedom) manipulators of four links and 2-DOF, 3-DOF and 4-DOF manipulators of three links, four links and five links, are enumerated based on a set of conventions and some assumptions. Finally, 96 1-DOF manipulators of four links, 641 2-DOF manipulators of 5 links, 4 2-DOF manipulators of three links, 8 3-DOF manipulators of four links and 15 4-DOF manipulators of five links are presented.

翻译：本研究针对空间机器人机械臂的枚举问题展开，该工作是后续机械臂尺寸综合研究的重要基础，二者共同为机械臂综合提供了更广泛的应用价值。采用邻接矩阵概念实现机械臂的枚举。本文提出了一种将邻接矩阵应用于包含四种关节类型（旋转关节、棱柱关节、圆柱关节和球面关节）的空间机械臂的新方法，并探讨了该概念在三维机械臂中适用性的局限性。基于一系列约定规则和假设条件，对四连杆单自由度机械臂以及三连杆、四连杆、五连杆的二自由度、三自由度和四自由度机械臂进行了枚举。最终得到：四连杆单自由度机械臂96种、五连杆二自由度机械臂641种、三连杆二自由度机械臂4种、四连杆三自由度机械臂8种、五连杆四自由度机械臂15种。