平面含复铰及齿轮-连杆运动链的拓扑结构自动综合可为机构方案创新设计提供各种优选类型，是研究机构结构组成的有效方法，是构思、发明新机构的基础。研究平面含复铰和齿轮-连杆运动链的多色拓扑图描述及借助拓扑图描述实现的单开链迭加结构自动综合方法。详细地讨论平面含复铰和齿轮-连杆运动链的双色拓扑图和三色拓扑图描述，为机构的分析与综合提供良好的数学工具。借助于相应的多色拓扑图描述，给出综合相应输入参数的基于单开链迭加的平面含复铰及齿 轮-连杆运动链结构自动综合方法，并给出相应的综合实例来验证该自动综合方法的有效性及可靠性。

Topological structural synthesis of planar multiple joint and geared-linkage kinematic chains which can provide various comparable schemes for innovative mechanism designs; it is an effective method to researching the structure composition of mechanisms. Multicolor topological graph descriptions and structural automatic synthesis of planar multiple joint and geared-linkage kinematic chains based on single-open-chains adding method is discussed. Multicolor topological graphs of planar multiple joint and a geared-linkage kinematic chain are discussed in detail, which provide good mathematical tool for mechanism structure analysis and synthesis. With the help of multicolor topological graphs, planar multiple joint and geared-linkage kinematic chains with specified input parameters can be automatically synthesized in batch by the single-open-chains adding method. Finally, the comprehensive examples are given to verify the validity and reliability of the automatic synthesis method.