The representation and elimination of kinematic chains (KCs) with multiple joints are crucial issues to be solved in mechanism research. First, the importance of mechanical innovative design and the limitations of existing methods are introduced, then the Yan’s innovative design method is introduced, by comparing the shortcomings of traditional topological graphs in representing multiple joints, A modified graph—planar face graph (PF graph), is proposed. As a key concept, “face” has been put forward to represent the case that a single, specific relationship is incident with multiple incidents, and the concepts of adjacency and incidence matrices are defined, making the representation of multiple joints more accurate and easier for computer processing. Subsequently, a new method based on PF topology graphs and dendrograms is proposed to eliminate the multiple joints, which eliminates multiple joints by reducing constraints. Meanwhile, the generation of isomers in the elimination process and their naming rules are revealed. Furthermore, the generalization process of KCs containing multiple joints is discussed and the application of elimination of multiple joints in innovative mechanism design is illustrated by taking a typical SAR antenna deployable mechanism as an example. Finally, the innovativeness of the PF graph and its contribution to multiple joints elimination and mechanism generalization are summarized, the potential and value of this method in mechanical innovative design are demonstrated. It not only provides new theoretical support and practical tools for mechanical innovative design but also offers a new perspective and approach for research in related fields.