Mechanism development has traditionally relied on designers’ experience and intuition, creating subjective processes. While systematic methodologies following Hartenberg and Denavit’s three-stage approach provide structured frameworks for mechanism synthesis through kinematic chain enumeration and evaluation, contemporary methods lack systematic classification of practical mechanical characteristics. This absence constrains computational filtering development, maintaining designer-dependent processes with considerable subjectivity. This study presents a novel methodology for automating kinematic chain filtering in number synthesis through topological requirements that enable systematic observation and quantification of characteristics in state-of-the-art mechanisms via graph analysis. The methodology comprises nine stages introducing topological requirements categorized into degree requirements (DR), subchain requirements (SR), and relationship requirements (RR). The C-paths concept for classifying kinematic pairs and subchain classification into isolated and shared categories are introduced. Computational algorithms filter chains based on these requirements, validated through three case studies: vehicle rear suspension, finger exoskeletons, and excavator articulated arms. Results demonstrate substantial candidate reduction while preserving viable solutions: rear suspension from 35 to 6 graphs, exoskeleton from 6,856 to 117 chains, and excavator from 83,547 to 1,235 solutions. The approach eliminates human error and enables systematic evaluation with enhanced precision and efficiency, establishing a more structured, objective, and computationally efficient design process for mechanism synthesis.