Loop-Constrained Connectivity Calculation for Planar Multi-Loop Mechanisms: Base–End-Effector Localization and Functional-Constraint Screening

Planar multi-loop mechanisms often generate a large number of non-isomorphic candidate topological graphs during automatic synthesis, making it difficult to efficiently identify configurations that satisfy engineering-oriented functional requirements. To address this issue, a loop-constrained connectivity calculation method and a connectivity-based localization and screening procedure are proposed. The proposed connectivity calculation is directly formulated for general planar non-fractionated kinematic chains (NFKCs), including those with multiple joints. For planar fractionated kinematic chains (FKCs), however, the present method is not applied directly at the full-system level, but only to decomposed non-fractionated subchains after system-level decomposition. Starting from a structurally admissible set of candidate topological graphs, a connectivity matrix is established for automatic localization of the base and the end-effector (EE). Functional screening is then performed by combining the connectivity criterion with object-oriented rules on hydraulic driving-pair arrangement and driving-redundancy patterns. The method was validated using the 10-link, 3-DOF single-joint equivalent of the KC1 subchain of a mine scaler manipulator arm. Under the prescribed structural and functional constraints, 249 admissible configurations were obtained. The results indicate that the proposed method provides an effective basis for application-oriented topological screening and subsequent dimensional synthesis.