Automatic Synthesis of Planar Multi-Loop Fractionated Kinematic Chains with Multiple Joints: Topological Graph Atlas and a Mine Scaler Manipulator Case Study

Planar multi-loop fractionated kinematic chains (FKCs)—kinematic chains that can be decomposed into two or more coupled subchains by separating joints or links—are widely used in heavy-duty manipulators, yet their large design space makes automatic synthesis and application-oriented screening challenging. The novelty of this paper is a general automated synthesis-and-screening framework for planar fractionated kinematic chains, regardless of whether multiple joints are present; multiple-joint chains are handled via an equivalent transformation to single-joint models, enabling the construction of a deduplicated topological graph atlas. In the mine scaler manipulator case study, an 18-link, 5-DOF (N18_M5) FKC with two multiple joints is taken as the target and converted into a single-joint equivalent N20_M7 model consisting of three subchains (KC1–KC3). Atlases of the required non-fractionated kinematic chains (NFKCs) for KC1 and KC3 are generated according to their link counts and DOFs. The subchains are then combined as building blocks under joint-fractionation (A-mode) and link-fractionation (B-mode) to enumerate fractionated candidates, and a WL-hash-based procedure is employed for isomorphism discrimination to obtain a non-isomorphic N20_M7 atlas. Finally, a connectivity-calculation-based screening is performed under task-driven structural and functional constraints, yielding 249 feasible configurations for the overall manipulator arm. The proposed pipeline provides standardized representations and reproducible outputs, offering a practical and transferable route from large-scale enumeration to engineering-feasible configuration sets for planar multi-loop FKCs, including those with multiple joints.