Branch-reachable and quasistatic two-layer optimization design of an underactuated five-bar mechanism for adhesion-peeling tasks

Underactuated closed-loop mechanisms exploit passive internal degrees of freedom to improve configurational adaptability, but an active input often cannot uniquely determine the passive configuration, creating a gap between configuration-level potential and mechanically realized motion. Existing optimization methods usually prescribe active-passive coupling or perform full quasistatic analysis for every candidate; the former may restrict passive adjustment under load and contact, whereas the latter is computationally expensive. This paper proposes a branch-reachable/quasistatic two-layer optimization method for an underactuated five-bar suction mechanism performing adhesion-peeling tasks. The first layer constructs a branch-reachable stable domain in the active-passive configuration space and screens candidates using ordered adhesion-peeling functional state regions. The second layer uses a quasistatic model to confirm stable paths under a single active input and determine an optimized candidate. The method reduces quasistatic evaluations by 96.45% and validates the optimized candidate. Theoretical and statistical analyses show that quasistatic paths are continuous subpaths of the branch-reachable stable domain and that the configuration-level score enriches feasible and high-performing designs. This provides an efficient framework for screening and confirming underactuated linkage designs governed by ordered functional-state tasks.