In this work we propose a new way to group screw systems into types or families based on an objective criterion. Specifically, we propose that families of screw systems should be distinguished by their symmetry groups. This does not affect the standard classification of screw systems as given by Gibson and Hunt in [1, 2], it is just a slight modification of the types used in the literature. To this end we review the various different groupings that have been made in the past and find the symmetry groups of every class of screw system.
This work presents a higher-order kinematic formulation for planar compliant mechanisms based on epicyclic pseudo-rigid models of flexible hinges. A compliant four-bar linkage is transformed into an equivalent epicyclic pseudo-rigid four-bar linkage (E-PR4B), for which position, velocity, acceleration, and jerk equations are derived analytically. The formulation determines instantaneous poles, Bresse circles, polodes, the cubic of stationary curvature, and the Ball point, extending classical rigid-body kinematic tools to compliant systems. These invariants are used in an output-port synthesis procedure to identify coupler points providing prescribed motion characteristics, focusing on locally straight-line trajectories. The methodology is assessed through two case studies differing in scale, hinge topology, and material, and validated against nonlinear flexible multibody models. Overall agreement is obtained for the kinematic invariants and synthesized trajectories: maximum pointwise trajectory deviations remain below 5% of each mechanism’s characteristic length over the investigated ranges, although a larger Ball-point location error is observed in the first case study. The framework provides a geometry-based route to the analysis and synthesis of compliant mechanisms with higher-order motion requirements.
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.
