Multi-configuration recognition of a 3-RSR parallel mechanism with zero-torsion characteristics based on screw algebra and high-order kinematics

Abstract

In this paper, a comprehensive high-order kinematic analysis of a geometrically symmetric 3-RSR parallel mechanism is conducted based on screw algebra. A screw-based modeling framework is first established to represent the pose and evaluate the mobility under zero-torsion characteristics, revealing the mechanism's intrinsic 2R1T motion pattern. The bifurcation configurations of the 3-RSR mechanism under singularity are then identified, deriving five distinct motion modes: decoupled limb-swinging, parallel translation, two interfering rotational modes, and axis rotation. Eleven bifurcated motion branches are subsequently derived through high-order velocity constraints and symmetry extension. In particular, a complete symmetry-based configuration space is constructed for the first time, which enables systematic recognition and classification of multimodal motion. Moreover, the feasibility of connectivity among motion branches is verified through constraint screw evolution. These findings not only deepen the understanding of singularity-induced bifurcations in reconfigurable parallel mechanisms, but also establish the constraint principles that govern configuration transitions of reconfigurable parallel mechanisms under singular configurations.