High-fidelity interactive digital assets are essential for embodied intelligence and robotic interaction, yet articulated objects remain challenging to reconstruct due to their complex structures and coupled geometry-motion relationships. Existing methods suffer from instability in geometry-motion joint optimization, while their generalization remains limited on complex multi-joint or out-of-distribution objects. To address these challenges, we propose GEAR, an EM-style alternating optimization framework that jointly models geometry and motion as interdependent components within a Gaussian Splatting representation. GEAR treats part segmentation as a latent variable and joint motion parameters as explicit variables, alternately refining them for improved convergence and geometric-motion consistency. To enhance part segmentation quality without sacrificing generalization, we leverage a vanilla 2D segmentation model to provide multi-view part priors, and employ a weakly supervised constraint to regularize the latent variable. Experiments on multiple benchmarks and our newly constructed dataset GEAR-Multi demonstrate that GEAR achieves state-of-the-art results in geometric reconstruction and motion parameters estimation, particularly on complex articulated objects with multiple movable parts.