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We study 4D generation to synthesize temporally coherent sequences of 3D geometry for animation and content creation. In contrast to existing SDS-based optimization methods and video-driven animation approaches, we adopt a skeleton-driven animation framework aligned with standard industrial pipelines, which enables explicit control and editing. To this end, we propose SkelGen4D, a weakly supervised feed-forward framework for text-driven mesh animation that generates explicit skeleton motions without requiring per-frame skeleton annotations. SkelGen4D first recovers temporally consistent pseudo-skeletons from animated meshes via differentiable fitting, and then generates text-conditioned skeleton motion sequences in a feed-forward manner, further refined with Motion-GRPO to ensure temporally coherent, physically plausible, and articulated animation. We evaluate our method on two large-scale benchmarks, Truebones Zoo and Diffusion4D. Our results show that our weakly supervised skeleton modeling matches or surpasses fully supervised baselines while scaling to diverse object categories for high-quality text-driven mesh animation. Further, our method supports flexible motion editing and is aligned with standard animation production pipelines.