Most existing self-supervised learning methods for skeleton-based temporal action segmentation (TAS) fail to capture the short-term motion semantics essential for dense frame-level prediction, as they typically learn representations that are either too coarse or motion-insensitive. This issue is reflected in local dimension collapse, which highlights the limitations of current approaches and suggests directions for improvement. Specifically, to address the issue of local dimension collapse for self-supervised learning in TAS, we propose the Local Dimension Enhancement (LoDE) framework, which introduces the local effective rank (LER) as a metric to measure and a learning objective to reduce this collapse. A new fine-grained representation scale, termed a motion unit, is defined as a temporal clip of consecutive skeleton frames to model skeleton data. Centered on this representation scale, we analyze existing methods (sequence-scale and frame-scale learning) with the tool of LER and theoretically demonstrate that introducing motion unit-scale learning is essential to alleviate local dimension collapse. Inspired by our theoretical insights, we design a multi-scale semantics module that integrates frame-, sequence-, and motion unit-scale learning, with LER-based regularization to enrich local representation diversity. These designs effectively alleviate local dimension collapse and lead to significant improvements in TAS, as evidenced by LoDE's superior performance over state-of-the-art methods on three large-scale untrimmed datasets: PKUMMD, TSU, and BABEL. Our project website is available at https://carefreesun.github.io/LoDE_TIP_2026/.