This paper presents a novel approach for recognizing and interpreting dimensions in engineering drawings. It starts by detecting potential dimension frames, each comprising only the line and text components of a dimension, then verifies them by detecting the dimension symbols. By removing the prerequisite of symbol recognition from detection of dimension sets, our method is capable of handling low quality drawings. We also propose a reconstruction algorithm for rebuilding the drawing entities based on the recognized dimension annotations. A coordinate grid structure is introduced to represent and analyze two-dimensional spatial constraints between entities; this simplifies and unifies the process of rectifying deviations of entity dimensions induced during scanning and vectorization.