The effectiveness of deep neural network models is intricately tied to the distribution of training data. However, in pose estimation, potential discrepancies in root joint positions and inherent variability in biomechanical features across datasets are often overlooked in current training strategies. To address these challenges, a novel Hand Pose Biomechanical Model (HPBM) is developed. In contrast to the traditional 3D coordinate-encoded pose, it provides a more intuitive depiction of the anatomical characteristics of the hand. Through this model, a data normalization approach is implemented to align the root joint and unify the biomechanical features of training samples. Furthermore, the HPBM facilitates a weakly supervised strategy for dataset expansion, significantly enhancing the data diversity. The proposed normalized method is evaluated on two widely used 3D hand pose estimation datasets, RHD and STB, demonstrating superior performance compared to the models trained without normalized datasets. Utilizing ground truth 2D keypoints as input, a reduction of 45.1% and 43.4% in error is achieved on the STB and RHD datasets, respectively. When leveraging 2D keypoints from MediaPipe, a reduction in error by 11.3% and 14.3% is observed on the STB and RHD datasets.