Musculoskeletal and neurological disorders are common devastating companions of ageing, leading to a reduction in quality of life and increased mortality. Gait analysis is a popular method for diagnosing these disorders. However, manually analysing the motion data is a labour-intensive task, and the quality of the results depends on the experience of the doctors. In this paper, we propose an automatic framework for classifying musculoskeletal and neurological disorders among older people based on 3D motion data. We also propose two new features to capture the relationship between joints across frames, known as 3D Relative Joint Displacement (3DRJDP) and 6D Symmetric Relative Joint Displacement (6DSymRJDP), such that relative movement between joints can be analyzed. To optimize the classification performance, we adapt feature selection methods to choose an optimal feature set from the raw feature input. Experimental results show that we achieve a classification accuracy of 84.29% using the proposed relative joint features, outperforming existing features that focus on the movement of individual joints. Considering the limited open motion database for gait analysis focusing on such disorders, we construct a comprehensive, openly accessible 3D full-body motion database from 45 subjects.