In this paper, we propose a novel shape-theoretic framework for dynamical analysis of human movement from 3D data. The key idea we propose is the use of global descriptors of the shape of the dynamical attractor as a feature for modeling actions. We apply this approach to the novel application scenario of estimation of movement quality from a single-marker for future usage in home-based stroke rehabilitation. Using a dataset collected from 15 stroke survivors performing repetitive task therapy, we demonstrate that the proposed method outperforms traditional methods, such as kinematic analysis and use of chaotic invariants, in estimation of movement quality. In addition, we demonstrate that the proposed framework is sufficiently general for the application of action and gesture recognition as well. Our experimental results reflect improved action recognition results on two publicly available 3D human activity databases.