Trajectory-Based Motion-Plane Modeling in Sports Biomechanics: A Comprehensive Review of Computational and Analytical Approaches

The purpose of this review was to evaluate the current literature using plane-based analyses to describe open-chain proximal-to-distal sport motions and to clarify how these approaches can extend to other activities to advance biomechanical assessment. Open-chain sport motions typically rely on a coordinated rotational axis that allows momentum to be transferred efficiently through the kinetic chain. Although this directional organization is central to performance, most biomechanical studies have relied on discrete, event-based variables rather than modeling the continuous trajectory structure of the movement. This review summarizes applications of motion-plane models in sports and discusses how their conceptual foundations can apply to other movements. Four primary approaches for deriving optimal-fit planes from three-dimensional trajectories are described: Principal Component Analysis (PCA), Singular Value Decomposition (SVD), Orthogonal Least Squares (OLS), and the Functional Swing Plane (FSP). These methods rely on different algebraic formulations to model kinematic trajectories. By comparing their mathematical foundations, strengths, and limitations, we highlight how plane-based models provide a meaningful perspective for examining movement efficiency, movement strategy, and potential injury risk across open-chain proximal-to-distal sports. Future research should apply these models across multiple sports to generate individualized trajectory planes, quantify plane deviation, and integrate measures of joint loading and performance, and may combine models to build motion planes.