A Computational Framework for Load-Constrained Human Squat Motion with Nonlinear Joint Modeling

Human squat motion is commonly analyzed using inverse dynamics, where joint moments are computed from experimentally measured kinematics. Such analyses typically assume that the observed motion is mechanically feasible and do not explicitly account for limitations of joint moment capacity. In this study, a computational framework is proposed for the load-constrained reconstruction of squat motion that integrates kinematic motion generation with a mechanical model of moment-limited joints. The human body is represented as a multi-segment system consisting of feet, shanks, thighs, pelvis, and torso. Joint behavior is modeled using nonlinear rotational springs with bounded moment capacity, allowing elastic response followed by progressive softening when critical moments are approached. A reference squat trajectory is first generated kinematically, after which a constrained optimization problem is solved at each motion frame to obtain a mechanically admissible posture under external loading. The objective function combines trajectory tracking with joint energy contributions, while gravitational loading from a barbell applied at the shoulders introduces external work. The formulation enables automatic correction of the reference motion when joint moment limits are exceeded, resulting in mechanically admissible squat postures. Numerical examples illustrate the evolution of pelvis trajectory, torso inclination, lower-limb segment angles, and reconstructed body configurations throughout the squat cycle.