A Simplified Multibody Kinematic Model of Human Squat-to-Stand Motion in the Sagittal Plane

This paper develops a simplified multibody kinematic model of the symmetric human squat-to-stand motion in the sagittal plane. The human body is represented as a serial kinematic chain composed of the foot, shank, thigh, pelvic segment, and generalized trunk, interconnected by ideal revolute joints at the ankle, knee, hip, and lumbosacral level. A consistent set of generalized coordinates, including one absolute angle and four relative joint angles, is introduced, and explicit direct kinematic equations are derived for the characteristic points of the model. For a representative adult with standard anthropometric proportions, a literature-based nominal motion law is reconstructed and used to generate graphical dependencies describing angular displacements, velocities, accelerations, planar trajectories, and linear kinematic characteristics of the characteristic points and joints. The obtained results show that the movement is governed primarily by knee and hip extension, whereas ankle motion is smaller in amplitude but essential for balance regulation, while lumbopelvic coordination remains non-negligible. In the nominal case, the relative excursions are approximately 42∘ at the ankle, 120∘ at the knee, 110∘ at the hip, and 13∘ at the lumbosacral joint. The greatest vertical rise and the highest linear kinematic intensity are observed at the proximal point representing the lumbosacral region. The proposed formulation is analytically transparent, anatomically interpretable, and suitable for subsequent inverse-kinematic fitting, parameter identification, sensitivity analysis, predictive simulation, and future dynamic extension.