Inertial coupling between swing and stance legs shapes ankle torque profile during running

Abstract

The spring-loaded inverted pendulum (SLIP) model has effectively explained center of mass (CoM) and ground reaction force (GRF) dynamics during human gait despite its simplicity, describing both walking and running within the same mechanical principles. A recent study extended the explanatory capability of the SLIP model to joint dynamics by reproducing ankle joint dynamics during walking. However, during running, the model did not capture the empirical ankle torque profile, suggesting that such mechanical unification may not hold at the joint level. Because the previous model represented the body as a single point mass, it neglected leg inertia, which may become important during running as rapid motion generates substantial angular momentum. To address this limitation, we propose an extended two-mass model that separates the whole-body mass into the swing-leg and the remaining body mass, thereby explicitly incorporating swing-leg inertia into stance-leg joint dynamics. The swing leg is modeled using a linear spring and a torsional spring at the hip joint for its radial and rotational motion. Through inertial coupling, swing-leg dynamics influence the stance-leg ankle torque. Consequently, the proposed model reproduces the symmetric, single-peaked ankle torque profile observed experimentally while preserving the CoM and GRF of the previous model. These findings suggest that the discrepancy of the previous model during running may be explained by the omission of swing-leg inertia. By accounting for the gait-mode-dependent contribution of swing-leg inertia, the proposed model provides a unified mechanical framework for extending simple gait models from CoM-level behavior to joint dynamics.