Accurately Modeling the Output Torque and Stiffness of Ankle-Foot Orthoses with a Compliant Linkage Model

The stiffness of passive lower-limb exoskeletons and orthoses governs their assistance. A common practice in the design of these systems is to assume the stiffness of the device is determined only by the intended elastic element (e.g., spring), while the structural components, human attachments, and soft tissues are considered rigid. In practice, the mechanical behavior of orthoses is significantly affected by the compliance of these elements, which drastically impacts the assistance provided. In this work, we present a linkage model with compliant elements that can accurately predict the applied stiffness of ankle-foot orthoses, and retroactively estimate the stiffness of unintended spring elements from published data. The compliant model accurately predicted the torque trajectories of two published passive orthoses with modeled peak torques within 4 % to 7 % of measured values. In contrast, the rigid model greatly overestimated the peak torques, predicting 203 % to 376 % of the measured values. The compliant model also indicated that an onboard joint encoder could only measure 52 % to 69 % of the peak ankle angle recorded with motion capture. The compliant model was also used to reassess the stiffness range of a variable-stiffness orthosis, indicating that its adjustable range is likely 69 % of rigid model predictions. Overall, this work highlights the need to consider how unmodeled compliance affects the mechanical behavior of orthoses and provides a foundation for further exploration.