Actuator-level kinematic analysis of a PAM-driven dual four-bar knee exoskeleton for rehabilitation gait assistance

Stroke-related gait impairment commonly produces reduced knee coordination and insufficient toe clearance, motivating the development of compliant rehabilitation exoskeletons. Pneumatic artificial muscles (PAMs) offer compliant, biomimetic actuation well suited to rehabilitation gait training; however, existing four-bar linkage exoskeleton studies have focused on mechanism synthesis and joint-level trajectory reproduction without analytically characterising the continuous actuator-level kinematic demands that PAM actuation imposes across the gait cycle. This study develops a closed-loop kinematic framework for a PAM-driven dual four-bar knee exoskeleton, actuated by Festo DMSP-20 fluidic muscles, that maps prescribed rehabilitation knee trajectories to actuator displacement and contraction-rate demands at the preliminary design stage. The mechanism was reconstructed from the KNEXO structural concept using MotionGen simulation and modelled analytically through vector loop-closure analysis and Freudenstein’s equation. A continuous quartic stroke-map formulation was introduced to replace repeated inverse-kinematic computation with a single analytical expression, enabling efficient actuator evaluation throughout the gait cycle. The reconstructed mechanism reproduced the normative knee trajectory with a root-mean-square error of 2.69° over the eight gait-event boundaries, with all gait-event angles remaining within the Perry normative variability band and Freudenstein loop-closure residuals below 5% for both the primary and secondary mechanisms. All PAM contractions remained below 20% of the nominal actuator length, within the 25% practical operating limit of the selected actuator, while the quartic stroke-map reproduced the actuator-contraction relationship with root-mean-square errors of 0.23 cm and 0.37 cm. The proposed framework provides designers with an analytical tool for evaluating actuator contraction displacement, contraction-rate demands, and transmission kinematics in dual four-bar rehabilitation exoskeletons before committing to hardware fabrication.