3-UPU-1-S Parallel Mechanism for Biomechanical Emulation of Human Ankle Motion in a Transtibial Prosthesis: Mechanical Design, Kinematic Evaluation, and Control Implementation

The human ankle exhibits complex multiplanar behavior involving plantarflexion, dorsiflexion, inversion, eversion, and coupled orientation changes that are essential for balance and terrain adaptation. This work presents the design, kinematic evaluation, mechanical implementation, and control validation of a transtibial prosthesis based on a parallel robotic mechanism. Three candidate architectures, 3-SPS-1-S, 3-UPU-1-S, and 3-UCU-1-S, were compared through inverse and forward kinematics, orientational workspace, Jacobian conditioning, constructability, and mechatronic-integration criteria. The corresponding workspace coverages were 74.1%, 75.7%, and 72.2%, respectively. The 3-UPU-1-S architecture exhibited a median Jacobian condition number of 12.63, a 95th-percentile value of 20.56, no numerically singular configurations within the evaluated feasible workspace, and the highest VDI-2225 technical score (0.913), supporting its final selection. The selected mechanism was manufactured and integrated into a functional laboratory prototype with distributed ESP32-S3-based electronics, position sensing, inertial measurement, and closed-loop actuation. Experimental periodic tests showed that the decentralized PID controller achieved dominant-axis RMSE values of 3.53° in pitch during dorsiflexion–plantarflexion and 4.61° in roll during inversion–eversion. A revised formal LQRI controller was evaluated separately using the identified actuator-space model. Its nominal closed-loop system was asymptotically stable, with maxRe(λ)=−1.6896, and robustness simulations showed mean-RMSE reductions of approximately 9.4–16.6% relative to PID across the evaluated perturbation scenarios. These results demonstrate the feasibility of the proposed 3-UPU-1-S mechanism as an integrated laboratory platform for multiplanar transtibial-prosthesis research while identifying the need for future dynamic load-bearing and user-centered validation.