Citation: Leopaldi, M.; Brugo, T.M.; Tabucol, J.; Zucchelli, A. Parametric Design of an Advanced Multi-Axial Energy-Storing-and-Releasing Ankle–Foot Prosthesis. Prosthesis 2024, 6, 726–743. https://doi.org/10.3390/ prosthesis6040051 Academic Editor: Arnab Chanda Received: 10 April 2024 Revised: 31 May 2024 Accepted: 7 June 2024 Published: 24 June 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Article Parametric Design of an Advanced Multi-Axial Energy-Storing-and-Releasing Ankle–Foot Prosthesis Marco Leopaldi 1,2 , Tommaso Maria Brugo 1, * , Johnnidel Tabucol 1 and Andrea Zucchelli 1 1 Department of Industrial Engineering, University of Bologna, 40131 Bologna, Italy; marco.leopaldi@unibo.it (M.L.); johnnidel.tabucol2@unibo.it (J.T.); a.zucchelli@unibo.it (A.Z.) 2 Interdepartmental Centre for Industrial Research in Advanced Mechanical Engineering Applications and Materials Technology, University of Bologna, 40131 Bologna, Italy * Correspondence: tommasomaria.brugo@unibo.it; Tel.: +39-349-254-5001 Abstract: The ankle joint is pivotal in prosthetic feet, especially in Energy-Storing-and-Releasing feet, favoured by individuals with moderate to high mobility (K3/K4) due to their energy efficiency and simple construction. ESR feet, mainly designed for sagittal-plane motion, often exhibit high stiffness in other planes, leading to difficulties in adapting to varied ground conditions, potentially causing discomfort or pain. This study aims to present a systematic methodology for modifying the ankle joint’s stiffness properties across its three motion planes, tailored to individual user preferences, and to decouple the sagittal-plane behaviour from the frontal and transverse ones. To integrate the multi-axial ankle inside the MyFlex-η, the designing of experiments using finite element analysis was conducted to explore the impact of geometric parameters on the joint’s properties with respect to design constraints and to reach the defined stiffness targets on the three ankle’s motion planes. A prototype of the multi-axial ankle joint was then manufactured and tested under FEA-derived load conditions to validate the final configuration chosen. Composite elastic elements and complementary parts of the MyFlex-η, incorporating the multi-axial ankle joint, were developed, and the prosthesis was biomechanically tested according to lower limb prosthesis ISO standards and guidelines from literature and the American Orthotic and Prosthetic Association (AOPA). Experimental tests showed strong alignment with numerical predictions. Moreover, implementing the multi-axial ankle signifi- cantly increased frontal-plane compliance by 414% with respect to the same prosthesis with only one degree of freedom on the sagittal plane without affecting the main plane of locomotion performance. Keywords: multi-axial ankle joint; lower-limb prosthesis; prosthetic foot; energy-storing-and- releasing prosthesis; finite element analysis (FEA); design of experiments (DOE); regression analysis; biomechanics 1. Introduction Currently, Energy-Storing-and-Releasing (ESR) feet are the most widespread foot prostheses, particularly for individuals with lower-limb amputations exhibiting ambulatory level K3 (active individuals not restricted to low-cadence walking, unlike K2-ambulatory- level amputees) and K4 (sports activities individuals). ESR feet are simple and energy- efficient devices made of composite elastic elements in carbon and/or glass-fiber-reinforced plastic (CFRP/GFRP). They store elastic energy in the mid-stance phase and release it during the push-off phase, partially reducing the metabolic energy cost of the gait [1]. Certain ESR feet incorporate an ankle joint to provide wider range of motion (ROM) and enhance ankle power in the sagittal plane while concurrently alleviating contralateral limb load [2], offering a smoother rollover and easier ambulation on stairs and ramps [3]. Most ESR feet on the market offer only the sagittal-plane degree of freedom (DOF), a limitation that may pose challenges in adapting the user to diverse ground conditions and may lead to gait asymmetry, which may increase torsional stress on the stump [4], gait instability [5], discomfort or pain [6] and skin breakdown [7]. Daily activities, such as turning steps and Prosthesis 2024, 6, 726–743. https://doi.org/10.3390/prosthesis6040051 https://www.mdpi.com/journal/prosthesis