This thesis, titled "Passive Dynamic System for Energy Returning on Transtibial Prosthesis," by Edwin Nikolay Prieto Parrado, is a doctoral dissertation in Engineering from the Universidad Nacional de Colombia. The research focuses on developing a customizable, low-cost transtibial prosthesis that can store and return energy during the gait cycle, particularly during the initial contact phase, to improve the walking performance and energy efficiency of amputees. The study begins with a literature review, highlighting the gap between bionic and energy storage and return (ESR) prostheses, emphasizing the need for more affordable and efficient solutions, especially in developing countries. The research then delves into the characterization of ankle dynamics in amputees and able-bodied individuals, using gait data from various studies to compare the quasi-stiffness (QS) of the ankle joint. A dynamic model of the ankle-foot prosthesis is developed, based on the ISO 22675 standard, and a global sensitivity analysis is performed to identify the most influential design variables (shape, size, and laminate thickness). A surrogate-model-based optimization algorithm, specifically Bayesian optimization, is applied to find the optimal design variables that maximize the mechanical net work during the final stance phase. The results show that the proposed passive dynamic system can achieve significant energy return, comparable to or better than active prostheses, at a lower cost and with fewer maintenance requirements. The thesis concludes with a discussion on the implications of the findings, including the potential for additive manufacturing to customize the prosthesis for individual users, and the limitations of the study, such as the inability to validate the model with real-world experiments due to resource constraints. Overall, the research aims to provide a comprehensive framework for designing and optimizing low-cost, energy-efficient transtibial prostheses, particularly for users in developing countries who may not have access to advanced, expensive prosthetic devices.This thesis, titled "Passive Dynamic System for Energy Returning on Transtibial Prosthesis," by Edwin Nikolay Prieto Parrado, is a doctoral dissertation in Engineering from the Universidad Nacional de Colombia. The research focuses on developing a customizable, low-cost transtibial prosthesis that can store and return energy during the gait cycle, particularly during the initial contact phase, to improve the walking performance and energy efficiency of amputees. The study begins with a literature review, highlighting the gap between bionic and energy storage and return (ESR) prostheses, emphasizing the need for more affordable and efficient solutions, especially in developing countries. The research then delves into the characterization of ankle dynamics in amputees and able-bodied individuals, using gait data from various studies to compare the quasi-stiffness (QS) of the ankle joint. A dynamic model of the ankle-foot prosthesis is developed, based on the ISO 22675 standard, and a global sensitivity analysis is performed to identify the most influential design variables (shape, size, and laminate thickness). A surrogate-model-based optimization algorithm, specifically Bayesian optimization, is applied to find the optimal design variables that maximize the mechanical net work during the final stance phase. The results show that the proposed passive dynamic system can achieve significant energy return, comparable to or better than active prostheses, at a lower cost and with fewer maintenance requirements. The thesis concludes with a discussion on the implications of the findings, including the potential for additive manufacturing to customize the prosthesis for individual users, and the limitations of the study, such as the inability to validate the model with real-world experiments due to resource constraints. Overall, the research aims to provide a comprehensive framework for designing and optimizing low-cost, energy-efficient transtibial prostheses, particularly for users in developing countries who may not have access to advanced, expensive prosthetic devices.