Vol. 29 No. 1 (2024): January-April


Biomedical Engineering

Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle

Modelo dinámico del movimiento del miembro inferior en el plano sagital durante el ciclo de marcha



Biomechanics, Euler-Lagrange, Human gait, PID control, Simulink (en).


Biomecánica, Euler-Lagrange, Marcha humana, Control PID, Simulink (es).

Abstract (en)

Context: This work presents the development of a dynamic model for human lower limb motion in the sagittal plane during the gait cycle. The primary objective of this model is to serve as a powerful tool for the design of rehabilitation and assistive devices, such as exoskeletons, prostheses, and orthoses. It achieves this by facilitating the estimation of joint torques, the detailed analysis of kinematic variables, optimal actuator selection, and the exploration of advanced control techniques.

Method: The dynamic model consists of two primary components: (1) the plant model and (2) a closed-loop controller. The plant model represents the forward dynamics of human gait and is based on a multi-mass pendulum composed of three segments of the lower limb (thigh, lower leg, and foot) and three joints (hip, knee, and ankle). It is analyzed using the Euler-Lagrange formulation and the nonlinear second-order differential equations are implemented in MATLAB’s Simulink. To reproduce reference human gait trajectories and simulate the functioning of the neuromusculoskeletal system and the central nervous system, a closed-loop PID controller is incorporated into the plant model. It is noteworthy that the scope of this dynamic model is specifically confined to the sagittal plane.

Results: The dynamic model is evaluated in terms of angular displacement tracking using the relative maximum error (RME) and the root mean square error (RMSE) for reference trajectories of healthy adult male human gait as reported in the literature. The model demonstrates tracking with errors below 2.2 [°] in magnitude and 3,5% for all three considered segments (thigh, lower leg, and foot).

Conclusions: The quantitative results show that the dynamic model developed in this work is reliable and allows for a precise reproduction of human gait trajectories.

Abstract (es)

Contexto: Este trabajo presenta el desarrollo de un modelo dinámico del movimiento del miembro inferior humano en el plano sagital durante el ciclo de marcha. El objetivo principal de este modelo es servir como una herramienta poderosa para el diseño de dispositivos de rehabilitación y asistencia, como exoesqueletos, prótesis y órtesis. Esto lo logra facilitando la estimación de torques en las articulaciones, el análisis detallado de variables cinemáticas, la selección óptima de actuadores y la exploración de técnicas avanzadas de control.

Método: El modelo dinámico se consiste en dos componentes principales: (1) el modelo de la planta y (2) un controlador de lazo cerrado. El modelo de la planta representa la dinámica directa de la marcha humana y se basa en un péndulo de múltiples masas compuesto por tres segmentos del miembro inferior (muslo, pantorrilla y pie) y tres articulaciones (cadera, rodilla y tobillo). Este es analizado utilizando la formulación de Euler-Lagrange y las ecuaciones diferenciales de segundo orden no lineales se implementan en Simulink de MATLAB. Para reproducir las trayectorias de referencia de la marcha humana y simular el funcionamiento del sistema musculoesquelético y del sistema nervioso central, se implementa un controlador PID de lazo cerrado en el modelo de la planta. Es importante destacar que el alcance de este modelo dinámico se limita específicamente al plano sagital.

Resultados: El modelo dinámico es evaluado en términos del seguimiento del desplazamiento angular usando el error relativo máximo (RME) y el error medio cuadrático (RMSE) para trayectorias de referencia de la marcha humana de adultos masculinos sanos reportadas en la literatura. El modelo demuestra un seguimiento con errores por debajo de 2.2 [°] en magnitud y 3,5 % para los tres segmentos considerados (muslo, pantorrilla y pie).

Conclusiones: Los resultados cuantitativos muestran que el modelo dinámico desarrollado en este trabajo es confiable y permite reproducir precisamente las trayectorias de la marcha humana.

Author Biography

Jose Luis Sarmiento-Ramos, Universidad Santo Tomás

Mechanical Engineer and Master of Science in Mechanical Engineering from Universidad Industrial de Santander, Bucaramanga, Colombia. From 2015 to 2016, he served as a Teaching Assistant in the School of Mechanical Engineering at Universidad Industrial de Santander, Bucaramanga, Colombia. From 2019 to 2022, he worked as Professor and Researcher in the Department of Biomedical Engineering at Universidad Manuela Beltrán, Bucaramanga, Colombia.


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How to Cite


Sarmiento-Ramos, J. L., Meneses-Castro, A. F., and Jaimes-Mantilla, P. J. (2024). Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle. Ingeniería, 29(1), e20333.


Sarmiento-Ramos, J.L. et al. 2024. Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle. Ingeniería. 29, 1 (Jan. 2024), e20333. DOI:


Sarmiento-Ramos, J. L.; Meneses-Castro, A. F.; Jaimes-Mantilla, P. J. Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle. Ing. 2024, 29, e20333.


SARMIENTO-RAMOS, Jose Luis; MENESES-CASTRO, Andrés Felipe; JAIMES-MANTILLA, Pedro José. Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle. Ingeniería, [S. l.], v. 29, n. 1, p. e20333, 2024. DOI: 10.14483/23448393.20333. Disponível em: Acesso em: 23 feb. 2024.


Sarmiento-Ramos, Jose Luis, Andrés Felipe Meneses-Castro, and Pedro José Jaimes-Mantilla. 2024. “Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle”. Ingeniería 29 (1):e20333.


Sarmiento-Ramos, J. L., Meneses-Castro, A. F. and Jaimes-Mantilla, P. J. (2024) “Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle”, Ingeniería, 29(1), p. e20333. doi: 10.14483/23448393.20333.


J. L. Sarmiento-Ramos, A. F. Meneses-Castro, and P. J. Jaimes-Mantilla, “Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle”, Ing., vol. 29, no. 1, p. e20333, Jan. 2024.


Sarmiento-Ramos, Jose Luis, et al. “Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle”. Ingeniería, vol. 29, no. 1, Jan. 2024, p. e20333, doi:10.14483/23448393.20333.


Sarmiento-Ramos, Jose Luis, Andrés Felipe Meneses-Castro, and Pedro José Jaimes-Mantilla. “Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle”. Ingeniería 29, no. 1 (January 13, 2024): e20333. Accessed February 23, 2024.


Sarmiento-Ramos JL, Meneses-Castro AF, Jaimes-Mantilla PJ. Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle. Ing. [Internet]. 2024 Jan. 13 [cited 2024 Feb. 23];29(1):e20333. Available from:

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