Síntesis de levas mediante funciones polinomiales para simular el ciclo de marcha de una persona
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Date
2024
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Universidad Nacional de Trujillo
Abstract
La presente investigación tuvo por objetivo diseñar un perfil de leva capaz de simular con precisión el ciclo de marcha humano. La investigación se centró en identificar y modelar los puntos críticos del ciclo de marcha, que son los máximos y mínimos de la fuerza ejercida por una persona en un ciclo de 0,5 segundos. Se determinaron seis puntos críticos (𝑃1 a 𝑃6) y se dividió el ciclo en dos segmentos; en el primero se incluye las fases de subida-bajada-subida-bajada (𝑃1 a 𝑃5), se empleó una función polinomial de grado 8 para definir el desplazamiento del seguidor de la leva, derivando esta función tres veces para obtener la velocidad, la aceleración y la sobreaceleración. En el segundo segmento (𝑃5 a 𝑃6), el seguidor permanece en reposo, con desplazamiento, velocidad y aceleración nulos. Se utilizaron estas funciones polinomiales para generar gráficos que representan el desplazamiento, la velocidad, la aceleración y la curva fuerza versus tiempo. Los resultados mostraron que el diseño del perfil de la leva cumple con la ley fundamental de levas, garantizando que no haya fuerzas de impacto entre la leva y el seguidor. Las dimensiones de la leva establecen un radio primario 𝑅𝑝 de 3 pulgadas, una excentricidad 𝜀 de 0 pulgadas, un radio de seguidor 𝑅𝑓 de 1 pulgada, y un radio de base 𝑅𝑏 de 2 pulgadas; el ángulo de presión máximo obtenido fue de 26,6° en la subida y −25,7° la bajada. El perfil resultante de la leva fue modelado en SolidWorks. La investigación proporciona un método detallado para diseñar y modelar el perfil de una leva que puede simular con precisión el ciclo de marcha humano, utilizando una aproximación polinómica, proporcionando una herramienta útil para mejorar la eficiencia y precisión en diversas aplicaciones biomecánicas.
The objective of this research was to design a cam profile capable of accurately simulating the human gait cycle. The research focused on identifying and modeling the critical points of the gait cycle, which are the maximums and minimums of the force exerted by a person over a 0.5-second cycle. Six critical points (𝑃1 to 𝑃6) were determined, and the cycle was divided into two segments. In the first segment, which includes the phases of rise-fall-rise-fall (𝑃1 to 𝑃5), an 8th-degree polynomial function was used to define the cam follower's displacement, and this function was derived three times to obtain velocity, acceleration, and jerk. In the second segment (𝑃5 to 𝑃6), the follower remains at rest, with zero displacement, velocity, and acceleration. These polynomial functions were used to generate graphs representing displacement, velocity, acceleration, and the force versus time curve. The results showed that the cam profile design meets the fundamental cam law, ensuring that there are no impact forces between the cam and the follower. The cam dimensions establish a primary radius 𝑅𝑝 of 3 inches, an eccentricity 𝜀 of 0 inches, a follower radius 𝑅𝑓 of 1 inch, and a base radius 𝑅𝑏 of 2 inches; the maximum pressure angle obtained was 26.6° on the rise and −25.7° on the fall. The resulting cam profile was modeled in SolidWorks. This research provides a detailed method for designing and modeling a cam profile that can accurately simulate the human gait cycle using a polynomial approximation, offering a useful tool to improve efficiency and accuracy in various biomechanical applications.
The objective of this research was to design a cam profile capable of accurately simulating the human gait cycle. The research focused on identifying and modeling the critical points of the gait cycle, which are the maximums and minimums of the force exerted by a person over a 0.5-second cycle. Six critical points (𝑃1 to 𝑃6) were determined, and the cycle was divided into two segments. In the first segment, which includes the phases of rise-fall-rise-fall (𝑃1 to 𝑃5), an 8th-degree polynomial function was used to define the cam follower's displacement, and this function was derived three times to obtain velocity, acceleration, and jerk. In the second segment (𝑃5 to 𝑃6), the follower remains at rest, with zero displacement, velocity, and acceleration. These polynomial functions were used to generate graphs representing displacement, velocity, acceleration, and the force versus time curve. The results showed that the cam profile design meets the fundamental cam law, ensuring that there are no impact forces between the cam and the follower. The cam dimensions establish a primary radius 𝑅𝑝 of 3 inches, an eccentricity 𝜀 of 0 inches, a follower radius 𝑅𝑓 of 1 inch, and a base radius 𝑅𝑏 of 2 inches; the maximum pressure angle obtained was 26.6° on the rise and −25.7° on the fall. The resulting cam profile was modeled in SolidWorks. This research provides a detailed method for designing and modeling a cam profile that can accurately simulate the human gait cycle using a polynomial approximation, offering a useful tool to improve efficiency and accuracy in various biomechanical applications.
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Keywords
Síntesis de levas, Funciones polinomiales, Simulación, Fuerzas de marcha