Name: finding forces with virtual work in linked bodies
Uploaded: 2023-09-22T11:49:36.000Z
Duration: 1 min 6 s
Channel: JoVE

El principio del trabajo virtual se puede aplicar a máquinas con múltiples cuerpos rígidos conectados bajo cargas para resolver problemas involucrados en él.
Considere un tornillo de banco, donde se aplica una fuerza en su punto medio, lo que resulta en una fuerza de reacción ejercida por el bloque de madera sobre el tornillo de banco.
En el diagrama de cuerpo libre, se desprecia la fricción y se considera un desplazamiento virtual positivo.
Elija un sistema de ejes de coordenadas y defina los incrementos positivos y negativos.
Las fuerzas de reacción en el punto izquierdo y la fuerza normal no funcionan durante este desplazamiento.
Como resultado, solo es necesario calcular el trabajo virtual realizado por las fuerzas aplicadas y de reacción.
Expresando las coordenadas en términos del ángulo theta y diferenciando, se puede determinar el trabajo virtual total de ambas fuerzas.
Si se establece el trabajo virtual total en cero, se obtiene la ecuación de la fuerza de reacción ejercida por el bloque de madera sobre el tornillo de banco.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica: Estática. Decimocuarta edición, Nueva Jersey: Pearson. Sección 11.1, págs. 586 y 587.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. y Self, B.P. (2016). Mecánica vectorial para ingenieros. Undécima Edición, Nueva York: McGraw-Hill Education. Págs. 578-579.</li>
</ol>

trabajo virtual para un sistema de cuerpos rígidos conectados

El trabajo virtual es un método poderoso utilizado para resolver problemas que involucran varios cuerpos rígidos conectados. Cuando el sistema está en equilibrio, el trabajo virtual es cero. Esto permite el cálculo de las fuerzas resultantes cuando un sistema experimenta un desplazamiento virtual. Al intentar analizar dicho sistema, primero se utiliza un diagrama de cuerpo libre, donde una coordenada independiente representa la configuración de los vínculos, y se marca su posición deformada como resultado del desplazamiento virtual positivo. A continuación, se mide las coordenadas de posición desde un punto fijo en el diagrama de cuerpo libre y se dirige hacia las fuerzas que realizan el trabajo. Esto permite que cada desplazamiento virtual se exprese en términos de la coordenada independiente. El siguiente paso es escribir la ecuación del trabajo virtual, lo cual ayuda a determinar las fuerzas y momentos resultantes. También es importante tener en cuenta aquí que si una fuerza o un momento del par actúa en la dirección del desplazamiento virtual positivo, entonces su trabajo se determina como trabajo virtual positivo; de lo contrario, es trabajo virtual negativo. La principal ventaja de utilizar este método es que se puede utilizar para resolver problemas que involucran un sistema de varios cuerpos rígidos conectados. Cada uno de estos sistemas se dice que tiene solo un grado de libertad, ya que la disposición de los vínculos se puede especificar completamente utilizando solo una coordenada. Esto simplifica en gran medida los cálculos complejos y ayuda a comprender mejor cómo se relacionan entre sí diferentes variables dentro de sistemas complejos. En resumen, la evaluación analítica de problemas de equilibrio que involucran múltiples cuerpos rígidos conectados se puede hacer de manera efectiva con el trabajo virtual, lo que permite no solo obtener respuestas precisas, sino también una comprensión clara de su funcionamiento interno.

Trabajo virtual para un sistema de cuerpos rígidos conectados

El trabajo virtual es un método poderoso que se utiliza para resolver problemas que involucran varios cuerpos rígidos conectados. Cuando el sistema está en equilibrio, el trabajo virtual es ...

virtual-work-for-a-system-of-connected-rigid-bodies

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Virtual Work

Trabajo virtual

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Virtual Work for a System of Connected Rigid Bodies

finding forces with virtual work in linked bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero.

To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin.

Next, measure position coordinates from a fixed point on the diagram. Direct those coordinates toward the forces that do work. This lets each virtual displacement be written in terms of the independent coordinate. After that, write the virtual work equation to determine the resulting forces and moments.

The sign of the work depends on the direction of motion. If a force or couple moment acts along the positive virtual displacement, the work is positive. If it acts opposite that direction, the work is negative.

This method is especially helpful for systems with several connected rigid bodies because they often have only one degree of freedom. That means the full link arrangement can be described by one coordinate. Virtual work simplifies the calculations and also shows how the variables in the system are related.

Finding Forces with Virtual Work in Linked Bodies

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virtual work for a system of connected rigid bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

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Virtual Work for Finding Unknown Forces

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key terms and concepts

Learn how virtual work is used with connected rigid bodies to find forces and moments using a free-body diagram, one coordinate, and equilibrium.

Finding Forces with Virtual Work in Linked Bodies | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Finding Forces with Virtual Work in Linked Bodies

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