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

Il principio del lavoro virtuale può essere applicato a macchine con più corpi rigidi collegati sotto carico per risolvere i problemi ad esso coinvolti.
Si consideri una morsa a ginocchiera, in cui viene applicata una forza nel suo punto medio, con conseguente forza di reazione esercitata dal blocco di legno sulla morsa.
Nel diagramma a corpo libero, l'attrito viene trascurato e viene considerato uno spostamento virtuale positivo.
Scegliere un sistema di assi di coordinate e definire gli incrementi positivi e negativi.
Le forze di reazione nel punto sinistro e la forza normale non funzionano durante questo spostamento.
Di conseguenza, è necessario calcolare solo il lavoro virtuale svolto dalle forze applicate e di reazione.
Esprimendo le coordinate in termini di angolo theta e differenziando, è possibile determinare il lavoro virtuale totale di entrambe le forze.
Impostando il lavoro virtuale totale a zero si ottiene l'equazione per la forza di reazione esercitata dal blocco di legno sulla morsa.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica: Statica. Quattordicesima edizione, New Jersey: Pearson. Sezione 11.1, pp. 586-587.</li>
	<li>Birra, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Meccanica vettoriale per ingegneri. Undicesima edizione, New York: McGraw-Hill Education. Pagine 578-579.</li>
</ol>

lavoro virtuale per un sistema di corpi rigidi collegati

Il lavoro virtuale è un metodo potente utilizzato per risolvere problemi che coinvolgono diversi corpi rigidi collegati. Quando il sistema è in equilibrio, il lavoro virtuale è zero. Ciò consente di calcolare le forze risultanti quando un sistema subisce uno spostamento virtuale. Quando si tenta di analizzare un tale sistema, in primo luogo, si utilizza un diagramma dei corpi liberi, in cui una coordinata indipendente rappresenta la configurazione dei collegamenti e si segna la sua posizione deflessa, risultante dallo spostamento virtuale positivo.

Successivamente, si misurano le coordinate di posizione da un punto fisso sul diagramma dei corpi liberi e orientarli verso le forze che compiono il lavoro. Ciò consente di esprimere ogni spostamento virtuale in termini di coordinata indipendente. Il passo successivo è scrivere l'equazione del lavoro virtuale, che aiuta a determinare le forze e i momenti risultanti. È anche importante notare che se una forza o un momento a coppia agisce lungo la direzione dello spostamento virtuale positivo, allora il loro lavoro è determinato come lavoro virtuale positivo; altrimenti, è un lavoro virtuale negativo.

Il principale vantaggio nell'utilizzare questo metodo è che può essere utilizzato per risolvere problemi che coinvolgono un sistema di diversi corpi rigidi collegati. Ognuno di questi sistemi ha un solo grado di libertà poiché l'arrangiamento dei collegamenti può essere completamente specificato utilizzando una sola coordinata. Ciò semplifica notevolmente i calcoli complessi e aiuta a comprendere meglio come diverse variabili sono correlate tra loro all'interno di sistemi complessi.

In conclusione, valutare analiticamente i problemi di equilibrio che coinvolgono più corpi rigidi collegati può essere fatto in modo efficace con il lavoro virtuale, consentendo non solo risposte accurate ma anche una chiara comprensione del loro funzionamento interno.

Lavoro virtuale per un sistema di corpi rigidi collegati

Il lavoro virtuale è un metodo potente utilizzato per risolvere problemi che coinvolgono diversi corpi rigidi collegati. Quando il sistema è in equilibrio, il lavoro virtuale è ...

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

Education

Didattica

JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Virtual Work

Lavoro virtuale

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

finding-forces-with-virtual-work-in-linked-bodies

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virtual work

Virtual Work in Force Equilibrium

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement. A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by...

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,...

principle of virtual work: problem solving

principle-of-virtual-work-problem-solving

Virtual Work for Finding Unknown Forces

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Conservative Forces and Path-Independent Work

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potential energy

Gravitational and Elastic Energy Stored

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Stable Equilibrium Through Potential Energy

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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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