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

Das Prinzip des virtuellen Arbeitens kann auf Maschinen mit mehreren miteinander verbundenen starren Körpern unter Lasten angewendet werden, um damit verbundene Probleme zu lösen.
Stellen Sie sich einen Knebelschraubstock vor, bei dem in der Mitte eine Kraft ausgeübt wird, die zu einer Reaktionskraft führt, die vom Holzblock auf den Schraubstock ausgeübt wird.
Im Freikörperdiagramm wird die Reibung vernachlässigt und eine positive virtuelle Verschiebung berücksichtigt.
Wählen Sie ein System von Koordinatenachsen aus, und definieren Sie die positiven und negativen Inkremente.
Die Reaktionskräfte am linken Punkt und die Normalkraft machen bei dieser Verschiebung keine Arbeit.
Infolgedessen muss nur die virtuelle Arbeit der aufgebrachten und Reaktionskräfte berechnet werden.
Durch die Angabe der Koordinaten in Form des Winkeltheta und die Differenzierung kann die gesamte virtuelle Arbeit beider Kräfte bestimmt werden.
Wenn Sie die gesamte virtuelle Arbeit auf Null setzen, erhalten Sie die Gleichung für die Reaktionskraft, die der Holzblock auf den Schraubstock ausübt.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik: Statik. Vierzehnte Auflage, New Jersey: Pearson. Abschnitt 11.1, S. 586-587.</li>
	<li>Bier, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. und Self, B.P. (2016). Vektormechanik für Ingenieure. Elfte Auflage, New York: McGraw-Hill Education. S. 578-579.</li>
</ol>

virtuelle arbeit für ein system von verbundenen starren körpern

Virtuelle Arbeit ist eine leistungsstarke Methode zur Lösung von Problemen, die mehrere verbundene starre Körper betreffen. Wenn das System im Gleichgewicht ist, ist die virtuelle Arbeit null. Dies ermöglicht die Berechnung der resultierenden Kräfte, wenn ein System eine virtuelle Verschiebung durchläuft. Beim Versuch, ein solches System zu analysieren, verwenden Sie zuerst ein Freikörperdiagramm, bei dem eine unabhängige Koordinate die Konfiguration der Verbindungen darstellt, und markieren Sie ihre abgelenkte Position, die sich aus der positiven virtuellen Verschiebung ergibt. Messen Sie als Nächstes die Koordinatenpositionen von einem festen Punkt auf dem Freikörperdiagramm aus und richten Sie sie auf die Kräfte aus, die die Arbeit verrichten. Dadurch kann jede virtuelle Verschiebung in Bezug auf die unabhängige Koordinate ausgedrückt werden. Der nächste Schritt besteht darin, die Gleichung der virtuellen Arbeit aufzuschreiben, die bei der Bestimmung der resultierenden Kräfte und Momente hilft. Es ist auch wichtig zu beachten, dass bei einer Kraft oder Moment, die entlang der Richtung der positiven virtuellen Verschiebung wirkt, ihre Arbeit als positive virtuelle Arbeit bestimmt wird. Andernfalls ist es negative virtuelle Arbeit. Der Hauptvorteil dieser Methode besteht darin, dass sie zur Lösung von Problemen verwendet werden kann, die ein System aus mehreren verbundenen starren Körpern betreffen. Jedes dieser Systeme hat nur einen Freiheitsgrad, da die Anordnung der Verbindungen nur mit einer Koordinate vollständig beschrieben werden kann. Dies vereinfacht komplexe Berechnungen erheblich und hilft dabei, ein besseres Verständnis dafür zu entwickeln, wie verschiedene Variablen in komplexen Systemen miteinander zusammenhängen. Alles in allem können Gleichgewichtsprobleme, die mehrere verbundene starre Körper betreffen, mit virtueller Arbeit effektiv analytisch evaluiert werden. Dies ermöglicht nicht nur genaue Antworten, sondern auch ein klares Verständnis ihrer internen Abläufe.

Virtuelle Arbeit für ein System von verbundenen starren Körpern

Virtuelles Arbeiten ist eine leistungsfähige Methode, um Probleme zu lösen, an denen mehrere miteinander verbundene starre Körper beteiligt sind. Wenn sich das System im Gleichgewicht befindet, wird virtuelles Arbeiten ...

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

Education

Lehre

JoVE Core

Mechanical Engineering

Maschinenbau

Unit 1

Einheit 1

Virtual Work

Virtuelle Arbeit

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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

work

Work in Force and Motion

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Couple Moment Work in Rotation

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance. When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points. During the...

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

The principle of virtual work helps find unknown forces and moments in equilibrium problems. It is an important idea in mechanics and engineering. The method uses a small, hypothetical motion called a virtual displacement. If the system is in equilibrium, the work done by the forces during that displacement is zero. To apply this principle, the positions of the internal and external forces must be written in terms of one common coordinate parameter. That parameter can be an angle, a distance,...

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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

Potential energy helps determine when a mechanical system is stable at equilibrium. When a system is acted on by gravitational and elastic forces, its total potential function is the algebraic sum of gravitational potential energy and elastic potential energy. If the system is already in equilibrium and is given a small displacement, the work done on the system equals the negative of the change in potential energy between the starting and ending positions. For a virtual displacement, which is...

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Types of Equilibrium in Mechanical Systems

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stability of equilibrium configuration: problem solving

stability-of-equilibrium-configuration-problem-solving

Equilibrium Stability Through Potential Energy

Stability of equilibrium in physics and engineering can be studied by using a system’s potential energy. An equilibrium configuration is a state where the system can remain at rest. Stability describes whether the system tends to return to that state after a small disturbance. Problem solving begins by finding the equilibrium points of the system. This is done by setting the derivative of the potential energy function equal to zero and solving for the independent variable values that satisfy...

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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