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

가상 작업의 원리는 하중이 가해진 여러 개의 연결된 강체가 있는 기계에 적용하여 이와 관련된 문제를 해결할 수 있습니다.
토글 바이스를 생각해 보십시오., 중간점에 힘이 가해지면 바이스에 나무 블록이 가해지는 반력이 발생합니다.
자유물체 다이어그램에서는 마찰이 무시되고 양의 가상 변위가 고려됩니다.
좌표 축 시스템을 선택하고 양수 및 음수 증분을 정의합니다.
왼쪽 점의 반력과 수직력은 이 변위 동안 작동하지 않습니다.
결과적으로 적용된 힘과 반력에 의해 수행된 가상 작업만 계산하면 됩니다.
각도 세타로 좌표를 표현하고 미분함으로써 두 힘의 총 가상 작업을 결정할 수 있습니다.
총 가상 작업을 0으로 설정하면 바이스에 나무 블록이 가하는 반력에 대한 방정식이 제공됩니다.

<ol>
	<li>히벨러, R.C. (2016). 엔지니어링 역학: 정적. 14판, 뉴저지: 피어슨. 섹션 11.1, pp. 586-587.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. 및 Self, B.P. (2016). 엔지니어를 위한 벡터 역학. 제 11 판, 뉴욕 : McGraw-Hill Education. 578-579쪽.</li>
</ol>

연결된 강체 시스템을 위한 가상일

가상일은 연결된 여러 강체를 포함하는 문제를 해결하는 데 사용되는 강력한 방법입니다. 시스템이 평형 상태에 있을 때 가상일은 0입니다. 이것은 시스템이 가상변위를 겪을 때 생기는 힘을 계산할 수 있게 해줍니다. 이러한 시스템을 분석하려고 할 때는 먼저 자유 물체 도표를 사용하고, 여기서 독립 좌표는 링크의 구성을 나타내고 양의 가상변위로 인해 편향된 위치를 표시합니다.
다음으로 자유 물체 도표의 고정된 점으로부터 위치 좌표를 측정하고 일을 하는 힘을 향하도록 합니다. 이를 통해 각 가상변위를 독립적인 좌표로 표현할 수 있습니다. 다음 단계는 가상일의 방정식을 작성하여 합력과 모멘트를 결정하는 데 도움이 됩니다. 여기서 주의해야 할 점은 힘이나 우력 모멘트가 양의 가상변위 방향으로 작용하면 이들의 일이 양의 가상일로 결정된다는 것입니다. 그렇지 않으면 음의 가상일이 된다는 것입니다.
이 방법을 사용하면 여러 개의 연결된 강체로 구성된 시스템을 포함하는 문제를 해결하는 데 사용할 수 있다는 것이 가장 큰 장점입니다. 이 시스템들은 하나의 좌표를 사용하여 링크의 배열을 완전히 지정할 수 있기 때문에 각각 하나의 자유도만 가지고 있다고 합니다. 이것은 복잡한 계산을 크게 단순화하고 복잡한 시스템 내에서 서로 다른 변수들이 서로 어떻게 관련되어 있는지 더 잘 이해하도록 도와줍니다. 
일반적으로 여러 연결된 강체가 포함된 평형 문제를 분석적으로 평가하는 작업은 가상일을 통해 효과적으로 수행할 수 있으므로 정확한 답변뿐만 아니라 내부 작업에 대한 명확한 통찰력을 얻을 수 있습니다.

가상 작업은 여러 개의 연결된 강체와 관련된 문제를 해결하는 데 사용되는 강력한 방법입니다. 시스템이 평형 상태일 때 가상 작업은 ...

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

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Virtual Work

가상일

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position. Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In...

work of a couple moment

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,...

mechanical efficiency of real machines

Friction’s Role in Machine Efficiency

Mechanical efficiency shows how well a machine turns input work into output work. It is calculated as the ratio of output work to input work. An ideal machine has an efficiency of one, which means the input work equals the output work. Real machines are never perfectly ideal because some energy is lost. Friction is one of the main causes of that loss. In a toggle vise used to compress wooden blocks, the sliding block rubs against the horizontal plane and creates friction. To find the...

conservative forces

Conservative Forces and Path-Independent Work

Conservative forces are forces whose work depends only on an object’s starting and ending positions. The path between those positions does not change the amount of work done. This idea is important in mechanical engineering because it helps describe how energy moves through a system. A conservative force also conserves energy in the sense that its work is path independent. Gravity is one example. Electrostatic forces and springs modeled by Hooke’s law are also examples. A ball rolling down a...

potential energy

Gravitational and Elastic Energy Stored

Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum. For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational...

potential-energy criterion for equilibrium

potential-energy-criterion-for-equilibrium

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...

stability of equilibrium configuration

Types of Equilibrium in Mechanical Systems

Types of equilibrium in mechanical systems are stable, neutral, and unstable. These three cases help explain how a structure or object responds when it is pushed slightly away from balance. They are important for predicting whether a system will return to its original position, stay where it is, or move farther away. Stable equilibrium occurs when a system returns toward its original position after a small displacement. In this case, the potential energy is at a minimum. A cantilever beam...

one-degree-of-freedom system

Spring-Mass Motion and Energy Stability

A one-degree-of-freedom system uses a single independent variable to describe its state and behavior. In mechanical engineering, this kind of model helps explain how parts in a larger system respond to force. It also gives engineers a way to predict motion before a design is built in real life. A simple harmonic oscillator is one example of a one-degree-of-freedom system. A mass attached to a spring moves along one axis, and that position determines the system’s state. The spring force makes...

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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