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

仮想作業の原理は、荷重がかかった状態で複数の接続された剛体を持つ機械に適用して、それに関連する問題を解決することができます。
トグルバイスでは、中点に力が加えられ、木製のブロックがバイスに反力を加えることができます。
自由体線図では、摩擦は無視され、正の仮想変位が考慮されます。
座標系の座標軸を選択し、正と負の増分を定義します。
この変位中は、左ポイントの反力と垂直抗力は機能しません。
その結果、適用力と反力によって行われる仮想作業のみを計算する必要があります。
座標を角度θで表し、微分することで、両方の力の合計仮想仕事を決定できます。
仮想仕事の合計をゼロに設定すると、木製のブロックが万力に加える反力の方程式が得られます。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス:静力学。第14版、ニュージャージー州:ピアソン。セクション11.1、586-587ページ。</li>
	<li>ビール、FP、ジョンストン、ER、マズレック、DF、コーンウェル、PJおよびセルフ、BP(2016)。エンジニアのためのベクトル力学。第11版、ニューヨーク:マグロウヒル教育。578-579ページ。</li>
</ol>

連結剛体系の仮想仕事

仮想仕事は、数個の連結剛体を含む問題を解くために使用される強力な方法です。システムが平衡状態にある場合、仮想仕事はゼロになります。これにより、システムが仮想変位を受けるときの結果的な力の計算が可能になります。このようなシステムを解析しようとする場合、まず、自由物体図を使用します。自由物体図では、独立座標がリンクの配置を表し、正の仮想変位による変形後の位置を示します。

次に、自由物体図上の固定点から位置座標を測定し、仕事を行う力の方向に向けます。これにより、各仮想変位を独立座標の形式で表現することが可能になります。次に、仮想仕事の方程式を記述し、それによって結果的な力やモーメントを決定します。また、ここで重要なことは、力やモーメントが正の仮想変位の方向に作用する場合、それらの仕事は正の仮想仕事として決定されることです。それ以外の場合、負の仮想仕事となります。

この方法の主な利点は、数個の連結剛体を含む問題を解決するのに使用できることです。これらのシステムのそれぞれは、リンクの配置を1つの座標のみを使用して完全に指定できると言われています。これにより、複雑な計算が大幅に簡略化され、複雑なシステム内のさまざまな変数がどのように関連しているかをより良く理解することができます。

全体として、複数の連結剛体を含む平衡問題を解析的に評価することは、仮想仕事によって効果的に行うことができます。これにより、正確な答えだけでなく、内部の機能についても明確な理解が得られます。

バーチャルワークは、複数の接続された剛体が関係する問題を解決するために使用される強力な方法です。システムが均衡状態にあるとき、仮想作業は...

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

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Virtual Work

仮想仕事

KEY TERMS AND CONCEPTS

主要用語と概念

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 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Finding Forces with Virtual Work in Linked Bodies

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