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

Sanal çalışma ilkesi, içerdiği sorunları çözmek için yükler altında birden fazla bağlı katı gövdeye sahip makinelere uygulanabilir.
Orta noktasına bir kuvvetin uygulandığı ve mengene üzerindeki tahta blok tarafından uygulanan bir tepki kuvveti ile sonuçlanan bir geçiş mengenesi düşünün.
Serbest cisim diyagramında, sürtünme ihmal edilir ve pozitif bir sanal yer değiştirme düşünülür.
Bir koordinat eksenleri sistemi seçin ve pozitif ve negatif artışları tanımlayın.
Sol noktadaki reaksiyon kuvvetleri ve normal kuvvet bu yer değiştirme sırasında hiçbir iş yapmaz.
Sonuç olarak, yalnızca uygulanan ve tepki kuvvetleri tarafından yapılan sanal işin hesaplanması gerekir.
Koordinatları teta açısı ve farklılaşma cinsinden ifade ederek, her iki kuvvetin toplam sanal işi belirlenebilir.
Toplam sanal işi sıfıra ayarlamak, tahta bloğun mengene üzerine uyguladığı reaksiyon kuvvetinin denklemini verir.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği: Statik. On Dördüncü Baskı, New Jersey: Pearson. Bölüm 11.1, sayfa 586-587.</li>
	<li>Bira, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. ve Öz, B.P. (2016). Mühendisler için Vektör Mekaniği. On Birinci Baskı, New York: McGraw-Hill Eğitimi. Sayfa 578-579.</li>
</ol>

bağlantılı katı cisimler sistemi İçin sanal İş

Sanal iş, birçok bağlantılı katı cisim içeren problemlerin çözümünde kullanılan güçlü bir yöntemdir. Sistem dengede olduğunda sanal iş sıfırdır. Bu, bir sistem sanal bir deplasmana uğradığında ortaya çıkan kuvvetlerin hesaplanmasını sağlar. Böyle bir sistem analiz edilmeye çalışıldığında öncelikle bağımsız bir koordinatın bağlantıların konfigürasyonunu temsil ettiği bir serbest cisim diyagramı kullanılır ve pozitif sanal deplasman sonucu sapma durumu işaretlenir.

Sonraki adım, serbest cisim diyagramındaki bir sabit noktadan pozisyon koordinatlarının ölçülmesi ve iş yapan kuvvetlere doğru yönlendirilmesidir. Bu, her sanal deplasmanın bağımsız koordinat olarak ifade edilmesine olanak sağlar. Sonraki adım ise sanal işin denklemi yazmaktır, bu denklem sonuç kuvvetlerinin ve momentlerin belirlenmesine yardımcı olur. Ayrıca burada önemli bir nokta olarak belirtmek gerekir ki, bir kuvvet veya çift moment pozitif sanal deplasman yönünde etki ediyorsa, onların işi pozitif sanal iş olarak belirlenir; aksi halde, negatif sanal iş olarak belirlenir.

Bu yöntemin temel avantajı, birçok bağlantılı katı cisimleri içeren problemlerin çözümünde kullanılabilecek olmasıdır. Her bir bu sistemlerin yalnızca bir serbestlik derecesi olduğu söylenir çünkü bağlantıların düzenlemesi yalnızca bir koordinat kullanılarak tamamen belirlenebilir. Bu karmaşık hesaplamaları büyük ölçüde basitleştirir ve karmaşık sistemler içinde farklı değişkenlerin birbirleriyle nasıl ilişkili olduklarını daha iyi anlamamıza yardımcı olur.

Sonuç olarak, bağlantılı katı cisimler içeren denge problemlerinin analitik olarak değerlendirilmesi, sanal iş kullanılarak etkili bir şekilde yapılabilmekte ve sadece doğru yanıtlara değil, aynı zamanda iç işleyişlerine de net bir anlayış sağlamaktadır.

Bağlantılı Katı Cisimler Sistemi İçin Sanal İş

Sanal çalışma, birbirine bağlı birkaç katı cismi içeren sorunları çözmek için kullanılan güçlü bir yöntemdir. Sistem dengede olduğunda, sanal çalışma ...

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

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Virtual Work

Sanal İş

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Finding Forces with Virtual Work in Linked Bodies

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