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

يمكن تطبيق مبدأ العمل الافتراضي على الآلات ذات الأجسام الصلبة المتصلة المتعددة تحت الأحمال لحل المشكلات التي ينطوي عليها ذلك.
ضع في اعتبارك ملزمة التبديل ، حيث يتم تطبيق قوة عند نقطة منتصفها ، مما يؤدي إلى قوة رد فعل تمارسها الكتلة الخشبية على الملزمة.
في مخطط الجسم الحر ، يتم إهمال الاحتكاك ، ويتم النظر في الإزاحة الافتراضية الإيجابية.
اختر نظاما لمحاور الإحداثيات، وحدد الزيادات الموجبة والسالبة.
لا تعمل قوى التفاعل عند النقطة اليسرى والقوة العادية أثناء هذا الإزاحة.
نتيجة لذلك ، يجب حساب العمل الافتراضي الذي تقوم به قوى التفاعل والقوى المطبقة فقط.
من خلال التعبير عن الإحداثيات من حيث زاوية ثيتا والتمايز ، يمكن تحديد إجمالي العمل الافتراضي لكلتا القوتين.
يعطي ضبط إجمالي العمل الافتراضي على الصفر معادلة قوة التفاعل التي تمارسها الكتلة الخشبية على الملزمة.

<ol>
	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية: الإحصاء. الطبعة الرابعة عشرة ، نيو جيرسي: بيرسون. القسم 11.1 ، ص 586-587.</li>
	<li>بير ، إف بي ، جونستون ، إي آر ، مازوريك ، دي إف ، كورنويل ، بي جيه وسيلف ، ب. (2016). ميكانيكا النواقل للمهندسين. الطبعة الحادية عشرة ، نيويورك: McGraw-Hill Education. ص 578-579.</li>
</ol>

العمل الافتراضي لنظام الأجسام الصلبة المتصلة

<div style="direction:rtl">العمل الافتراضي هو أسلوب قوي يُستخدم لحل المشكلات التي تتضمن عدة أجسام صلبة متصلة. عندما يكون النظام في حالة توازن، يكون العمل الافتراضي صفرًا. هذا يتيح حساب القوى الناتجة عندما يتعرض النظام لإزاحة افتراضية. عند محاولة تحليل مثل هذا النظام، يجب أولًا استخدام رسم توضيحي للجسم الحر، حيث تمثل الإحداثيات المستقلة تكوين الروابط، مع علامة توضح الموضع المنحرف الناتج عن الإزاحة الافتراضية الموجبة. بعد ذلك، يتم قياس إحداثيات الموضع من نقطة ثابتة على الرسم التوضيحي للجسم الحر وتوجيهها نحو القوى التي تؤدي العمل. يسمح ذلك بتعبير كل إزاحة افتراضية باستخدام المصطلحات المتعلقة بالإحداثي المستقل. الخطوة التالية هي كتابة معادلة العمل الافتراضي، التي تساعد في تحديد القوى والعزوم الناتجة. من المهم أيضًا ملاحظة أنه إذا عملت قوة أو عزم مزدوج على طول اتجاه الإزاحة الافتراضية الموجبة، فإن عملهما يُعتبر عملًا افتراضيًا إيجابيًا؛ أما إذا كان في الاتجاه المعاكس، فإن عملهما يكون سلبيًا. الميزة الرئيسية لاستخدام هذه الطريقة هي أنها يمكن تطبيقها لحل المشكلات التي تشمل نظامًا من الأجسام الصلبة المتصلة. يُقال إن لكل من هذه الأنظمة درجة حرية واحدة فقط، حيث يمكن تحديد ترتيب الروابط بالكامل باستخدام إحداثية واحدة فقط. هذا يبسط بشكل كبير الحسابات المعقدة ويساعد على فهم أفضل لكيفية ارتباط المتغيرات المختلفة ببعضها البعض في الأنظمة المعقدة. في النهاية، يمكن تقييم المشكلات المتعلقة بالتوازن تحليليًا وتأثيراتها على الأجسام الصلبة المتصلة المتعددة بشكل فعال باستخدام العمل الافتراضي، مما يوفر إجابات دقيقة ورؤية واضحة لكيفية عملها الداخلي أيضًا.</div>

العمل الافتراضي هو طريقة قوية تستخدم لحل المشكلات التي تنطوي على العديد من الأجسام الصلبة المتصلة. عندما يكون النظام في حالة توازن ، يكون العمل الافتراضي ...

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

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Virtual Work

العمل الافتراضي

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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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