Name: resultant force and wrench motion
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 23 s
Channel: JoVE

Un système tridimensionnel a une force résultante équivalente et un moment de couple résultant qui ne sont pas mutuellement perpendiculaires.
Le moment de couple résultant peut être résolu en composantes parallèles et perpendiculaires à la ligne d'action de la force résultante.
Le composant perpendiculaire peut être remplacé si la force résultante est déplacée d’une distance perpendiculaire.
Cette combinaison d’une force résultante et d’un moment de couple colinéaire déplace et fait tourner le corps autour de son axe, ce qu’on appelle une clé ou une vis.
Considérons trois forces agissant sur la brique. Replacez-les par une clé à molette et trouvez le point où elle coupe la brique.
Tout d’abord, déterminez la force résultante et son amplitude.
Considérons ensuite les vecteurs position du point d’application des forces au point d’intersection.
Leur produit vectoriel avec les forces correspondantes donne le moment de couple résultant.
Maintenant, déterminez le vecteur unitaire de la force résultante.
Le moment résultant est égal au produit de sa norme et du vecteur unitaire.
L’équivalence des composantes et la résolution des équations donnent les coordonnées du point d’intersection.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 179 et 189.</li>
</ol>

simplification d'un système de forces et de moments couple ii

Simplification of a Force and Couple System: II

Dans un système tridimensionnel, plusieurs forces peuvent agir sur un objet. Ces forces peuvent être combinées en une seule force équivalente, appelée force résultante. De même, les moments générés par ces forces peuvent être combinés en un seul moment équivalent, le moment couple résultant. Dans certaines situations, ces deux entités peuvent ne pas être mutuellement perpendiculaires, c'est-à-dire qu'elles n'ont pas un angle de 90 degrés entre elles. Cette condition unique nécessite une compréhension plus approfondie de l'interaction entre la force résultante et le moment couple. Pour analyser davantage cette situation, le moment couple résultant peut être décomposé en deux composantes : l'une parallèle et l'autre perpendiculaire à la ligne d'action de la force résultante. Cette décomposition nous permet de nous concentrer sur chaque composante séparément et de comprendre leurs effets individuels sur le système. La composante parallèle du moment couple ne provoque aucune rotation autour de l'axe perpendiculaire à la force résultante. On peut la considérer comme un effet de "torsion" le long de la direction de la force. En revanche, la composante perpendiculaire du moment couple provoque une rotation autour d'un axe perpendiculaire à la fois à la force et au moment. Cette composante perpendiculaire peut être remplacée si la force résultante est déplacée d'une distance perpendiculaire. Cela signifie que la combinaison de la force originale et de la composante perpendiculaire du moment couple peut être substituée par une seule force agissant à un emplacement différent, ce qui donne un système équivalent. La combinaison de la force résultante et du moment couple colinéaire (composante parallèle) peut être visualisée comme une clé ou une vis qui à la fois déplace et fait tourner le corps autour de son axe. En d'autres termes, le corps rigide subit un mouvement linéaire simultané le long de la direction de la force et un mouvement de rotation autour d'un axe parallèle à la force. Ce mouvement unique est appelé clé ou vis et possède de nombreuses applications en ingénierie, en robotique et en biomécanique. Par exemple, en robotique, le concept de clé est crucial pour comprendre la cinématique et la dynamique des manipulateurs robotiques, où l'effecteur final doit effectuer des tâches complexes impliquant à la fois translation et rotation. De même, en biomécanique, le concept de clé est appliqué pour étudier les forces et les moments agissant sur les os et les articulations lors de différentes activités, ce qui aide les chercheurs à concevoir de meilleures prothèses et dispositifs orthopédiques.

Simplification d'un système de forces et de moments couple II

Dans un système tridimensionnel, plusieurs forces peuvent agir sur un objet. Ces forces peuvent être combinées en une seule force équivalente, connue sous le nom de ...

simplification-of-a-force-and-couple-system-ii

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Génie mécanique

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Force System Resultants

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resultant force and wrench motion

Resultant force and resultant couple moment describe how several forces and moments act together on a rigid body in three dimensions. When many forces act on an object, they can be replaced by one equivalent force. The moments from those forces can also be combined into one equivalent couple moment.

In some cases, the resultant force and the resultant couple moment are not mutually perpendicular. That means the angle between them is not 90 degrees. To study this situation, the couple moment is split into two parts. One part is parallel to the line of action of the resultant force, and the other part is perpendicular to it.

The parallel component acts like a twisting effect along the direction of the force. It does not create rotation about an axis perpendicular to the resultant force. The perpendicular component causes rotation about an axis that is perpendicular to both the force and the moment.

The perpendicular component can be replaced by moving the resultant force a certain perpendicular distance. This lets the original force and the perpendicular moment component be represented by a single force at a new location. The remaining force and parallel couple moment then form a wrench, also called a screw.

A wrench or screw motion combines translation and rotation at the same time. The body moves along the direction of the force and rotates about an axis parallel to that force. This idea is useful in engineering, robotics, and biomechanics. In robotics, it helps describe the motion of robotic manipulators and their end-effectors. In biomechanics, it helps researchers study forces and moments on bones and joints during movement and support better prosthetics and orthopedic devices.

Resultant Force and Wrench Motion

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Torque, or the moment of a force, describes how a force can make an object turn about an axis. It is a vector quantity, so it has both size and direction. This idea is important in physics, mechanics, and engineering. A simple flywheel example shows how torque works. The flywheel rotates about point O when a force is applied to it. The moment arm is the perpendicular distance from point O to the line of action of the force. The moment, in newton-meter (N-m), is found by multiplying the force...

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Torque from a Couple: Solving Forces

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simplification of a force and couple system i

simplification-of-a-force-and-couple-system-i

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simplification of a force and couple system: ii

Resultant force and resultant couple moment describe how several forces and moments act together on a rigid body in three dimensions. When many forces act on an object, they can be replaced by one equivalent force. The moments from those forces can also be combined into one equivalent couple moment. In some cases, the resultant force and the resultant couple moment are not mutually perpendicular. That means the angle between them is not 90 degrees. To study this situation, the couple moment is...

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key terms and concepts

Learn how a resultant force and couple moment can be split into parallel and perpendicular parts, then combined into wrench motion in 3D systems.

Resultant Force and Wrench Motion | 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.

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Resultant Force and Wrench Motion

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