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

Un sistema tridimensional tiene una fuerza resultante equivalente y un momento de acoplamiento resultante que no son mutuamente perpendiculares.
El momento de acoplamiento resultante puede resolverse en componentes paralelas y perpendiculares a la línea de acción de la fuerza resultante.
El componente perpendicular se puede reemplazar si la fuerza resultante se mueve a una distancia perpendicular.
Esta combinación de una fuerza resultante y un momento de par colineal traduce y gira el cuerpo alrededor de su eje, lo que se conoce como llave o tornillo.
Consideremos tres fuerzas que actúan sobre el ladrillo. Reemplázalos con una llave inglesa y encuentra el punto donde se cruza con el ladrillo.
En primer lugar, encuentra la fuerza resultante y su magnitud.
A continuación, considere los vectores de posición desde el punto de aplicación de las fuerzas hasta el punto de intersección.
Su producto cruzado con las fuerzas correspondientes da el momento de pareja resultante.
Ahora, determine el vector unitario de la fuerza resultante.
El momento resultante es igual al producto de su magnitud y el vector unitario.
Igualando los componentes y resolviendo las ecuaciones se obtienen las coordenadas del punto de intersección.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 179 y 189.</li>
</ol>

la simplificación de un sistema de fuerzas y momentos del par ii

En un sistema tridimensional, varias fuerzas pueden actuar sobre un objeto. Estas fuerzas se pueden combinar en una única fuerza equivalente, conocida como la fuerza resultante. De manera similar, los momentos generados por estas fuerzas se pueden combinar en un único momento equivalente, el momento resultante del par. En ciertas situaciones, estas dos entidades pueden no ser mutuamente perpendiculares, lo que significa que no tienen un ángulo de 90 grados entre ellas. Esta condición única requiere una comprensión más profunda de la interacción entre la fuerza resultante y el momento del par. Para analizar aún más esta situación, el momento resultante del par se puede descomponer en dos componentes: uno paralelo y otro perpendicular a la línea de acción de la fuerza resultante. Esta descomposición nos permite centrarnos en cada componente por separado y entender sus efectos individuales en el sistema. La componente paralela del momento del par no causa ninguna rotación alrededor del eje perpendicular a la fuerza resultante. Se puede pensar en ella como un efecto de "torsión" a lo largo de la dirección de la fuerza. Por otro lado, la componente perpendicular del momento del par causa una rotación alrededor de un eje perpendicular tanto a la fuerza como al momento. Esta componente perpendicular se puede reemplazar si la fuerza resultante se mueve una distancia perpendicular. Esto significa que la combinación de la fuerza original y la componente perpendicular del momento del par se puede sustituir con una única fuerza que actúa en una ubicación diferente, lo que resulta en un sistema equivalente. La combinación de la fuerza resultante y el momento colineal del par (componente paralela) se puede visualizar como una llave o tornillo que tanto traslada como rota el cuerpo alrededor de su eje. En otras palabras, el cuerpo rígido experimenta un movimiento lineal simultáneo a lo largo de la dirección de la fuerza y un movimiento de rotación alrededor de un eje paralelo a la fuerza. Este movimiento único se conoce como una llave o tornillo y tiene numerosas aplicaciones en ingeniería, robótica y biomecánica. Por ejemplo, en robótica, el concepto de una llave es crucial para entender la cinemática y dinámica de los manipuladores robóticos, donde se requiere que el efector final realice tareas complejas que involucran tanto traslación como rotación. De manera similar, en biomecánica, el concepto de llave se aplica para estudiar las fuerzas y momentos que actúan sobre los huesos y las articulaciones durante diversas actividades, lo que ayuda a los investigadores a diseñar mejores prótesis y dispositivos ortopédicos.

La simplificación de un sistema de fuerzas y momentos del par II

En un sistema tridimensional, múltiples fuerzas pueden actuar sobre un objeto. Estas fuerzas pueden combinarse en una sola fuerza equivalente, conocida como fuerza ...

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

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Force System Resultants

Resultantes de Sistemas de Fuerzas

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Simplification of a Force and Couple System: II

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

moment of a force: scalar formulation

Torque on a Flywheel: Direction and Size

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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Calculating Force Moments in Problem Solving

Calculating force moments in problem solving helps students analyze rotation in mechanical systems. The scalar form of the moment of a force is used to work through these problems step by step. Start by drawing a free-body diagram, or FBD. An FBD is a sketch that shows every force acting on the system. Each force must be identified and included. Next, identify the axis or point about which the moment is calculated. In some problems, that axis or point is given. In other cases, you must choose...

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Net Moment Sign Convention in 2D Forces

Net moment in two-dimensional force systems shows how multiple forces can cause rotation about a fixed point. The scalar formulation helps analyze equilibrium in structures that are acted on by several forces. It focuses on the x-y plane and uses a simple sign rule to describe the direction of rotation. To find the resultant moment, the moments from all forces in the system are considered about a chosen point A. Each moment is assigned a sign based on its sense of rotation. Positive moments...

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The moment of force describes the twisting effect a force can have on an object. It shows why a force may cause rotation instead of straight-line motion. The moment arm is the perpendicular distance from the force’s line of action to the axis of rotation. The moment of force is a vector quantity, not a scalar. Its vector form comes from the cross product of the position vector and the force vector. A cross product gives a vector that is perpendicular to both input vectors. The moment about a...

cartesian form for vector formulation

Calculating Moment with Cartesian Vectors

Calculating moment with Cartesian vectors shows how position and force vectors work together. The moment of force is the cross product of these vectors, so it is a vector quantity. In Cartesian form, unit vectors help write the vectors in component form. The cross product can be arranged in determinant form. That determinant is then expanded to find the Cartesian vector form of the moment of force. This method gives a clear way to work through the calculation step by step. A revolving door...

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Resultant moment describes the total turning effect of multiple forces acting on an object. It shows how several forces can combine to make a body rotate about a point. In physics, moment is the tendency of a force to cause rotation. The resultant moment of a force system is a vector quantity. That means it can be added and subtracted like other vectors. For a system with two forces, F1 and F2, acting on a pole at points A and B, the resultant moment is written as MR = (rA x F1) + (rB x F2).

principle of moments

Resolving Forces in Moment Calculations

The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces. The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a...

principle of moments: problem solving

Torque About an Axis in 3D Systems

The principle of moments helps solve torque problems in physics and engineering. It describes how forces and moments balance around a pivot point or axis. It is used in many real-life cases, including construction, sports, and everyday actions like opening doors and pushing objects. The problem here uses a pole in a three-dimensional system with a cable attached. When tension acts in the cable, the goal is to find the moment about the z-axis through the base. One method is to project the force...

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Bicycle Torque and Moment About an Axis

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Torque on a Bicycle Wheel: Vector Method

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Torque from a Couple: Solving Forces

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system of forces and couples

Equivalent Force and Moment Systems

Structural systems often experience several forces and couple moments at the same time. Engineers simplify these loading cases by replacing them with an equivalent force and moment system at a chosen point O. This makes the analysis easier while keeping the same external effects on the member. A key idea in this process is the principle of transmissibility. A force is a sliding vector, which means it can be moved anywhere along its line of action without changing how the body behaves...

simplification of a force and couple system i

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

Resultant Forces in Force and Couple Systems

Force and couple systems can be reduced to a simpler equivalent system. This makes rigid body analysis easier because the external effect of the forces is captured with fewer elements. When the resultant force and resultant couple moment have perpendicular lines of action, the system may be reduced further to a single resultant force along a new line of action. Three common force systems can be simplified this way: concurrent, coplanar, and parallel. A concurrent force system has lines of...

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...

distributed loads

Load Distribution on Shelves and Dams

Load distribution helps engineers describe how force spreads across a surface or structure. A distributed load is a continuous force per unit area, rather than a single point force. It is a common idea in many practical situations. A bookshelf full of stacked books is one simple example. The weight of the books is spread along the shelf, so the pressure changes across the surface. This pressure is measured in Newtons per square meter, or Pascals. A hydroelectric dam gives another clear...

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distributed loads: problem solving

Equivalent Resultant Loads on Beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

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.

mechanical engineering

Resultant Force and Wrench Motion

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