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

一个三维系统具有一个合力和一个合力偶矩，二者并不相互垂直。
所得的力偶矩可分解为平行于和垂直于合力作用线的分量。
如果将合力移动一段垂直距离，则可以替换其垂直分量。
这种合力与共线力偶矩的组合会使物体绕其轴线发生平移和旋转，被称为力螺旋或螺旋运动。
考虑作用在砖块上的三个力。用一个力螺旋代替它们，并求出该力螺旋与砖块的交点。
首先，求出合力及其大小。
然后考虑从力的作用点到交点的位置矢量。
它们与相应力的叉积给出了合力偶矩。
现在，确定合力的单位矢量。
合力矩等于其大小与单位矢量的乘积。
令各分量相等并解方程，可得到交点的坐标。

<ol>
	<li>希伯勒，RC（2016 年）。工程力学 \u2012 静力学和动力学。新泽西州霍博肯:Pearson Prentice Hall。第 179、189 页。</li>
</ol>

力和力偶系统的简化 ii

Simplification of a Force and Couple System: II

在三维系统中，一个物体上可以有多个力在发挥作用。这些力可以合并成一个单一的等效力，并将其称为合力。同样，由这些力所产生的力矩也可以合并成一个单一的等效力矩，即合力偶矩。在某些情况下，这两个实体可能不是互相垂直的，也就是说它们之间没有90度的角度。这种独特的条件需要对合力和力偶矩之间的相互作用进行更深入地理解。 为了能够进一步分析这种情况，合力偶矩可以分解为两个分量：一个使平行于合力作用线方向的分量，另一个是垂直于合力作用线方向的分量。这种分解的方法使我们能够分别关注到每个分量，并理解它们对系统中的个体所产生的影响。力偶矩的平行分量不会导致其围绕合力垂直轴的方向所进行的旋转。它可以被看作是沿着力的方向所发生的“扭转”效应。 另一方面，力偶矩的垂直分量会导致其围绕力和力矩的垂直轴来进行旋转。如果可以合力的垂直距离进行移动，可以对这个垂直的分量来进行替换。这意味着原始力和力偶矩的垂直分量的组合可以被替换为在不同的位置所产生作用的单一力，从而以此得到一个等效的系统。 合力和共线的力偶矩（平行分量）的组合可以被看作是一个扳手或螺丝钉，它可以使物体在轴线周围同时进行平移运动和旋转。换句话说，刚体在力的方向上所同时经历的线性运动和绕与力平行的轴线所产生的旋转运动。因此这种独特的运动被称为扳手或螺丝钉运动，在工程学、机器人学和生物力学等领域有许多应用。 例如，在机器人领域，扳手的概念对于理解机器人进行操作的运动学和动力学至关重要，其中末端的执行器需要执行涉及到平移运动和旋转运动的复杂任务。同样，在生物力学中，扳手的概念被应用于研究骨骼和关节在各种活动中所受到的力和力矩，以此来帮助研究人员设计出更好的假肢和矫形装置。

力和力偶系统的简化 II

在三维系统中，多个力可以同时作用于一个物体。这些力可以合成为一个单一的等效力，称为合力……

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

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Force System Resultants

力系合力

KEY TERMS AND CONCEPTS

关键术语与概念

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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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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