Name: couple moment in force systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 29 s
Channel: JoVE

カップルは、同じ大きさを持つが、垂直な距離で分離された反対方向に作用する平行な力のペアです。
カップルは、力の平面に垂直な軸を中心に体を回転させる回転力を引き起こし、その結果生じるモーメントはカップルモーメントと呼ばれます。
ラグレンチでボルトを締めることを検討してください。力のカップルは、2つの等しい反対の力がポイントAとBでレンチに加えられ、垂直な距離で離れて形成されます。
位置ベクトル rA と rB は、座標系の原点から適用点に向けられます。
原点に関するカップルモーメントは、位置ベクトルと力の外積の合計です。
位置ベクトル rA と rB の差は、位置ベクトル r であり、これは 2 つの対立する力の間の距離です。
カップルモーメントは、力の間の位置ベクトル r にのみ依存し、位置ベクトル rA と rB には依存しません。したがって、それは自由ベクトルと見なされます。

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	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス \u2012 静力学と力学。 ニュージャージー州ホーボーケン:ピアソンプレンティスホール。154ページ</li>
	<li>ビール、FP;ジョンストン、ER;マズレック、D.F;クロムウェル、PJおよびセルフ、BP(2019)。エンジニアのためのベクトル力学 \u2012 静力学と動力学。ニューヨーク:マグロウヒル。PP - 120。</li>
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カップル

カップル（couple）は、大きさは等しく方向が反対の平行な力の組み合わせです。この力は、カップルの腕として知られる垂直な距離によって分離されています。カップルは、力の平面に垂直な軸を中心に体を回転させる力またはモーメントを引き起こします。その結果として生じるモーメントはカップルモーメントと呼ばれます。カップルモーメントのSI単位はニュートンメートル（N・m）です。

この概念を理解するための典型的な例は、プラグレンチを使ってボルトを締めることです。ポイントAとBで等しく逆向きの力が垂直な距離でレンチに加えられたとき、力のカップルが形成されます。それぞれの位置ベクトルは、座標系の原点から適用点まで向かう方向に指示されます。原点についてのカップルモーメントは、位置ベクトルと力のクロス積の和です。対向する力の位置ベクトルの差が反対側の力の位置ベクトルrであり、これは対向する力の間の距離です。

興味深いことに、カップルモーメントは、2つの力の個々の位置ベクトルに依存せず、力の間の位置ベクトルrのみに依存します。位置ベクトルrは原点に依存しません。これは、異なる点を中心に同じ力のモーメントを計算することができることを意味します。カップルモーメントは自由ベクトルです。一方、カップルモーメントとは異なり、力のモーメントは測定される位置に依存します。もし2つのカップルが同じ大きさと方向のモーメントを生成する場合、これら2つのカップルは等価です。等価なカップルは、位置、方向、大きさに関係なく同じトルクまたは回転効果を持ちます。

カップルモーメントを計算し、その影響を理解することは、外部力に耐えられる安定かつ堅牢なシステムの設計に重要です。

カップルは、大きさが等しいが反対方向にある平行な力のペアです。力は、...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Force System Resultants

力の系の合力

KEY TERMS AND CONCEPTS

主要用語と概念

Couple

couple moment in force systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push.

This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m).

A common example is tightening a bolt with a lug wrench. In that case, two equal and opposite forces act at points A and B on the wrench. These points are separated by a perpendicular distance, so they form a force couple.

The couple moment about the origin is found by adding the cross products of the position vectors and the forces. The position vector between the two opposing forces is r, which is the distance between them. The couple moment depends only on this vector r, not on the separate position vectors of the forces.

Because r does not depend on the origin, the same couple moment is obtained even if the moments are taken about a different point. This is why a couple moment is a free vector. A moment of a single force is different because it depends on where it is measured.

If two couples create moments with the same magnitude and direction, they are equivalent couples. Equivalent couples have the same torque, or turning effect, even if their positions, directions, or magnitudes differ. Understanding couple moments helps in designing stable systems that can resist external forces.

Couple Moment in Force Systems

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couple

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push. This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m). A common example is tightening a bolt with a lug wrench. In...

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key terms and concepts

Learn how a couple creates rotation, why couple moment depends on the distance between forces, and how equivalent couples are identified in force systems.

Couple Moment in Force Systems | JoVE K12

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mechanical engineering

Couple Moment in Force Systems

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