Name: 3d support types for stability and motion
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 27 s
Channel: JoVE

機械工学では、その用途に応じてさまざまな支持体が採用されています。3次元力システムにおけるこれらの支持体反応により、システムの並進や回転が防止されます。
ロボットアームが重りを持ち上げることを考えてみましょう。ここで、ジョイントAはボールとソケットのジョイントです。アームは、ボールとソケットのジョイントの回転を制限する瞬間がないため、任意の軸を中心に自由に回転できます。ただし、3次元に沿った3つの反力のため、並進運動が制限されます。
また、アームのジョイントBは、1つの滑らかなピンサポートです。このサポートは、3つの反力と2つのカップルモーメントを作成し、ピンの軸に沿った回転運動を可能にします。
ロボットアームの基部は固定支持体で、3つの方向すべてに反力とモーメントがあります。
別のタイプのサポートは、ドアで一般的に使用されるヒンジサポートです。サポートの3つの反力はドアの並進運動を制限し、2つのモーメントはドアの回転を制限します。

<ol>
	<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。245-248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。208ページ</li>
	<li>メリアム、J.L.;Kraige、LGおよびBolton、JN(2020)。エンジニアリングメカニクス \u2012 静力学。ニュージャージー州ホーボーケン:ジョン・ワイリー。145ページ</li>
</ol>

三次元の支持反応

Support Reactions in Three Dimensions

三次元の支持反応は、さまざまな構造物やシステムの安定性と平衡を保つのに役立ちます。これらの反応は、システムが移動および回転しないようにし、設計が外部の力に耐え、効率的かつ安全に機能することを確保します。以下では、三次元で支持反応を提供する一部の支持について説明します。

ボールとソケットジョイントは、任意の軸周りの自由な回転を可能にする支持の一つです。この回転の制限時にモーメントがないため、ボールとソケットジョイントでは回転の自由度が可能です。ただし、ジョイントは三次元での反応力により、平行移動の制限を行います。

もう一つのタイプの支持は、単一の平滑なピン支持です。この支持では、三つの反応力と二つの対カップルモーメントが作られ、ピンの軸に沿った回転運動が可能になりますが、他の方向への移動は制限されます。

固定支持は、三つの方向に沿った反力とモーメントを提供します。このタイプの支持は、さまざまな荷重や条件下で全体のシステムが安定し、安全に保たれることを保証し、システムの機能に影響を及ぼす可能性のある望ましくない移動や変形を防ぎます。

ヒンジ支持は、機械工学でよく用いられるもう一つの一般的な支持です。ドアや他の類似の応用に頻繁に使用されます。ヒンジ支持では、支持での三つの反力がドアの平行移動を制限し、二つのモーメントがドアの回転を制限します。この配置により、ドアは単一の軸を中心に回転し、安定性と制御を保ちながら動作します。

3次元でのサポート反応は、さまざまな構造やシステムの安定性と平衡を維持するのに役立ちます。これらの反応は、システムを防ぎます...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Equilibrium of a Rigid Body

剛体のつり合い

KEY TERMS AND CONCEPTS

主要用語と概念

3d support types for stability and motion

Support reactions in three dimensions keep structures stable and in equilibrium. They stop unwanted translation and rotation, so a design can handle external forces safely and work as intended. These reactions are important in many structures and systems.

A ball and socket joint is one support that allows free rotation about any axis. It does not provide a moment that resists turning. At the same time, it restricts motion in space with three reaction forces along the three dimensions.

A single smooth pin support works differently. It creates three reaction forces and two couple moments. This setup allows rotation along the axis of the pin while restricting movement in the other directions.

Fixed supports provide reaction forces and moments in all three directions. They help keep the system stable and secure under different loads and conditions. This also helps prevent unwanted movement or deformation that could affect function.

Hinge support is another common support used in mechanical engineering, especially in doors and similar applications. It produces three reaction forces that block translational motion of the door. Two moments restrict the door’s rotation, but it can still turn about one axis.

3D Support Types for Stability and Motion

3d-support-types-for-stability-and-motion

conditions of equilibrium

Rigid Body Force Balance in Equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero. Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body. The...

support reactions

Types of Structural Supports

Types of structural supports control how a coplanar force system moves and reacts under load. A coplanar force system is a set of forces that all lie in the same plane. The supports create reactions at the point of contact. These reactions help keep a structure stable under external forces. Supports work by stopping translation with an equal and opposite force. They can also stop rotation by applying a couple moment in the opposite direction. In structural design, these reactions are important...

internal forces and center of gravity

Forces Inside a Body and Balance

Internal forces and the center of gravity help explain how objects stay in balance. These mechanics ideas matter for structures, machines, and vehicles that must remain stable under different loads and conditions. Internal forces are created inside a body when its particles interact. They can appear as tension, compression, or shear forces. These forces act in collinear pairs with equal magnitude and opposite direction. Between connected parts, they cancel each other and help keep the body in...

alternative sets of equilibrium equations

alternative-sets-of-equilibrium-equations

Equilibrium Conditions for a Supported Plate

Equilibrium conditions for a supported plate are used to describe when forces and moments balance. In this state, the plate has no net movement and no rotation. Engineers use these equations to study how structures behave under external loads. In many cases, the standard equilibrium equations are enough. But some systems need an alternative set of equations to match the geometry of the support points. A rectangular plate supported at points A, B, and C is one example. For this plate, the...

two force member

Two-Force Body Equilibrium

A two-force body is a rigid body acted on by only two external forces. In equilibrium, those two forces must have the same magnitude, the same line of action, and opposite directions. This balance is what keeps the body at rest. For a plate with forces F1 and F2 applied at points A and B, equilibrium means the sum of moments about any axis is zero. If moments are summed about point A, the moment from F2 must be zero. That means the line of action of F2 must pass through point A. The same idea...

three force member

Solving a Three-Force Member Example

A three-force member is a rigid body acted on by three forces at three points. The forces must have concurrent lines of action. If the forces are parallel, their lines of action stay parallel instead. A dumpster provides the example used here. It is connected to a pin support at point A and to a pin on a hydraulic cylinder at point B. The hydraulic cylinder acts as a two-force member in equilibrium. The dumpster weight acts through the center of gravity, and the support reaction acts at point...

equations of equilibrium in three dimensions

equations-of-equilibrium-in-three-dimensions

Checking Force Balance in 3D Structures

Checking force balance in 3D structures is a key step when a system is at rest. The vector and scalar equations of equilibrium are used to test whether a body is stable and will not collapse or fall apart. These equations give a clear way to study the forces acting on a body. The vector equations of equilibrium require the vector sum of all external forces on a body to equal zero. They also require the vector sum of the couple moments and the moments of all forces about a point to equal zero.

support reactions in three dimensions

Support reactions in three dimensions keep structures stable and in equilibrium. They stop unwanted translation and rotation, so a design can handle external forces safely and work as intended. These reactions are important in many structures and systems. A ball and socket joint is one support that allows free rotation about any axis. It does not provide a moment that resists turning. At the same time, it restricts motion in space with three reaction forces along the three dimensions. A...

constraints and statical determinacy

Constraints in Structural Equilibrium

Constraints in structural engineering control how a body can move and help keep it in mechanical equilibrium. A constraint is a restriction on motion. When the right number of constraints is used, the system can stay balanced with the fewest supports needed. A system with the proper number of supports is called statically determinate. In that case, the unknown reaction forces can be found from equations of equilibrium. These systems are the easiest to analyze and design because the forces can...

key terms and concepts

Learn how ball and socket joints, smooth pin supports, fixed supports, and hinge supports control movement and keep 3D structures stable under load.

3D Support Types for Stability and Motion | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

3D Support Types for Stability and Motion

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