Name: wedges and self-locking stability
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 24 s
Channel: JoVE

ウェッジは、構造部品や機械部品の高さを調整したり、重い物体を安定させたり、ボディを2つの部分に分割したりするのに役立つ機械です。
ウェッジを使用して重いスラブを持ち上げることを検討してください。
くさびは、加えられた力を増幅して、加えられた力にほぼ垂直に向けられたはるかに大きな力にします。
ウェッジの運動に適用される力と、6つの法線力と摩擦力を含む7つの未知数があります。
これらは、ウェッジとスラブに適用される4つの力平衡方程式と、各接触面に適用される3つの摩擦方程式を使用して決定できます。
スラブを下げるために、摩擦力は反対の意味で作用します。
摩擦係数が非常に小さいか、くさびの角度が大きい場合、加えられた力はスラブを保持するために右側に作用する必要があります。
加えられた力が取り除かれ、摩擦力がブロックを保持すると、ウェッジはセルフロックと見なされます。この条件は、くさびの角度が反力によってなされる角度の 2 倍未満である場合にのみ有効です。

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	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス:静力学。第14版、ニュージャージー州:ピアソン。430-431ページ。</li>
	<li>メリアム、JL、クレイジ、LGおよびボルテン、JN(2016)。エンジニアリングメカニクス:静力学とダイナミクス。第8版、シンガポール:John Wiley & Sons。353-354ページ。</li>
	<li>ビール、FP、ジョンストン、ER、マズレック、DF、コーンウェル、PJおよびセルフ、BP(2016)。エンジニアのためのベクトル力学。第11版、ニューヨーク:マグロウヒル教育。450ページ。</li>
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ウェッジ

ウェッジは、様々な目的で使用されるシンプルな機械であり、建築物や機械部品の高さを調整したり、重い物体に安定性を提供したり、物体を二つに分割したりする役割を果たします。この多目的ツールは、適用された力を増幅させ、大きな物体や重い物体を操作しやすくします。

重い板を持ち上げるためにウェッジを使用することを考えてみましょう。ここでは、ウェッジは適用された力を初期の力にほぼ垂直な方向に大きく変換することで機能します。この増幅によって、最小限の努力で重い物体を持ち上げることが可能となります。

ウェッジの運動に関与する未知の要素は7つあります：適用された力と6つの法線力と摩擦力です。自由物体図では、ウェッジの重さは負荷に比べて小さいため、しばしば無視されます。

<img alt="Figure 1" src="/files/ftp_upload/14317/14317_PT_Figure_1v2.svg" style="text-align: center; height: 300px;" />

これらの未知数は、ウェッジとスラブに適用される4つの力のつり合い方程式を使用して決定することができます。

<img alt="Equation 1" src="/files/ftp_upload/14317/14317_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 2" src="/files/ftp_upload/14317/14317_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 3" src="/files/ftp_upload/14317/14317_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 4" src="/files/ftp_upload/14317/14317_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" />

 また、残りの3つの摩擦方程式（F1、F2、F3）は、摩擦係数とそれぞれの法線力によって与えられます。

これらの方程式を解くことで、適用された力とウェッジの運動の関係を理解することができます。

板を下げる場合、摩擦力は逆方向に働きます。非常に小さな摩擦係数または大きなウェッジ角の場合、適用された力は板を保持するために右に働かなければなりません。これらの力のバランスにより、ウェッジは安定し、板の重さを支えながら位置を維持します。

一定の条件下では、ウェッジは自己保持と見なすことができます。これは、適用された力が除去され、摩擦力だけでブロックを保持できる場合に発生します。自己保持条件は、ウェッジ角が反応力の角度の2倍以下の場合にのみ有効です。

この場合、ウェッジの形状と接触面間の摩擦が共同して、望ましくない動きや滑りを防止します。

ウェッジの自己保持特性は、重い物体を操作する際に安定性とセキュリティを追加で提供するため、さまざまな応用において有利です。例えば、建築やエンジニアリングプロジェクトでは、自己保持ウェッジを使用することで、構造部品が組み立てや調整中にしっかりと固定されることを保証することができます。

ウェッジは、構造部品や機械部品の高さを調整したり、重量物に安定性を提供したりするなど、さまざまな目的を果たすシンプルな機械です...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Friction

摩擦

KEY TERMS AND CONCEPTS

主要用語と概念

Wedges

wedges and self-locking stability

A wedge is a simple machine that can lift, support, and split heavy objects. It can also change the height of structural or mechanical parts. Because it amplifies force, a wedge makes it easier to move or hold large loads with less effort.

One example is lifting a heavy slab. In that case, the wedge turns the applied force into a much larger force that acts almost perpendicular to the original push. That force change helps raise the load without requiring a large input force.

To analyze wedge motion, there are seven unknowns. These include the applied force, six normal forces, and frictional forces at the contact surfaces. The wedge weight is often ignored in the free-body diagrams because it is small compared with the load.

The unknowns can be found with four force equilibrium equations for the wedge and the slab. Three friction equations, F1, F2, and F3, are then applied at each contact surface. Each friction force equals the coefficient of friction times the normal force at that surface.

The same force balance also explains what happens when the slab is lowered. In that case, the friction forces act in the opposite direction. If the coefficient of friction is very small or the wedge angle is large, the applied force must act to the right to keep the slab in place.

A wedge can also be self-locking. This means that when the applied force is removed, friction alone can hold the block in place. The self-locking condition works only when the wedge angle is less than twice the angle made by the reaction forces.

This stability is useful in many settings. In construction or engineering work, a self-locking wedge can help keep parts firmly in place during assembly or adjustment. The geometry of the wedge and the friction between surfaces work together to reduce slipping and unwanted motion.

Wedges and Self-Locking Stability

dry friction

Dry Friction in Crates and Everyday Motion

Dry friction appears when two solid surfaces touch and try to move past each other. Students can see it when they walk, slide a box across a table, or rub their hands together. Even though it is common, the forces behind it are not easy to see. A simple crate on a rough horizontal floor helps explain the idea. When an external force pushes the crate sideways, two main forces act on it. The normal force acts perpendicular to the surface and helps balance the crate’s weight, while the frictional...

static friction

Static Friction at the Point of Slip

Static friction is the force that keeps two surfaces from starting to slide past each other. It acts when there is a tendency for motion, but not yet actual slipping. This force helps explain everyday actions like walking on the ground and driving a car. A towing example shows how static friction changes as force is applied. A truck pulls a car with a rope, and the car stays still at first. The car is in static equilibrium, which means the forces on it are balanced. Gravity and the normal...

kinetic friction

Sliding Friction Between Moving Surfaces

Kinetic friction is the sliding friction that acts when two surfaces move against each other. It opposes relative motion and acts parallel to the contact surface, in the opposite direction of travel. In the truck and car example, the car first stays still because static friction holds it in place. When the truck’s force becomes greater than the limiting static frictional force, the friction at the contact surface drops to a lower value. The car then begins to slide, and its speed increases. At...

characteristics of dry friction

Static and Kinetic Dry Friction

Dry friction is the resistance between two solid surfaces that move against each other without lubrication or any fluid. A common example is a gardener pushing a wheelbarrow across the ground. The wheel and the ground create dry friction that slows the motion. Before the wheelbarrow starts to move, static friction acts at the contact surface. Static friction is the force that opposes motion before slipping begins, and it helps keep the wheelbarrow stable. It is present only when there is no...

types of friction problems

Dry Friction in Crate, Ladder, and Frame Problems

Dry friction problems often focus on crates, ladders, and frames that are close to slipping. Dry friction is the force that resists relative motion, or the tendency for motion, between two surfaces in contact. In many physics and engineering problems, this force helps keep an object still or defines the point where motion is about to begin. One common case has no clear impending motion. A force may be applied to a crate, but the crate stays at rest. The friction force between the floor and the...

friction: problem solving

Friction on a Banked Road

Friction on a banked road affects whether a bus stays steady while it moves at constant speed. In this problem, a bus with a mass of three megagrams travels on a sloped road. The coefficient of static friction between the tires and the road is 0.5. The goal is to find the maximum bank angle where the bus will not slip or tip. To solve the motion part, the forces on the bus must be shown first. These include gravity, the normal force, and friction. The normal force is the push from the road,...

wedges

A wedge is a simple machine that can lift, support, and split heavy objects. It can also change the height of structural or mechanical parts. Because it amplifies force, a wedge makes it easier to move or hold large loads with less effort. One example is lifting a heavy slab. In that case, the wedge turns the applied force into a much larger force that acts almost perpendicular to the original push. That force change helps raise the load without requiring a large input force. To analyze wedge...

frictional forces on screws

Square-Thread Screw Mechanics and Friction

Square-threaded screws use a helical thread to turn force into lifting motion. They are common fasteners, but they are also useful for transmitting power and motion in machines. A jack with a square-threaded screw lifts heavy loads when force is applied at the handle and the screw turns. A screw can be viewed as a cylindrical shaft with an inclined square ridge wrapped around it. The distance between two neighboring threads is called the pitch. The lead is the distance the screw advances in...

upward impending motion

Screw Jack Force and Friction Analysis

A square-threaded screw jack lifts heavy loads by turning handle force into a twisting moment. Its upward motion depends on overcoming static friction between the screw threads and the jack. To study this motion, the thread can be treated as if it were a block on the groove of the jack after the thread is completely unraveled. A free-body diagram helps show the forces acting on this simplified system. The force at the handle creates a horizontal force that pushes the movable thread up the...

self-locking screw

Screw Jack Self-Locking Behavior

A square-threaded screw jack can hold a heavy load because of its self-locking behavior. This feature makes the device more reliable when it is used to lift large weights or apply a strong force. If the screw keeps its position after the turning moment is removed, the jack is self-locking. Self-locking happens because friction changes the way the forces act on the thread. The friction force reverses direction, and the reaction force moves to the other side of the thread’s normal. In this case,...

screw: problem solving

Screw Torque and Self-Locking

Screw torque and self-locking are analyzed by looking at a threaded screw shaft and a plate gear. The shaft has a mean radius and a lead. The plate gear also has a mean radius. The coefficient of static friction between the screw and the gear is part of the setup. The first step is to find the static friction angle, φ. This angle is defined by the coefficient of static friction. Next, the lead angle is calculated from the lead and the mean radius of the shaft. It gives the screw geometry...

frictional forces on flat belts

Flat Belt Tension and Friction

Flat belt tension and friction control how power moves from one pulley to another. Flat belts are used in many industrial systems to transmit power between pulleys. As the belt wraps around the pulleys, the tension changes because of friction between the belt and the pulley surface. When a pulley turns counterclockwise, the belt side moving away from the pulley has the higher tension, called T2. The side moving toward the pulley has the lower tension, called T1. To estimate these tensions, the...

flat belts: problem solving

Flat Belt Forces and Pulley Moment

Flat belts transmit power from one pulley to another, and the forces on the belt help determine the moment on a pulley. In this example, a belt wraps around pulleys A and B, with radii of 30 cm and 10 cm. The belt meets the pulleys at a 20 degree angle from the horizontal, which sets up the force balance in the system. As pulley B rotates clockwise, it drives pulley A. That motion creates tension T2 on one side of the belt and tension T1 on the other side. The belt-to-surface contact angle, β,...

pivot bearings

Axial Load Support in Pivot Bearings

Pivot bearings support axial loads on a rotating shaft. A bearing helps two parts move relative to each other while reducing friction and wear. In this design, the pivot is placed at the end of the shaft to carry the axial thrust. The pivot surface can be flat, conical, or truncated, depending on the application. In a flat pivot bearing, the axial load is spread over the bearing area. The pressure is uniform and can be found by dividing the load by the area. To study the forces more closely,...

collar bearings

Friction Torque in Collar Bearings

Collar bearings support axial loads on rotating shafts, and their friction helps determine the torque needed to start motion. They are used in many machines and may have a single collar or multiple collars, depending on the application and load needs. For a single collar bearing under an axial load, the contact area is the ring-shaped region between the external radius and the internal radius of the collar. If the bearing is assumed to support the load evenly, the uniform normal pressure is...

journal bearings

Friction Moment in Journal Bearings

Journal bearings support rotating shafts and axles while helping keep them stable. They are used in machines such as engines, turbines, and pumps. Their job is to reduce friction, wear, and vibration. A journal bearing works by keeping a thin film of lubricant between the bearing surface and the rotating shaft. This film limits direct contact and lowers frictional force. The video uses a rope winch with dry or only partly lubricated journal bearings to show the idea. As the spool turns...

bearings: problem solving

Double-Collar Bearing Torque Calculations

Double-collar bearing torque calculations show how friction and axial force affect bearing performance. Engineers use these calculations to test whether the bearing can handle the forces and moments it experiences during operation. This helps them choose and design bearings for specific applications and setups. For a double-collar bearing with set dimensions and an axial force applied, the maximum frictional moment can be found with a standard expression. The equation is rearranged, and the...

rolling resistance

Tire Deformation and Rolling Resistance

Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force. A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact...

rolling resistance: problem solving

Lawn Roller Force Calculation

Rolling resistance is the force that makes a rolling object harder to move across a surface. It is also called rolling friction. It comes from deformation in the object and the surface that touch each other. Internal friction, hysteresis, and other energy losses in the materials also play a role. Because of this force, extra energy is needed to keep a wheel, tire, or ball moving. The video applies this idea to a lawn roller. The roller has a mass of 100 kg, a radius of 25 cm, and a coefficient...

key terms and concepts

Learn how wedges amplify force, lift heavy slabs, and stay in place through friction. Explore equilibrium, contact forces, and self-locking stability.

Wedges and Self-Locking Stability | 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

Wedges and Self-Locking Stability

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