What Is a Double Pulley?

Pulley is a simple machine used to lift heavy objects and save effort. ^[1]

A pulley is a small wheel with grooves around it, which can rotate around an axis. A simple machine composed of a disc with grooves that can rotate around the central axis and a flexible cable (rope, tape, steel cable, chain, etc.) that crosses the disc and can rotate around the central axis is called a pulley.

Chinese name: pulley
Foreign name: pulley

Definition: Round wheel that can rotate around the central axis
Principle: Leverage principle

Introduction to pulleys

In mechanics, a typical pulley is a round wheel that can rotate around a central axis. There is a groove on the circumferential surface of the round wheel, the rope is wound around the groove, and any one of the two ends of the rope is pulled strongly, the friction between the rope and the round wheel will promote the round

pulley The wheel rotates around the central axis. The pulley is actually a deformed, rotatable lever. The main function of the pulley is to pull the load, change the direction of force application, transmit power and so on. A mechanism composed of multiple pulleys is called a "pulley group", or a "double pulley". The mechanical advantage of the pulley block is large, which can pull heavier loads. The pulley can also be a component of a chain drive or a belt drive, transmitting power from one rotating shaft to another.

According to whether the position of the central axis of the pulley moves, the pulley can be divided into "fixed pulley" and "moving pulley"; the central axis of the fixed pulley is fixed and the central axis of the movable pulley can be moved, each with its own advantages and disadvantages. The fixed pulley and the movable pulley can be assembled to form a pulley group, which not only saves labor but also changes the direction of the force.

The pulley appears in the form of knowledge points in junior high school physics textbooks, and requires answers to questions such as the direction of the force, the distance the rope end moves, and the performance of work.

Basic information of pulley

Classification and number of pulleys

Fixed pulley, movable pulley, pulley group (or divided into single pulley, double pulley, three pulley, four pulley and even multiple wheels, etc.).

Pulley material

Wooden pulley, steel pulley and engineering plastic pulley can be made of various materials according to the actual use requirements.

Pulley action

Pull the load, change the direction of force application, transmit power, etc.

Pulley connection method

Hook type, chain link type, wheel type, ring type and chain type, oblique pull type, etc.

Pulley size and material

Small-sized pulleys (D <350mm) that do not bear much load are generally made into solid pulleys.

pulley Q235 or cast iron (such as HT200).

Heavy-duty pulleys are usually made of ductile iron or cast steel (such as ZG270-500), cast into structures with ribs and holes or spokes

Large pulleys (D> 800mm) are generally welded with steel and steel plates.

Pulley history

The drawing on the pulley first appeared in an Assyrian relief in the eighth century BC. This relief shows a very simple pulley, which can only change the direction of force application. The main purpose is to facilitate the force application without giving any mechanical benefits. In China, pulley installations

Pulleys were called pulleys in ancient times The earliest paintings appeared in the portrait bricks and pottery molds of the Han Dynasty. There is also an account of the pulley in the Mo Jing.

The ancient Greeks classified pulleys as simple machines. As early as 400 BC, the ancient Greeks knew how to use double wheels. Around 330 BC, Aristotle's eighteenth question in his book "Mechanical Problems" devoted to the study of the "duplex pulley" system. Archimedes contributed a lot about simple machinery. Knowledge to explain the kinematic theory of pulley in detail. It is said that Archimedes once used a double pulley to pull a sea boat full of cargo and passengers. In the first century BC, Alexandro Hiro analyzed and wrote the theory about the double pulley, which proved the load and the force The ratio is equal to the number of rope segments that bear the load, which is the "pulley principle".

In 1608, in the book "Mathematical Collection", the Dutch physicist Simon Stefan showed that the length ratio of the moving path between the force and the load of the pulley system is equal to the length between the force and the load. Inverse ratio. This is the prototype of virtual work.

In 1788, the French physicist Joseph Lagrange deduced the principle of virtual work using the principle of pulleys in the great work "Mécanique analytique", which opened the prelude to Lagrange's mechanics.

Fixed pulley

Pulley definition

When using a pulley, the pulley whose shaft position is fixed is called a fixed pulley.

The fixed pulley is essentially an equal arm lever

Pulley principle

When in use, the position of the pulley is fixed; the fixed pulley is essentially an equal-arm lever, which does not save effort or effort, but can change the direction of the force. The power arm and the resistance arm of the lever are the radius of the pulley. The arm is equal to the resistance arm, and the lever is neither effort nor effort. Using the principle of leverage, the formula is derived (F is the pulling force, G is the gravity of the object, and L ₁ L ₂ is shown in the figure):

Pulley Features

The fixed pulley can not save effort, and under the condition that the rope weight and the friction between the rope and the wheel are not taken into account, the force used to lift the weight is the same regardless of the direction of the load on the string, because the power arm and the resistance arm Equal and equal to the radius of the pulley.

Pulley pulley

Pulley definition

Definition 1: When using a pulley, the pulley whose axis position moves with the object being pulled is called a moving pulley.

Pulleys and levers

Definition 2: If a heavy object is directly hung on the pulley, the pulley also rises when lifting the heavy object. Such a pulley is called a pulley.

Pulley principle

The moving pulley saves 1/2 force and doubles the distance. This is because when using the moving pulley, the hook code is suspended by two ropes. Each rope only bears half the weight of the hook code, and the direction of the force cannot be changed. In essence, it is a lever with twice the power arm (L1) as the resistance arm (L2): In the figure, O is the fulcrum, F1 is the power to lift the object, and F2 is the gravity of the object (also can be understood as the force used to lift the object when no machinery is used ), We have (l ₁ is the power arm, l ₂ is the resistance arm):

According to the principle that no machinery saves work, we have (s1 is the distance that the free end of the rope moves, and s2 is the distance that the object moves, which can also be understood as the distance that the object lifts when no machinery is used):

Pulley note

The moving pulley saves 1/2 force and doubles the distance, and it is limited to the vertical upward force. The larger the angle of the force, the more force is used. Moreover, the weight of the pulley has an influence on the force used when using the movable pulley. Without ignoring the gravity of the pulley and exerting force upward, we have: F = (G _wheel + G _thing ) / 2

Pulley block

Pulley definition

Pulley group: a pulley device composed of a fixed pulley and a movable pulley. Save effort and change the direction of the force.

But you can't save effort, because the pulley set saves effort, but it takes distance. In order to save both energy and change the direction of power, the fixed pulley and the movable pulley can be combined into a pulley group.

Rope winding method

The pulley unit is made up of several fixed pulleys and movable pulleys, which can achieve the purpose of saving labor and changing the direction of force application. In use, how much effort is saved and how the rope is wound depends on the use of the pulley set. Roping principle

Deformed pulley block Yes: When the number of fixed pulleys and moving pulleys are equal, the free end of the rope can come out of the fixed pulley or from the fixed pulley, and when coming out of the fixed pulley, the fixed end of the rope hangs on the fixed pulley; The fixed end hangs on the moving pulley. The difference between the number of fixed and movable pulleys will not exceed 1. When their numbers are not equal, the free end of the rope comes out from the more side, and the fixed end of the rope hangs from the less side. When the moving pulley is fixed, when the fixed end of the rope is hung on the moving pulley, the pulley set saves labor than when the fixed end of the rope is hung on the fixed pulley (because there are more ropes to bear the weight).

Let n be the number of rope segments that can bear the weight (such as the left pulley group n = 5 above, the right n = 4), then n ropes can be equipped with n or n-1 pulleys. When n wheels are equipped, the number of moving pulleys and fixed pulleys Equal, and the fixed end of the rope is on the fixed pulley; when n-1 pulleys are used, n is an odd number, and the fixed end of the rope is on the moving pulley.

When using a pulley set, several ropes bear the weight, and the force used to lift the object is a fraction of the weight.

Pulley Features

The pulley block uses several pieces of rope to suspend the object, and the force used to lift the object is a fraction of the total weight. The free end of the rope bypasses the moving pulley, and the fixed pulley does not. Although using a pulley set saves effort, but it takes a distance, the distance of power movement is greater than the distance of the weight. The amount of distance depends mainly on the number of segments of the rope of the pulley. Using the pulley set as an experiment, it is easy to see that Saves energy, but costs distance-the distance that the power moves is greater than the distance that the cargo rises.

Pulley relationship

Several relationships (when the pulley set is placed vertically, friction is not counted):

Where s is the distance the rope end moves, h is the height at which the object rises, and G1: the gravity of the object. G2: the gravity of the moving pulley (note that it is the gravity of the moving pulley, not the gravity of all the pulleys) F: the force applied by the rope end n: the number of segments of the rope that pulls the weight.