Levers and Pulleys: Principles of Mechanical Advantage

Understanding Levers: Simple Machines

What is a Lever?

Levers are simple machines. They are made up of a rigid bar and a point of support, which is also called a fulcrum. They are normally used to exert a large force using only a small force; they are a type of force multiplier.

Key Elements of a Lever

Resistance is the force that must be overcome by the applied force. The point of support, or fulcrum, is the point about which the lever swings. The arms, the force arm and the resistance arm, correspond to the distance between the fulcrum and the applied force or resistance, respectively.

• The force arm is the distance between the fulcrum and the applied force.
• The resistance arm is the distance between the fulcrum and the resistance.

The Law of the Lever Explained

The Law of the Lever is expressed mathematically using the following equation:

F · Bf = R · Br

Where:

• F is the applied force
• Bf is the length of the force arm
• R is the resistance force
• Br is the length of the resistance arm

Three Classes of Levers

• First-Class Levers: The fulcrum is located between the applied force and the resistance.
• Second-Class Levers: The resistance is located between the applied force and the fulcrum.
• Third-Class Levers: The applied force is located between the resistance and the fulcrum.

Pulleys and Hoists: Lifting Mechanisms

Defining Pulleys

Pulleys are wheels with their lateral surface adapted, usually in the form of a channel (groove), allowing a rope or belt to make contact without coming off.

Understanding Hoists

A hoist is a combined set of pulleys that allows lifting a heavy weight by applying less force (strength).

Mechanical Advantage with Hoists

The more pulleys a hoist has, the less force is needed to lift the load, but the greater the amount of rope that must be pulled.

Pulley Transmission Systems

How Pulley Transmission Works

The pulley transmitting the movement is called the motor or driving pulley. The pulley that receives the movement is called the output or driven pulley.

Types of Pulley Transmissions

• Unitary Transmissions: If both pulleys are equal in size, the output pulley rotates at the same speed as the motor pulley.
• Multiplier Transmissions: If the output pulley is smaller than the motor pulley, it rotates faster. This is a speed multiplication mechanism.
• Reductive Transmissions: If the output pulley is larger than the motor pulley, it rotates more slowly. This is a speed reduction mechanism.

Pulley Transmission Calculation

The relationship between pulley diameters and speeds is given by the equation:

Dm · Nm = Ds · Ns

Where:

Dm

Diameter of the motor pulley

Nm

Speed of the motor pulley

Ds

Diameter of the output pulley

Ns

Speed of the output pulley