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Chapter 2: Mechanical Systems. Engineering Mathematics. Introduction/Description. The mechanical systems lesson will cover the simple machines and the mechanical advantage of the lever simple machine. Student teams will complete a m echanical a dvantage t eam project. Chapter 2: Outline.

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Chapter 2 mechanical systems

Chapter 2: Mechanical Systems

Engineering Mathematics

Introduction description

  • The mechanical systems lesson will cover the simple machines and the mechanical advantage of the lever simple machine.

  • Student teams will complete a mechanical advantage team project.

Chapter 2 outline
Chapter 2: Outline

  • Introduction to Simple Machines

  • Calculating Weight and Friction

  • Mechanical Advantage and Friction of a Simple Machine

  • Calculating Power and Efficiency in Complex Machines

Objectives and result
Objectives and Result

  • Students will understand the meaning of mechanical systems.

  • Students will identify the different types of mechanical systems and the mechanical advantage of mechanical systems and simple machines.

  • Students will understand the careers and educational opportunities available in the mechanical engineering industry.

  • The result will be that student complete a mechanical advantage team project.


  • Mechanical Systems

  • Mathematical Principles

  • Simple Machines

  • Lever

  • Wheel and Axle

  • Pulley

  • Inclined Plane

  • Wedge

  • Screw

Vocabulary cont
Vocabulary, cont.

  • Linkages

  • Cams

  • Turnbuckles

  • Gears

  • Key Fasteners

  • V-belt Drives

  • Chain Drives

  • Fulcrum

  • Moment Arm

  • Force Arm

  • Resistance Arm

Mechanical engineering
Mechanical Engineering

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems.

  • It is the branch of engineering that involves the production and usage of heat and mechanical power for the design, production, and operation of machines and tools.

  • It is one of the oldest and broadest engineering disciplines.

Career educational opportunities
Career/Educational Opportunities

Career and educational opportunities include the following:

  • Mechanical engineers

  • Mechanical engineering technologists

  • Architectural and engineering managers

  • Electromechanical engineering technologists

  • Mechatronics technologists

Mechanical engineering assignment
Mechanical Engineering Assignment

  • Visit the O*Net website (

  • Write a one-page essay on the mechanical engineering profession.

  • Discuss at least one sub-specialty of mechanical engineering in your essay.

  • Use the O*Net website and at least one other primary source.

Simple machines
Simple Machines

Simple machines are mechanical systems that change the direction or magnitude of a force. The term refers to the six classical simple machines, which were defined by Renaissance scientists.

  • Lever – a simple machine consisting of a rigid bar that rests on a fulcrum, or pivot

  • Wheel and Axle – a simple machine consisting of a wheel connected to an axle so that turning the wheel also turns the axle

Simple machines cont
Simple Machines, cont.

  • Pulley – a simple machine consisting of a grooved wheel that is turned by a rope or chain

  • Inclined Plane – a simple machine consisting of a uniform sloped surface

  • Wedge – a simple machine consisting of an angled object used to separate two objects, lift an object, or hold an object in place

  • Screw – a simple machine consisting of an inclined plane wrapped around an axis

Simple machines challenge
Simple Machines Challenge

In teams of 2-3 students,

  • complete and sign the team contract spreadsheet for this unit,

  • build a simple machine,

  • compare and contrast the simple machine built by your team with a simple machine built by another team in your class, and

  • calculate the mechanical advantage of each type of simple machine built by each team in the class.

What are mechanical systems
What are Mechanical Systems?

  • Mechanical systems are machines that use energy to perform some activity.

  • Mechanical systems manage power to accomplish a task that involves forces and movement.

  • Mechanical systems are devices having parts that perform or assist in performing any type of work.

Types of mechanical systems
Types of Mechanical Systems

The most commonly used mechanical systems are listed below.


  • Levers are rigid bars that exert a force to move a load by turning on a pivot or fulcrum.

  • Levers are classified systems of torque; the moment of a force or system of forces tending to cause rotation around a fixed point.

Levers cont
Levers, cont.

  • Relative positions of force, resistance, and axis of rotation vary in the different types or classes of levers.

  • As with any torque calculations, operations on levers determine the tendency for some force to produce rotation around a fixed point.

Components of a lever
Components of a Lever

  • Fulcrum: the center or axis of rotation of the system

  • Moment Arm: the distance from any force or weight that produces torque to the fulcrum

  • Force Arm: the distance from an applied force to the fulcrum (the moment arm of the force)

  • Resistance Arm: the distance from the resistance to the fulcrum (the moment arm of the resistance)

Classes of levers
Classes of Levers

  • In a first class lever, the applied force and the resistance are on opposite sides of the fulcrum.

  • In a second class lever, the resistance is between the applied force and the fulcrum.

  • In a third class lever, the applied force is between the resistance and the fulcrum.

First class lever

applied force


force arm

resistance arm


First Class Lever

Second class lever

force arm

resistance arm


applied force


Second Class Lever

Third class lever

resistance arm

force arm


applied force


Third Class Lever

Torque produced in lever systems
Torque Produced in Lever Systems

  • Two torques are produced in lever systems:

    • By the applied force

    • By the resistance

  • The direction in which a lever system moves is dependent on the relative lengths of the force and resistance arms, as well as the magnitudes of force and resistance.

Mechanical advantage ma of levers
Mechanical Advantage (MA) of Levers

The effectiveness of a lever at moving a resistance is a calculated value:

Mechanical Advantage



Mechanical Advantage

Mechanical advantage of levers cont
Mechanical Advantage of Levers, cont.

  • Because of their different configurations, the mechanical advantage of

  • a first class lever can favor the force or resistance depending on the placement of the fulcrum,

  • a second class lever always favors the force arm, and

  • a third class lever always favors the resistance arm.

Ma first class lever

applied force


force arm

resistance arm


MA: First Class Lever

The fulcrum in a first class lever system can often vary in position to favor the force arm or the resistance arm.

Ma second class lever

force arm

resistance arm


applied force


MA: Second Class Lever

In a second class lever system, the mechanical advantage favors the force arm. The force arm will always be longer.

Ma third class lever

resistance arm

force arm


applied force


MA: Third Class Lever

The mechanical advantage of a third class lever system favors the resistance arm. The resistance arm is always longer.

Lever and pulley challenge
Lever and Pulley Challenge

In teams of 2-3 students,

  • research lever and pulley systems,

  • design a lever or pulley system to do some type of useful work,

  • describe the type or class of lever or pulley system you selected, and

  • present your lever or pulley system to the class and explain why you chose that type of system to do the work you selected.


  • Linkages include garage door mechanisms, car wiper mechanisms, gear shift mechanisms.

  • They are an important part of mechanical engineering.


  • Cams are rotating or sliding pieces in a mechanical linkage used especially in transforming rotary motion into linear motion or vice-versa.

  • A common example is the camshaft of an automobile, which takes the rotary motion of the engine and translates it into the reciprocating motion necessary to operate the intake and exhaust valves of the cylinders.


Turnbuckles are devices for adjusting the tension or length of ropes, cables, tie rods, and other tensioning systems.


  • Pulleys are wheels on an axle that are designed to support movement of a cable or belt along its circumference.

  • Pulleys are used in a variety of ways to lift loads, apply forces, and to transmit power.


  • Gears are rotating machine parts having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque.

  • Two or more gears working in tandem are called a gear train or a gear drive.

Key fasteners
Key Fasteners

Key fasteners are any of various devices, as a snap or hook and eye, for holding together two objects or parts sometimes required to be separate, as two edges or flaps of a piece of clothing.

V belt drives
V-belt Drives

  • V-belt drives are belts with a flat bottom and tapered sides, used to transmit motion between two pulleys.

  • Multiple V-belts are often used together in order to increase carrying power.

Chain drives
Chain Drives

  • Chain drives, or sprocket drives, provide a way of transmitting mechanical power from one place to another.

  • They are often used to convey power to the wheels of a vehicle, particularly bicycles and motorcycles.

  • They are also used in a wide variety of machines besides vehicles.

Mathematical principles challenge
Mathematical Principles Challenge

  • In teams of 2-3 students, calculate the mechanical advantage for the mechanical systems listed below:

  • Levers

  • Linkages

  • Cams

  • Turnbuckles

  • Pulley systems

  • Gear drives

  • Key fasteners

  • V-belt drives

  • Chain drives

  • Present your calculations to the class.

  • Write a five-page paper documenting your findings.


  • ClipArt;

  • Images;

  • Slide 24

    Mechanical Advantage video; from YouTube user; Science Online;