CHAPTER 2: MECHANICAL SYSTEMS Engineering Mathematics

CHAPTER 2: MECHANICAL SYSTEMS

Engineering Mathematics

Copyright © Texas Education Agency 2012. All rights reserved.

2

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.


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Chapter 2: Outline

1. Introduction to Simple Machines

2. Calculating Weight and Friction3. Mechanical Advantage and

Friction of a Simple Machine4. Calculating Power and

Efficiency in Complex Machines


4

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.


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Schedule of Assignments

Class/Period(s)

Topic Reading Assignment

1-2 • Introduction• Vocabulary• Mechanical Engineering O*Net

Chapter 2.1 #1-Individual Write a one-page paper about the Mechanical Engineering Occupation.

3-10 • Simple Machines

Chapter 2.2 #2-In teams of 2-3, complete the Simple Machines Challenge.

11-15 • Levers and Pulleys

Chapter 2.3 #3-In teams of 2-3, complete the Lever and Pulley Challenge.

16-20 • Mathematical Principles Challenge

Chapter 2.4 #4-In teams of 2-3, complete the Mathematical Principles Challenge.


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Vocabulary

Mechanical Systems Mathematical Principles Simple Machines

Lever Wheel and Axle Pulley Inclined Plane Wedge Screw


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Vocabulary, cont.

Linkages Cams Turnbuckles Gears Key

Fasteners V-belt Drives Chain Drives

Fulcrum Moment Arm Force Arm Resistance Arm


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.

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Career/Educational Opportunities

Career and educational opportunities include the following: Mechanical engineers Mechanical engineering technologists Architectural and engineering managers Electromechanical engineering

technologists Mechatronics technologists

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Mechanical Engineering Assignment

Visit the O*Net website (www.onetonline.org).

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.

http://www.onetonline.org/


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

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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

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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.

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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.

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Types of Mechanical Systems

The most commonly used mechanical systems are listed below.

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Levers Linkages Cams

Turnbuckles Pulleys Gears

Key Fasteners V-belt Drives Chain Drives


Levers

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.

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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.

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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)

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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.

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First Class Lever20

fulcrum

applied force

resistance arm

resistance

force arm


Second Class Lever21

fulcrum

resistanceapplied force

resistance arm

force arm


Third Class Lever22

fulcrum

resistance

applied force

resistance arm

force arm


Torque Produced in Lever Systems23

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 Levers24

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

Mechanical Advantage

𝐹𝑜𝑟𝑐𝑒𝑂𝑢𝑡𝐹𝑜𝑟𝑐𝑒 𝐼𝑛= or

Mechanical Advantage

http://www.youtube.com/watch?v=yfAdmRJDKIc


Mechanical Advantage of Levers, cont.25

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 Lever26

fulcrum

applied force

resistance arm

resistanceforce arm

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 Lever27

fulcrum

resistanceapplied force

resistance arm

force arm

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


MA: Third Class Lever28

fulcrum

resistance

applied force

resistance arm

force arm

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


Lever and Pulley Challenge29

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

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

They are an important part of mechanical engineering.

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Cams

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.

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Turnbuckles

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

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Pulleys

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.

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Gears

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.

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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.

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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.

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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.

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Mathematical Principles Challenge

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

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1. Levers2. Linkages3. Cams4. Turnbuckles5. Pulley systems

6. Gear drives7. Key fasteners8. V-belt drives9. Chain drives

Present your calculations to the class. Write a five-page paper documenting

your findings.


Credits39

ClipArt; http://www.clipart.com/en/

Images; http://commons.wikimedia.org/wiki/Main_Page

Slide 24Mechanical Advantage video; from YouTube user; Science Online; http://www.youtube.com/watch?v=yfAdmRJDKIc

http://www.clipart.com/en/

http://commons.wikimedia.org/wiki/Main_Page

http://commons.wikimedia.org/wiki/Main_Page



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CHAPTER 2: MECHANICAL SYSTEMS Engineering Mathematics