MECHANICAL SYSTEMS

This unit covers the following topics:

Motion Forces Levers Moments Linkages Free Body Diagrams Beams Gears Torque and Drive Systems Converting motion

Introduction

Mechanisms are widely used in industry and society

Many mechanisms will be familiar to you

(Intro continued)

Many industrial processes involve electronic control, mechanisms provide the muscle to do the work

All mechanisms involve:

Some kind of motion Some kind of force Make a job easier to do Need an input to make them work Produce some kind of product

4 Basic Kinds Of Motion

Rotary Turning in a circle

Linear Moving in a straight line

Reciprocating Backwards and forwards movement

Oscillating Swinging back and forwards

Motion Task 1

Identify the type of motion shown by the following activities.

Complete a systems diagram for each

Motion Task 2

Consider the tools and machines you have used/ seen in CDT

List up to three tools or machines for each basic type of motion

Rotary

Linear

Reciprocating

Oscillating

Forces

Force causes acceleration

Force is measured in Newtons (N)

There are several different types of forces that can be applied to bodies and structures

Static Forces

Static forces do not usually cause motion

Consider a tall building

The weight of the material it is built from, and thepeople and furniture inside it are static loads

Dynamic Loads

Usually causes a movement The value of the force can be variable

Again consider a tall building

Variable winds add an extra force or load to the structure

The engineer must allow for this

Bending Forces

Structures that carry loads across their length are subject to bending forces

Consider a car driving across a bridge

Shear Forces

These are tearing or cutting forces

Scissors are an example of these

Torsion Forces

Torque is a turning force which tries to twist a structure

Compression Forces

Compression forces try to squash a structure

Consider a column

The weight down is balanced by the reaction from the ground

The forces act to try and shorten the column

C O LU M N

W EIGHT FO R C E W(EXTER NAL FO R C EO N C O LUM N )

W

R

GROUND R EAC TIO N R(EXTER NAL FO R C E O N C O LU M N)

Forces in Tension

Tensile forces try to stretch a structure

Consider a crane’s lifting cable

The weight tries to stretch or pull the cable apart

Cables in tension can have small diameters compared to members in compression

LEVERS In its simplest form, a lever is a stick that is free to pivot or

move back and forth at a certain point.

Levers are probably the most common simple machine because just about anything that has a handle on it has a lever attached.

The point on which the lever moves is called the fulcrum.

By changing the position of the fulcrum, you can gain extra power with less effort.

LEVERS How do you move a heavy person?

If you put the fulcrum in the middle, you won't have a chance. But if you slide the fulcrum closer to the heavy person, it will be easier to lift.

Where's the trade-off?

Well, to get this helping hand, your side of the see-saw is much longer (and higher off the ground), so you have to move it a much greater distance to get the lift

LEVERS

Draw the universal system for a lever

Copy the line diagram of a lever

EFFO RT

LO AD

D ISTANC EM O VED

BY LO AD

D ISTANC EM O VED

BY EFFO RT

LEVER SYSTEM

INPUT FO RCE

INPUT M O TIO N

O UTPUT FO RCE

O UTPUT M O TIO N

Basic Types Of Lever

Levers can be either force or distance multipliers (not both)

EFFORT

LOAD

EFFORT

LOAD

Force Multiplier Ratio

Consider the lever shown

The LOAD is about 3 times more than the EFFORT

LOAD/EFFORT gives force multiplier ratio

EFFORT = 260 N

LOAD = 750 N

600 mm

Movement Multiplier Ratio

Something for nothing?

Applying less force to move the load must involve a trade off.

The effort must be moved through a greater distance

In our example the effort moves much more than the load

Movement multiplier ratio = distance moved by effort distance moved by load

Efficiency

The friction and inertia associated with moving an object means that some of the input energy is lost

Since losses occur, the system is not 100% efficient

Efficiency = = Force Ratio x 100 Movement Ratio

Losses in a lever could be friction in the fulcrum, strain in the lever as it bends slightly and maybe sound.

Complete the following tasks:

Task 1

Draw a universal system diagram for a lever

Complete the following diagram, indicating clearly the LOAD, EFFORT and FULCRUM

INPUT O U TPU T

Task 2

Calculate the force- multiplier ratio of the following levers, show all working

EFFORT1OO N

EFFORT300 N

EFFORT200 N

LOAD400 N

EFFORT50 N

LOAD100 NLoad

100N

Task 3

A diagram for a lever system is shown below. Find the force- multiplier of the lever system Calculate the movement- multiplier ratio of the lever Calculate the efficiency of the system Identify possible efficiency losses in the system

EFFORT = 150 N

LOAD = 450 N

650 mm

200 mm

Classes of Levers

 Levers can be divided into three distinct types (classes)

Determined by the position of the load, effort and fulcrum.  

Class 1

In class 1 levers the effort is on one side of the fulcrum and the load is on the opposite side.

Class 1 levers are the simplest to understand: the longer the crowbar the easier it is to prise open the lid.

  

  

CLASS of LEVER Class 2

In class 2 levers the fulcrum is at one end of the lever and the load and the effort are spaced out on the other end of the bar.

The load must be closer to the fulcrum than the effort

A wheelbarrow is a good example of a class 2 lever. The wheel is the fulcrum, the load is in the container area and the effort is applied to the handles. EFFORT

LOAD

FULCRUM

CLASS of LEVER

Class 3

Class 3 levers are similar to class 2 levers except that now the effort is closer to the fulcrum than the load

This means that more effort has to be applied to move the load. This type of lever is used when mechanisms require a large output movement for a small input movement.

EFFO RT

LO AD

FU LC R U M

Task 4

For each of the following tools, state the class of lever

M O M E N T S

A moment is a turning force

Consider the system shown:

A weight is attached to a metal rod

The rod is free to rotate around a hinge

What happens if the rope is cut?

The weight exerts a moment of 20Nm (Force x Distance)

TURNING EFFECT

2 m

HINGE P

ROPE

WEIGHT

Lever Systems The lever shown is in

equilibrium (a steady state)

The input force exerts an anticlockwise moment

The output force exerts a clockwise moment

To be in equilibrium both moments must be equal

The Principle of Moments

The sum of the moments must equal zero

CWM = ACWM

Example: Prove that the following system is in equilibrium

Solution

• For equilibrium, the CWM = ACWM. • A moment is a force multiplied by a distance

CWM = ACWMF1¹ d1 = F2 d2

•The load exerts a clockwise moment (tends to make the lever turn clockwise)

Clockwise moment = 200 N 2 m = 400 Nm

•The effort exerts a anticlockwise moment.

Anticlockwise moment = 400 N 1 m = 400 Nm CWM = ACWM

• Therefore the lever is in a state of equilibrium.

Task One

A car footbrake uses a lever action to amplify force transmitted by the driver to the braking system when the driver’s foot presses the foot-pedal. If the drivers foot can exert a force of 5000N, what force will be transmitted to the braking system?

100 mm

500 mm

5000 N INPUT

FULCRUM

FORCE TO BRAKINGSYSTEM (LOAD)

Solution

This is a class 2 lever. Take moments about the fulcrum to find the force on the braking system. Notice the distance from the fulcrum to the input is 600 mm.

The input tends to make the lever turn clockwise; the braking system is opposing the input and so acts to turn the lever anticlockwise.

The principle of moments states that: CWM = ACWM F1 d1 = F2 d2

5000 N 0.6 m = braking force 0.1 m

braking force = 5000 N 0.6 m 0.1 m

braking force = 30,000 N or 30 kN

Practice:

Questions:

For the system shown:

If the handle length is 250mm and the effort to turn it is 15N, what moment would close the tap valve?

What is the benefit of this type of tap?

Suggest a situation where this type of tap would be useful

Task 2

Calculate the force- multiplier ratio of the following levers, show all working. Calculate a suitable distance between effort and load to produce equilibrium.

EFFORT1OO N

EFFORT300 N

EFFORT200 N

LOAD400 N

EFFORT50 N

LOAD100 NLoad

600N

Task 3

A diagram for a lever system is shown below. Find the force- multiplier of the lever system Calculate the movement- multiplier ratio of the lever Calculate the efficiency of the system Identify possible efficiency losses in the system

EFFORT = 150 N

LOAD = 450 N

650 mm

200 mm