TECHNICALSCambridge

CAMBRIDGE TECHNICALS IN ENGINEERINGLEVEL 3 UNIT 3 – PRINCIPLES OF MECHANICAL ENGINEERING

DELIVERY GUIDEVersion 1

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CONTENTS

Introduction 3

Related Activities 4

Key Terms 5

Misconceptions 7

Suggested Activities:

Learning Outcome (LO1) 8

Learning Outcome (LO2) 10

Learning Outcome (LO3) 11

Learning Outcome (LO4) 12

Learning Outcome (LO5) 13

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INTRODUCTIONThis Delivery Guide has been developed to provide practitioners with a variety of creative and practical ideas to support the delivery of this qualification. The Guide is a collection of lesson ideas with associated activities, which you may find helpful as you plan your lessons.

OCR has collaborated with current practitioners to ensure that the ideas put forward in this Delivery Guide are practical, realistic and dynamic. The Guide is structured by learning outcome so you can see how each activity helps you cover the requirements of this unit.

We appreciate that practitioners are knowledgeable in relation to what works for them and their learners. Therefore, the resources we have produced should not restrict or impact on practitioners’ creativity to deliver excellent learning opportunities.

Whether you are an experienced practitioner or new to the sector, we hope you find something in this guide which will help you to deliver excellent learning opportunities.

If you have any feedback on this Delivery Guide or suggestions for other resources you would like OCR to develop, please email resources.feedback@ocr.org.uk.

Unit aimAll machines and structures are constructed using the principles of mechanical engineering. Machines are made up of components and mechanisms working in combination. Engineers need to understand the principles that govern the behaviour of these components and mechanisms. This unit explores these principles and how they are applied.

By completing this unit learners will develop an understanding of:

• systems of forces and types of loading on mechanical components

• the fundamental geometric properties relevant to mechanical engineering

• levers, pulleys and gearing

• the properties of beams

• the principles of dynamic systems

Unit 3 Principles of mechanical engineering

LO1 Understand systems of forces and types of loading on mechanical components

LO2 Understand fundamental geometric properties

LO3 Understand levers, pulleys and gearing

LO4 Understand properties of beams

LO5 Understand principles of dynamic systems

Opportunities for English and maths skills developmentWe believe that being able to make good progress in English and maths is essential to learners in both of these contexts and on a range of learning programmes. To help you enable your learners to progress in these subjects, we have signposted opportunities for English and maths skills practice within this resource. These suggestions are for guidance only. They are not designed to replace your own subject knowledge and expertise in deciding what is most appropriate for your learners.

English Maths

Please note

The timings for the suggested activities in this Delivery Guide DO NOT relate to the Guided Learning Hours (GLHs) for each unit.

Assessment guidance can be found within the Unit document available from www.ocr.org.uk.

The latest version of this Delivery Guide can be downloaded from the OCR website.

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This unit (Unit 3) Title of suggested activity Other units/LOs

LO1 Resolving forces Unit 1 Mathematics for engineering LO4 Be able to use trigonometry in the context of engineering problems

LO1 Resultant forces Unit 1 Mathematics for engineering LO1 Understand the application of algebra relevant to engineering problems

LO1 Tension and compression Unit 2 Science for engineering LO4 Understand properties of materials

LO5 Newton’s Laws of Motion Unit 2 Science for engineering LO2 Understand fundamental scientific principles of mechanical engineering

Unit 1 Mathematics for engineering LO1 Understand the application of algebra relevant to engineering problems

LO5 Constant acceleration formulae Unit 2 Science for engineering LO2 Understand fundamental scientific principles of mechanical engineering

Unit 1 Mathematics for engineering LO1 Understand the application of algebra relevant to engineering problems

LO5 Conservation of energy Unit 2 Science for engineering LO2 Understand fundamental scientific principles of mechanical engineering

LO5 Work done and energy Unit 1 Mathematics for engineering LO1 Understand the application of algebra relevant to engineering problems

LO5 Power Unit 1 Mathematics for engineering LO1 Understand the application of algebra relevant to engineering problems

LO5 Conservation of momentum Unit 1 Mathematics for engineering LO1 Understand the application of algebra relevant to engineering problems

The Suggested Activities in this Delivery Guide listed below have also been related to other Cambridge Technicals in Engineering units/Learning Outcomes (LOs). This could help with delivery planning and enable learners to cover multiple parts of units.

RELATED ACTIVITIES

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KEY TERMSUNIT 3 – PRINCIPLES OF MECHANICAL ENGINEERING

Explanations of the key terms used within this unit, in the context of this unit

Key term Explanation

Bending moment Bending moments result from loading on a beam. Bending moments result from equal and opposite tensile and compressive stresses that act on opposite edges of the beam and maintain the internal equilibrium of the cross section of the beam.

Cantilever Beam A beam that is supported at one end, preventing transverse and rotational movement. The other end is unsupported and is free to move as load is applied to the beam.

Centroid The point at which the weight of a component can be considered to act.

Concurrent forces A system of forces that not only act in the same plane but all pass through a single point. This is associated with problems of particle mechanics.

Coplanar forces A system of forces that all act in the same 2D plane.

Direct Strain Strain (ξ) is defined as the change in length (∆l) divided by the original length (l); ξ=∆l/l

Direct Stress Stress (σ) is defined as the load carried per unit area; σ = Force/Area = F/A

Equilibrium A component, or body, is said to be in equilibrium if all forces and moments acting on the component, or body, are balanced so there is no net force or moment.

Mechanical Advantage

Mechanical Advantage (MA) is the ratio of the output force to the input force of a simple machine (such as a lever or gear system).

Mechanical Energy A body, or component, can possess mechanical energy either because it has linear or rotational velocity (kinetic energy) or because of its position (height) relative to a defined datum position (potential energy).

Mechanical Power Mechanical power is the rate of change of mechanical energy or the rate at which work is done.

Momentum Momentum is a vector quantity defined as the product of its mass times its velocity. In a collision of two objects, if no external forces are involved, the total momentum of the system will always be conserved.

Non-concurrent forces

A system of forces that do not pass through the same point. This is associated with rigid body mechanics.

Particle mechanics An engineering situation that can reasonably be represented by a component that is a single point. All forces acting on the particle should, therefore, be concurrent.

Prism Component with a constant cross section along its length.

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Explanations of the key terms used within this unit, in the context of this unit

Key term Explanation

Rigid body mechanics

An engineering situation where the spatial relationship between forces must be represented.

Shear force A transverse force acting in the same plane as the cross section of a component.

Shear stress Shear stress (τ) is defined by as the shear force (SF) carried by each unit area of the cross section (A) carrying the shear force. τ = SF/A

Simply Supported Beam

A beam with two supports which prevent transverse movement but allow rotational movement at the support.

Velocity Ratio Velocity Ratio (VR) is the ratio of the output speed to input speed of a simple machine.

Work done The work done by a force is defined as the product of the force and the distance the force moves (in its direction of action).

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Some common misconceptions and guidance on how they could be overcome

What is the misconception? How can this be overcome? Resources which could help

Algebraic manipulation Practice of basic techniques. Unit 01 LO1 of this qualification

Vector and scalar quantities Learners should be alert to the difference between scalar and vector quantities - for example the displacement and the distance travelled by a particle in a given time are not necessarily the same.

Unit 02 LO2 of this qualificationhttp://www.physicsclassroom.com/class/1DKin/Lesson-1/Scalars-and-Vectors

Units of measurement Learners should always be required to state quantities using appropriate metric units. http://www.engineeringtoolbox.com/si-unit-system-d_30.html

MISCONCEPTIONS

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SUGGESTED ACTIVITIESLO No: 1

LO Title: Understand systems of forces and types of loading on mechanical components

Title of suggested activity Suggested activities Suggested timings Also related to

Types of loading Learners must understand different types of loading that could be applied to a mechanical component. This fundamental topic could be taught with reference to examples that are familiar to the learner. Common examples are:

• Direct forces

– lifting/pushing/pulling an object

• Turning forces

– tightening a bolt

– drive shaft in a car

• Shear forces

– riveted joints

– simple pinned connections (eg. clevis pins)

Learners should understand that turning forces are often produced by direct forces acting at a distance from the component.

30 minutes

Resolving forces This has considerable overlap with LO4 of Unit 1 dealing with trigonometric functions of sine, cosine and tangent. In this context it would be helpful for teachers to stress the need to define the positive axes (typically x and y) before carrying out calculations. Learners should always define the coordinate system they are using to define orthogonal forces. Understanding could be reinforced by working through suitable examples.

1 hour Unit 1 LO4

Concurrent and Non-concurrent systems of co-planar forces

Teachers could use real world examples to illustrate the difference between concurrent and non-concurrent force systems. For example for some calculations an aircraft in flight might be represented as a particle acted on by four forces (lift, weight, thrust, drag) whereas in other situations the same aircraft would be represented by a much more complex mathematical model involving many more forces. There are many other suitable contexts such as the human body and motor vehicles that could be used to illustrate this point.

In problems of particle mechanics all forces acting on an object should be shown passing through a single point (the particle). In problems involving rigid body mechanics, it is essential that the line of action (i.e. the exact placement) of forces is shown.

1 hour

Force diagrams

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Title of suggested activity Suggested activities Suggested timings Also related to

Equilibrium It is important that learners understand that for problems of particle mechanics there are two independent conditions of equilibrium (usually taken to be horizontal and vertical equilibrium), but for rigid body problems a third (rotational) equilibrium condition is added.

30 minutes

Resultant forces

See Lesson Element Equilibrium of a Rigid Body

This builds on work already covered (above), adding horizontal components and vertical components of several forces to find the result of all forces as orthogonal components. Learners should be able to use trigonometry to determine the angle at which the resultant will act. Learners should understand that the equilibrant is a force that is equal in magnitude but opposite in direction to the resultant of the set of forces.

For non-concurrent forces learners should be able to find the line of action of the resultant to produce the same turning effect as the individual forces.

1 hour Unit 1 LO1

Tension and compression It is important that teachers introduce learners to the concepts of Stress and Strain as a way of understanding the effects of loads on the material rather than the effects of loads on a component made from that material. Length, including the conditions required for the assumption of uniform stress and strain to be valid might be a good starting point. This is well presented in https://www.youtube.com/watch?v=ZiSwnUDnnIM

Discussion around the basic formula (Stress = Force/Area and Strain = Extension/Original) A simple model made from a soft elastic material (e.g. a synthetic sponge) could be useful to illustrate uniform stress and strain.

Learners could be provided with a selection of stress v strain curves representing different materials and asked to describe how a component made from the material would behave when put into axial tension or compression.

Learners could be set a task to research the behaviour of common engineering materials and thereby to develop an understanding of how the properties of the material can be identified from the graph of stress against strain.

A good overview of this topic can be seen at https://www.youtube.com/watch?v=0qGrbZPeQew

2 hours Unit 2 LO4

Direct stress and strain and Young’s Modulus

Stress v. strain graphs

Shear stress Teachers could make simple demonstration pieces to illustrate a clevis pin in single and double shear. This should help to make clear to learners the cross sectional area carrying the shear load. Worked examples and follow up questions could be used to reinforce understanding.

30 minutes

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LO No: 2

LO Title: Understand fundamental geometric properties

Title of suggested activity Suggested activities Suggested timings Also related to

Irregular 2D shapes Learners should practice breaking down a complex shape into a combination of simple rectangles, right angled triangles and semi-circles using addition and subtraction of these shapes.

30 minutes

The volume of a regular prism

These are straightforward calculations. Greater engineering context might be achieved by basing calculations on real examples (e.g. structural components around the school/college) using measured dimensions and researched material densities.

30 minutes

The mass of a body

The centroid of a body Learners must understand that the centroid of a body defines the point at which the weight of that body will act. This is important for many problems of rigid body mechanics.

15 minutes

Shapes with axes of symmetry

Learners should be able to use of axes of symmetry of a uniform 2D figure to find its centroid. This can be demonstrated by using 2D models of uniform material with two or more axes of symmetry: draw axes of symmetry to locate their crossing point. It should be possible to suspend the 2D shape from this point without any rotation of the body.

30 minutes

Centroids of common non-symmetrical 2D shapes

Learners should be taught the position of the centroids of

• Right angled triangles

• Semi circles

This is straightforward factual knowledge. No formal proof is required for this specification. The given values could be reinforced and demonstrated by using 2D models, as above.

15 minutes

Moment of area This is a straightforward technique. Results could be verified using the same 2D model technique as above. A clear presentation of the method can be found at https://www.youtube.com/watch?v=nAEBQQNAmzU

1 hour

SUGGESTED ACTIVITIES

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LO No: 3

LO Title: Understanding levers, pulleys and gearing

Title of suggested activity Suggested activities Suggested timings Also related to

Mechanical advantage (MA) and velocity ratio (VR)

It might be useful for teachers to emphasise that the terms MA and VR apply to many types of simple machines. MA being the ratio of output force to input force, and VR the ratio of the velocity output of the machine to the velocity of the input. It is useful for learners to know that VR is the inverse of MA (and vice versa).

30 minutes

Classes of lever

See Lesson Element Case study of levers: cycle brakes

Use common examples of levers to illustrate the different classes of lever. For example,• Class One - Oars in a rowing boat

• Class Two - Wheelbarrow

• Class Three - Tweezers

more examples at http://www.enchantedlearning.com/physics/machines/Levers.shtml

Learners must be able to identify the fulcrum of a lever and the distances from the fulcrum to the input and output forces, and use these to calculate the MA and VR for the system.

30 minutes

Gears and gear systems Learners should be able to identify and name different types of gears and gear systems, and their applications This could be set as a research activity, or examples given of different examples of applications of gears, for example those used in machine tools, especially lathes. There is considerable scope for extension beyond the immediate specification content to include involute gear profiles, helical cut gears etc.

1 hour

MA and VR for spur gears This is a straightforward calculation, but could be illustrated using one of the many types of construction kits (e.g. Lego, Fischer Technic) or ‘home’ made gears (see https://woodgears.ca/gear_cutting/template.html for suitable profiles).

1 hour

MA and VR for simple compound spur gear systems

This is a relatively simple extension of the above. Worked examples and practice exercises could be used to reinforce understanding.

1 hour

Pulley and belt drive systems There are many examples of belt driven systems in automotive and machine tool applications. These could form the basis for a research activity for learners to begin to understand the advantages and disadvantages of the different types of belts and their advantages and disadvantages compared to other methods of transmitting rotational motion.

1 hour

MA and VR for belt drive systems

See Lesson Case study for a belt and pulley drive system

The concepts involved are very similar to those for spur gears. 1 hour

SUGGESTED ACTIVITIES

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LO No: 4

LO Title: Understand properties of beams

Title of suggested activity Suggested activities Suggested timings Also related to

Types of beams Learners should know the definition of a beam - as a 2d component subject to only transverse loads. This gives two equilibrium conditions, and restricts the types of beams that can be analysed using static equilibrium to simply support and cantilever beams.

Loading is classified as dead loads and live loads (sometimes called self-weight and imposed loading).

30 minutes

Loading applied to beams

See Lesson Element Introduction to beams

Reactions of beams Learners need to be able to calculate the reactions for simply supported and cantilever beams. This could be taught as an extension of the work in LO1 of this unit, treating the beam as a rigid body. Learners should understand that vertical and rotational equilibrium can be used to find two unknown reactions; two equilibrium equations can be solved simultaneously to find two unknown values.

30 minutes

Bending Moments To understand bending moments, learners will need to understand the concept of ‘internal equilibrium’. This is well explained in this videohttps://www.youtube.com/watch?v=Hd8w_7s_78A

In doing so they will also need to understand shear forces in the beam section, although this will not be assessed in this qualification.

Learners will need to be able to calculate the bending moment at any point of a simply supported or cantilever beam. This will repeat work from LO1 of this unit, i.e. equilibrium of a rigid body.

The bending moment diagram can be presented as drawing a graph of the bending moment along the length of the beam.

2 hours

Bending moment diagrams

SUGGESTED ACTIVITIES

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LO No: 5

LO Title: Understand principles of dynamic systems

Title of suggested activity Suggested activities Suggested timings Also related to

Newton’s Laws of Motion Newton’s laws of motion underpin much of the content of this unit. Learners should understand that a state of equilibrium does not necessarily imply that the body in question is stationary, although in many practical engineering situations this may be true.

In particular Newton’s second law (represented by F = ma) is fundamental to this LO, so simple worked examples to show its application are worthwhile.See https://www.youtube.com/watch?v=QffUhiX2uSg

30 minutes Unit 2 LO2Unit 1 LO1

Constant acceleration formulae

The constant acceleration formula should initially be applied to problems of linear motion. There is considerable scope for worked examples and questions to be based in real world contexts such as falling objects, vehicles (or objects) travelling in a straight line, objects projected vertically. It is important that learners know that velocity, acceleration and displacement are vector quantities and so it is vital that they define the positive axis for all calculations.

Learners should also be introduced to problems involving objects moving in two dimensions. Typically these will be problems of projectiles moving under gravity.

3 hours Unit 2 LO2Unit 1 LO1

Conservation of energy Teachers could begin by introducing the concepts of Gravitational Potential Energy (GPE) and Kinetic Energy (KE) and the way in which one quantity is ‘converted’ to the other - for example when an object falls. Learners will need to be familiar with the range of questions that could arise and this is probably best accomplished through worked examples. Many examples of these questions will be found in any mechanics, physics or engineering textbook of the appropriate level. Many typical problems could be solved either using the principle of conservation of energy or using the constant acceleration formula. Where applicable it would be useful for learners to verify results obtained using both methods.

3 hours Unit 2 LO2

Work done and energy

See Lesson Element Work done and Energy

Teachers could show the equivalence of work done and energy gained by using the Newton’s second law and the constant acceleration formula. Learners need to know that the work done by forces acting on a body will cause an equivalent increase in the energy of the body and how this can be used to solve problems involving bodies moved by external forces. See https://www.youtube.com/watch?v=2WS1sG9fhOk for an introduction to this topic.

This topic could be taught using worked examples of progressive complexity. Many suitable questions will be found in standard texts (for example motion on inclined planes) and will enable learners to develop understanding and familiarity with the format of assessment.

1 hour

3 hours Unit 1 LO1

SUGGESTED ACTIVITIES

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SUGGESTED ACTIVITIESTitle of suggested activity Suggested activities Suggested timings Also related to

Power

See Lesson Element Understanding work, energy and power

Learners should understand that Power is the rate of work, or the rate of change of energy. Power problems will almost certainly include other topics within this LO and should bring many opportunities to use engineering contexts as their basis.

3 hours Unit 1 LO1

Friction

See Lesson Element Coefficient of friction/limiting friction

LE Coefficient of Friction suggests an experimental introduction to the topic of friction between two surfaces. Learners should be familiar with Newton’s third law and so understand the nature of the normal contact force acting between when two bodies are touching. Learners should know that the value of the coefficient of friction will lie between 0 and 1, and that the direction of the friction force will always oppose the motion of the body or bodies.

2 hours

Conservation of momentum Learners should understand that when two bodies collide momentum is always conserved but energy is only conserved if the collision is elastic. This is well presented in video: https://www.youtube.com/watch?v=V4vzNk4qppw

There is a wealth of information available to help learners understand this topic, for example;https://www.youtube.com/watch?v=rX9GBvCSLo4

https://www.youtube.com/watch?v=FeqUREuTnJw

Learners will need to practice solving problems involving elastic collision (conservation of momentum and conservation energy) and collisions where the two bodies coalesce (i.e. become linked together) so that they have a common final velocity. Many such examples will be found in standard textbooks.

2 hours Unit 1 LO1

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