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Cambridge TECHNICALS CAMBRIDGE TECHNICALS IN ENGINEERING LEVEL 3 UNIT 3 – PRINCIPLES OF MECHANICAL ENGINEERING DELIVERY GUIDE Version 1 OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING CONTENTS Introduction3 Related Activities 4 Key Terms 5 Misconceptions7 Suggested Activities: Learning Outcome (LO1) 8 Learning Outcome (LO2) 10 Learning Outcome (LO3) 11 Learning Outcome (LO4) 12 Learning Outcome (LO5) 13 PRINCIPLES OF MECHANICAL ENGINEERING 2 This 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. Unit 3 Principles of mechanical engineering LO1 Understand systems of forces and types of loading on mechanical components 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. LO2 Understand fundamental geometric properties LO3 Understand levers, pulleys and gearing 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. LO4 Understand properties of beams LO5 Understand principles of dynamic systems PRINCIPLES OF MECHANICAL ENGINEERING INTRODUCTION 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. Unit aim All 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 Opportunities for English and maths skills development We 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. EnglishMaths 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. 3 OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING If you have any feedback on this Delivery Guide or suggestions for other resources you would like OCR to develop, please email [email protected]. 3 OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING RELATED ACTIVITIES 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. 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 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 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 PRINCIPLES OF MECHANICAL ENGINEERING 4 UNIT 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 Equilibrium 5 Stress (σ) is defined as the load carried per unit area; σ = Force/Area = F/A 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. OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING Direct Stress PRINCIPLES OF MECHANICAL ENGINEERING KEY TERMS OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING 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). PRINCIPLES OF MECHANICAL ENGINEERING 6 7 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 qualification http://www.physicsclassroom.com/ class/1DKin/Lesson-1/Scalars-andVectors 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 PRINCIPLES OF MECHANICAL ENGINEERING Some common misconceptions and guidance on how they could be overcome OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING MISCONCEPTIONS OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING SUGGESTED ACTIVITIES LO No: 1 LO Title: Understand systems of forces and types of loading on mechanical components Title of suggested activity Suggested activities Suggested timings 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: 30 minutes Types of loading • • • Also related to 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. PRINCIPLES OF MECHANICAL ENGINEERING 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. Concurrent and Nonconcurrent systems of co-planar forces Teachers could use real world examples to illustrate the difference between concurrent and non1 hour 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. Force diagrams 1 hour Unit 1 LO4 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. 8 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 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. 1 hour Unit 1 LO1 2 hours Unit 2 LO4 PRINCIPLES OF MECHANICAL ENGINEERING Title of suggested activity See Lesson Element Equilibrium 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. of a Rigid Body Direct stress and strain and Young’s Modulus Stress v. strain graphs 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 Shear stress 9 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 OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING Tension and compression OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING SUGGESTED ACTIVITIES LO No: 2 LO Title: Understand fundamental geometric properties Title of suggested activity Suggested activities Suggested timings 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 30 minutes calculations on real examples (e.g. structural components around the school/college) using measured dimensions and researched material densities. 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 nonsymmetrical 2D shapes Learners should be taught the position of the centroids of 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 Also related to • 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. 1 hour PRINCIPLES OF MECHANICAL ENGINEERING 10 LO No: 3 LO Title: Understanding levers, pulleys and gearing Title of suggested activity Suggested activities Suggested timings 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 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 30 minutes Also related to PRINCIPLES OF MECHANICAL ENGINEERING SUGGESTED ACTIVITIES See Lesson Element Case study of levers: cycle brakes 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. 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 This is a relatively simple extension of the above. Worked examples and practice exercises could be compound spur gear systems 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 The concepts involved are very similar to those for spur gears. 1 hour See Lesson Case study for a belt and pulley drive system 11 OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING more examples at http://www.enchantedlearning.com/physics/machines/Levers.shtml OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING SUGGESTED ACTIVITIES LO No: 4 LO Title: Understand properties of beams Title of suggested activity Suggested activities Suggested timings 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. 30 minutes Loading applied to beams Loading is classified as dead loads and live loads (sometimes called self-weight and imposed loading). Also related to 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 video https://www.youtube.com/watch?v=Hd8w_7s_78A 2 hours Bending moment diagrams 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. PRINCIPLES OF MECHANICAL ENGINEERING The bending moment diagram can be presented as drawing a graph of the bending moment along the length of the beam. 12 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. 30 minutes Unit 2 LO2 Unit 1 LO1 PRINCIPLES OF MECHANICAL ENGINEERING SUGGESTED ACTIVITIES 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 Constant acceleration formulae The constant acceleration formula should initially be applied to problems of linear motion. There 3 hours 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. Unit 2 LO2 Unit 1 LO1 Learners should also be introduced to problems involving objects moving in two dimensions. Typically these will be problems of projectiles moving under gravity. Teachers could begin by introducing the concepts of Gravitational Potential Energy (GPE) and Kinetic 3 hours 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. 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. See Lesson Element Work done and Energy This topic could be taught using worked examples of progressive complexity. Many suitable questions 3 hours 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. Unit 2 LO2 1 hour Unit 1 LO1 OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING 13 Conservation of energy OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING SUGGESTED ACTIVITIES Title of suggested activity Suggested activities Suggested timings Also related to 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 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 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 2 hours See Lesson Element Understanding work, energy and power Friction See Lesson Element Coefficient of friction/limiting friction Conservation of momentum Unit 1 LO1 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. PRINCIPLES OF MECHANICAL ENGINEERING 14 PRINCIPLES OF MECHANICAL ENGINEERING If you do not currently offer this OCR qualification but would like to do so, please complete the Expression of Interest Form which can be found here: www.ocr.org.uk/expression-of-interest OCR Resources: the small print OCR’s resources are provided to support the teaching of OCR specifications, but in no way constitute an endorsed teaching method that is required by the Board and the decision to use them lies with the individual teacher. Whilst every effort is made to ensure the accuracy of the content, OCR cannot be held responsible for any errors or omissions within these resources. © OCR 2015 - This resource may be freely copied and distributed, as long as the OCR logo and this message remain intact and OCR is acknowledged as the originator of this work. OCR acknowledges the use of the following content: Thumbs up and down icons: alexwhite/Shutterstock.com Please get in touch if you want to discuss the accessibility of resources we offer to support delivery of our qualifications: [email protected] 15 OCR LEVEL 3 CAMBRIDGE TECHNICALS IN ENGINEERING We’d like to know your view on the resources we produce. By clicking on the ‘Like’ or ‘Dislike’ button you can help us to ensure that our resources work for you. When the email template pops up please add additional comments if you wish and then just click ‘Send’. Thank you. Cambridge TECHNICALS Contact us Staff at the OCR Customer Contact Centre are available to take your call between 8am and 5.30pm, Monday to Friday. Telephone: 02476 851509 Email: [email protected] For staff training purposes and as part of our quality assurance programme your call may be recorded or monitored. © OCR 2015 Oxford Cambridge and RSA Examinations is a Company Limited by Guarantee. Registered in England. 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