Lesson Plans: Principles of the Embodiment Design Phase

Topic 7 Embodiment Design
(detailed objectives) (available resources)
Goal: Equip students with practical analytical tools applicable to typical mechanical systems.
[standards: NS.5-12.5, NM-MEA.9-12.3, NM-ALG.6-12.3, NM-PROB.CONN.PK-12.3]

(to review the detailed content, download the low resolution pdf of available teacher presentation)
Summary
The embodiment design phase will take the abstract conceptual path, chosen in the conceptual design phase, and mold it into a system that can actually be produced. Decisions during this phase should be (as much as possible) justified by mathematical (and physical) proof. Collegiate engineering programs take years to equip their students with the basic tools for analysis. This topic is not even meant to be an overview. We can only provide some examples of what engineering analysis is. Qualitative principles are introduced as are quantitative ideas including center of gravity, torque, forces in springs, and internal stresses.

Background
Every engineer works within a framework of familiar physical principles. Each is trained to use analytical tools specific to the types of systems that he/she encounter every day. Because our project is inherently mechanical and because the mechanical systems tend to be more intuitive to most people, this topic focuses solely on embodiment principles of mechanical design. Sometimes the principles are qualitative and sometimes they are quantitative.

The rules of Clarity, Simplicity, and Safety are qualitative rules generally applicable to all engineering disciplines and should be considered constantly throughout the embodiment design phase. Clarity speaks to the aim of having a clearly defined role for each component and sub-component in the design. Simplicity refers to the aim to keep the overall design (and the design of each component) as simple as possible while still accomplishing the overall goal. Complexity in shape makes the outcome more difficult to predict, while adding more parts and sub-assemblies complicates assembly and maintenance. There is a difference between being safe and safe design. Adding a placard on a tool that says "beware of cutting blade" is no substitute for installing a blade guard that actually prevents the user from being able to touch the moving blade.

The principles of Force Transmission, Division of Tasks, and Self-Help are just three of many general principles that mechanical engineers should be attune to. When planning force transmissions one should avoid abrupt changes in direction of the forces, use the shortest possible path, match deformations in adjoining parts, and balance un-needed forces as much as possible. Assigning a single function (or task) to a specific component allows for better exploitation of the component, provides greater load capacity, and ensures unambiguous behavior. The Self-Help principle is especially broad in its application. Basically, the engineer looks for ways to use the natural system effects to achieve design objectives rather than continually fighting against the natural system effects. An example is found in the design of a typical paper clip. As more sheets of paper are added, the design needs to apply more forces to keep the sheets together. Fortunately, the design of the paper clip is such that the further it is expanded, the more force it naturally applies. (Obviously, there is a limit before the clip fails.) Looking for Self-Help solutions requires a lot of creativity and ability by the designer to abandon preconceptions.

Center of Gravity, Motor Torque, Levers, Spring Forces, and Gear Ratios are areas where students can easily make the connections between their tangible world and the abstract world of mathematics.

For realistically sized and shaped objects, gravity not only causes the object to fall towards the Earth but can also cause the object to rotate and tilt. It is important to know not only how much gravity force is acting, but where on the object it is acting.
The output of most motors is not a force, but rather a torque applied to the motor shaft. The magnitude of the output torque depends on the current applied to the motor. This torque can be used to apply various amounts of forces depending on the length of the output "lever."
A mechanical spring stores potential energy when its length is changed from its natural state. The amount of force required to deflect a spring is directly related to the amount of deflection. This mathematical relationship can be easily determined experimentally and is easily used to predict the response of a spring.
Gears can be used to change a motor's output speed and torque into more usable speeds and torques. Because the power of a motor is limited, if you increase the speed, you must decrease the torque and vis-a-versa. The relationship between the input and output of a set of gears is easily predicted if you know the sizes of the gears you are using.

With a little creativity you can contrive easy and inexpensive demonstrations of these principles and predict the results mathematically. All these principles are likely to be relevant in the class project. Some of them are covered in more detail in later topics. If students wish to engage this detail now, they can probably review those topics independently at their own pace.

Teacher Preparation

Prepare examples of the various embodiment design principles that are easy for the students to relate to.
Prepare simple diagrams and calculations to qualitatively analyze the examples.

Classroom Activities
Begin with class discussion about exactly how engineers can know that one design is better than another. Lead class discussions towards the fact that mathematics can be used to model and predict how physical systems will act. Discuss the difference between qualitative guidelines and quantitative predictions. Discuss some very intuitive examples where center of gravity, leverage, and internal stresses impact the effectiveness of a system. Use the simple math of gear ratios and motor parameters to convey the notion of quantitative engineering analysis. Use a mix of individual effort, small group effort, and full team discussions to keep all students actively engaged.

Objectives 7.1 Embodiment Design: General Guidelines Comprehend the objective and deliverables of the embodiment design phase Comprehend the basic rules of mechanical embodiment design Comprehend basic principles relating to force transmission Comprehend the quandary between "division of tasks" and "clarity" Comprehend the self-help principle and describe some examples	Activities Engage students with teacher presentation.
7.2 Embodiment Math Overview - Part 1 Comprehend concept of "center of gravity" and its general implications on mechanical design Calculate center of gravity for simple shapes Calculate center of gravity for complex shapes Comprehend the concept of torque and its units Know the basic torque-current relationship for a DC motor	Individually demonstrate basic math skills and intuition about center of gravity. Engage students with teacher presentation. Small group practice problem solving.
7.3 Embodiment Math Overview - Part 2 Comprehend the concept of leverage and how to use it when the applied force is limited Comprehend the difference and similarity between a lever and a pulley mounted to a motor Apply basic lever equation Comprehend basic definition of mechanical springs Apply basic spring equation Know how to perform experiments to find the spring constant	Individually demonstrate basic math skills and knowledge about levers. Engage students with teacher presentation. Small group practice problem solving.
7.4 Embodiment Math Overview - Part 3 Distinguish force and stress Apply relationship between force, area, and stress Comprehend why internal stresses and internal bending moments exist Comprehend relationship between internal stress, bending moment, and part geometry Comprehend the impact that width and height have on moment of inertia (and hence, the strength of a beam) Comprehend simple guidelines for designing part geometry to resist bending	Individually demonstrate basic intuition about internal forces. Engage students with teacher presentation.
7.5 Embodiment Math Overview - Part 4 Comprehend basic need for, and goal of, using gears Apply power, torque, speed relationship Apply the equations relating speed and radius of two gears Apply the equations relating torque and radius of two gears Comprehend how to calculate gear ratio	Individually demonstrate basic intuition about gears. Engage students with teacher presentation. Class discussion to identify applications of embodiment principles on class project.
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