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2.72 Elements of Mechanical Design

Spring 2006

3D color rendering of a robot leg.A SolidWorks® model of a hexapod robot's leg, as used in Homework #3 in this course's assignments section. (Diagram by Pablo Valdivia, based on a robot design by Alex Dirks).

Course Highlights

This course features selected notes and modeling files used in lectures, plus a complete set of assignments.

Course Description

This course provides an advanced treatment of machine elements such as bearings, springs, gears, cams, and mechanisms. Analysis of these elements includes extensive application of core engineering curriculum including solid mechanics and fluid dynamics. The course offers practice in skills needed for machine design such as estimation, drawing, and experimentation. Students work in small teams to design and build machines that address real-world challenges.

Technical Requirements

Special software is required to use some of the files in this course: .mcd, .sldasm, .sldprt, .swj, .wm, .xmcd, .xls, and .zip.





Syllabus

Amazon logo Help support MIT OpenCourseWare by shopping at Amazon.com! MIT OpenCourseWare offers direct links to Amazon.com to purchase the books cited in this course. Click on the Amazon logo to the left of any citation and purchase the book from Amazon.com, and MIT OpenCourseWare will receive up to 10% of all purchases you make. Your support will enable MIT to continue offering open access to MIT courses.

This course is a junior/senior level elective on machine elements and mechanical design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice.



Course Structure

This course meets in two classroom sessions and one lab session each week. We expect you to be present at these sessions and to participate thoughtfully.

The class sessions will be used to introduce new material, to amplify with examples, to do interactive exercises, and to provide feedback on homework assignments, exams, and the project. The weekly lab sessions are devoted to hands-on activities that support learning the content, advancing the term projects, and complementing homework and exam activities.



Projects

The team project is a central experience in this course, in which students apply electro-mechanical design principles for a variety of machine elements. Teams of 3 to 5 people will work on a project of their choice (from a list of suggested topics), and be limited to a $500 budget. The project requirements include:



Grading

The course grade will be determined as follows:


Activitiespercentages
Homework (8 Assignments at 5% each)40%
Exams (2 Exams at 15% each)30%
Project25%
Participation5%





Textbooks

There is no required textbook for the course, although the following books are suggested for purchase by students. They are sometimes used as a source of material in handouts and as a source of some questions in the problem sets.

Amazon logo Shigley, J. E., C. R. Mischke, and R. G. Budynas. Mechanical Engineering Design. 7th ed. Burr Ridge, IL: McGraw-Hill, 2003. ISBN: 9780072921939.

Amazon logo Hamrock, B. J., et al. Fundamentals of Machine Elements. 2nd ed. Burr Ridge, IL: McGraw-Hill, 2004. ISBN: 9780072465327.

Amazon logo Norton, R. L. Design of Machinery. 3rd ed. Burr Ridge, IL: McGraw-Hill, 2003. ISBN: 9780072864472.

Amazon logo Oberg, E., et al. Machinery's Handbook. 27th ed. New York, NY: Industrial Press, Inc., 2004. ISBN: 9780831127114.



Software

Computation is essential to modern mechanical engineering design. However, it is not a primary objective of this subject to develop your proficiency with any particular software tool. We have developed assignments that require substantial computation, but we leave it to each student to select the software to use. We will be using Mathcad® fairly extensively for in class demonstrations and exercises, so it behooves you to learn the basics of this program. However, you may turn in assignments done with MATLAB®, MiniTab®, Excel, Mathematica®, or whatever tools you wish to use.



Learning Objectives

In engineering design, it is helpful to give careful considerations to objectives and to the form in which they are expressed. To the extent possible, the learning objectives of this subject were developed following the guidelines articulated by Richard Felder including use of action verbs and inclusion of objectives in levels 4-6 of Bloom's taxonomy of educational objectives as shown below.


Educational ObjectivesAssociated Action Verbs
6. EvaluationJudge, Critique, Justify
5. SynthesisDesign, Invent, Propose
4. AnalysisPredict, Model, Derive
3. ApplicationCalculate, Solve
2. ComprehensionExplain, Paraphrase
1. KnowledgeList, Recite



After taking this course, students should be able to:

  • Analyze and refine the design of existing electro-mechanical devices making advanced use of the core mechanical engineering disciplines
    • Mechanics and Materials (2.001 and 2.002)
    • Systems, Modeling, and Dynamics (2.003 and 2.004)
    • Thermal-Fluids Engineering (2.005 and 2.006)
    • Design and Manufacturing (2.007 and 2.008)
  • For all the common machine elements including fasteners, joints, springs, bearings, gearing, clutches, couplings, belts, chains, and shafts
    • Describe the function of the element
    • List common uses in mechanical systems and give examples
    • Analyze its performance and failure modes based on core disciplines
    • Describe how they are manufactured and the implications of the alternatives
    • Select an element for a specific use based on information such as that typically available in a manufacturer's catalog
  • Apply experimentation and data analytic (statistical) principles relevant to mechanical design
    • Consider the effects of geometric variation on a design
    • Analyze data from performance evaluations of a mechanical system
    • Present data in appropriate graphical formats
    • Plan an experimental investigation to refine a system
    • Analyze the reliability of simple mechanical systems
  • Communicate a design and its analysis (written, oral, and graphical forms)
    • Read and interpret mechanical drawings of systems with moderate complexity
    • Create correct mechanical drawings of simple elements and systems
    • Make effective presentations in a design review format
    • Respond effectively in real time to technical questioning by experts


Time Commitment and Expectations

The units on an MIT subject correspond to the time that an adequately prepared student is expected to spend in a normal week. This is divided into three numbers associated with the subject (X-Y-Z) with X being class time, Y being laboratory time, and Z being work outside of class. The numbers associated with 2.72 are (3-3-6) making this a 12-unit subject. Thus, the overall weekly time commitment is expected to be about 12 hours. This includes to 6 hours per week scheduled in class and 6 hours per week out of class. The out-of-class time will roughly be split between homework assignments and project work.

This course will not be graded on a curve. In principle, everyone in the course can earn an A, but that is not usually what happens. Historically 50% to 25% of students earn a B and a small number earn a C or worse. All problems will be graded on a letter basis according to the MIT definition of grades:

A - Exceptionally good performance, demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge, and a skillful use of concepts and/or materials.

B - Good performance, demonstrating capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the subject.

C - Adequate performance, demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.

D - Minimally acceptable performance, demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

F - Unsatisfactory performance.

Plusses and minuses will be used in conjunction with the letters in grading all work. The final grade will include plusses and minuses.



Academic Honesty*

The fundamental principle of academic integrity is that one must fairly represent the source of the intellectual content of the work one submits for credit. Students are trusted to adhere to this principle and its meaning in the context of this subject as subsequently explained. Official Institute policy regarding academic honesty can be found in the current Bulletin under "Academic Procedures and Institute Regulations".

What is the policy on examinations?
The examinations in this subject are to represent individual work. You may not receive any help from other students or any other individuals.

What about home assignments? Can we work together?
We encourage students to work together in this subject to understand the homework assignments and to learn in general. There is much to be gained in sharing the learning process. However, the final submission should represent your own expression of the final response to the assignment and not a copy of someone else's expression thereof, whether directly from a person or as recorded on paper (e.g. a book) or electronically (e.g. on a Web site). Furthermore, you must fairly represent the authorship of the intellectual content of the work you submit for credit by acknowledging the contribution of sources (e.g., books, Web sites) you consult in the process of completing assignments. In addition, at the end of each assignment on which you collaborated with other students, you must cite the students and the interaction. The purpose of this is to acknowledge their contribution to your work. Some examples follow:

  1. You discuss concepts, approaches and methods which could be applied to a home assignment before starting your write-up. This process is encouraged. You are not required to make a written acknowledgment of this type of interaction.
  2. After working an assignment independently, you compare responses with another student which confirms your results and response. You should acknowledge that the other student's write-up was used to check your own. No credit will be lost if the response is correct, the acknowledgment is made, and no direct copying of the other response is involved.
  3. After working an assignment independently, you compare responses with another student which alerts you to an error in your own work which you then correct. You should state at the end of your submission that you corrected your error on the basis of checking responses with the other student. No credit will be lost if the response is correct, the acknowledgment is made, and no direct copying of the other response is involved.
  4. You and another student work through an assignment together exchanging ideas as the effort progresses. You both should state at the end of your individual submissions that you worked jointly. No credit will be lost if the responses are correct, the acknowledgment is made, and the assignment write-up is independent.
  5. You copy all or part of an assignment write-up from a reference such as a textbook or past solution (this is in contrast to referring to such a reference and developing the solution yourself). You must cite the reference. Partial credit will be given, since there is some educational value in reading and understanding the solution.
  6. You copy verbatim all or part of a write-up from another student. You must cite the person by name. Very little partial credit will be given.
  7. Verbatim copying of any material which you submit for credit without reference to the source is considered to be academically dishonest.

*This academic honesty policy is adapted from the policy used in 16.01 Unified Engineering.





Calendar

Instructors

DF = Prof. Daniel Frey
AS = Ms. Amy Smith

The calendar below provides information on the course's lecture (L) and lab (Lab) sessions.


Ses #TopicsInstructorsKey Dates
L1Course Introduction - Project IdeasDFProject ideas presented
L2Gears - Basics, Terminology, Involute CurveDFHomework 1 out
Lab 1Lab: Student Initiated Project IdeasProject preferences due
L3Gears - Force Transmission, Gear TrainsDFProject teams announced
L4Gears - Stress Analysis, Life, Reliability, SelectionDFHomework 2 out

Homework 1 due
Lab 2Lab: Gears
L5Mechanisms (2D Kinematic Analysis)DFHomework 3 out

Homework 2 due
Lab 3Lab: 2D Kinematic Analysis of Mechanisms
L6Mechanisms (Synthesis of 4 Bar Mechanisms)DF
L7Mechanisms Field Trip to MIT MuseumHomework 4 out

Homework 3 due
Lab 4Lab: Mechanism Synthesis
L8Mechanisms (Forces in 2D Mechanisms)DF
L9Mechanisms (3D Mechanisms)DFHomework 5 out

Homework 4 due
Lab 5Lab: Mechanisms - Force Analysis and Design
L10Journal BearingsDF
L11Rolling Element BearingsASHomework 6 out

Homework 5 due
Lab 6Lab: Bearings (Lawnmower Engine)
Exam 1
L12BeltsDF
Lab 7Project Work Only
L13CamsDF
Lab 8Mid-term Project Presentations (Oral)Homework 7 out

Homework 6 due
L14Bolted JointsDF
L15FastenersASHomework 8 out

Homework 7 due
Lab 9Lab: Cams, Clutches, Fasteners, etc.
L16Optics Modeling; Calibration; Machine Error PropagationGuest LecturerHomework 8 due
Lab 10Lab: Metrology Modeling and Calibration
L17BatteriesDF
L18Electric MotorsDF
Lab 11Lab: Electric Motors and Batteries
L19ActuatorsDF
L20HydraulicsAS
Lab 12Lab: Hydraulics (Front Loader)
L21MicrocontrollersDF
L22SensorsDF
Exam 2
L23Final Project Clinic
L24Course Summary / FeedbackProject final written report due




Lecture Notes

Special software is required to use some of the files in this section: .mcd, .sldasm, .sldprt, .swj, .wm, .xmcd, .xls, and .zip.


Amazon logo Help support MIT OpenCourseWare by shopping at Amazon.com! MIT OpenCourseWare offers direct links to Amazon.com to purchase the books cited in this course. Click on the Amazon logo to the left of any citation and purchase the book from Amazon.com, and MIT OpenCourseWare will receive up to 10% of all purchases you make. Your support will enable MIT to continue offering open access to MIT courses.

This page presents lecture slides and supplemental modeling files for a subset of the class sessions. The rest of the lectures slides are not available for copyright reasons.



Instructors

DF = Prof. Daniel Frey
AS = Ms. Amy Smith


Ses #TopicsInstructorsSupporting Files
L1Course Introduction - Project Ideas (PDF)DF
L2Gears - Basics, Terminology, Involute Curve (PDF)DFGear Model Files: Peg Gears, Spur Gears, Rack Cutting, Gear Train, and Involute Construction (ZIP) (The ZIP file contains: 1 .sldprt file and 4 .wm files.)
L3Gears - Force Transmission, Gear Trains (PDF)DF
L4Gears - Stress Analysis, Life, Reliability, SelectionDF
L5Mechanisms (2D Kinematic Analysis) (PDF)DFHTM Demonstrator (XMCD)
Hexapod Model (ZIP - 2.5 MB) (The ZIP file contains: 4 .sldasm files, 25 .sldprt files, and 1 .swj file.)
L6Mechanisms (Synthesis of 4 Bar Mechanisms) (PDF)DFDump Truck Files: Three Position Synthesis, Kinematics, and Path Generation (ZIP) (The ZIP file contains: 1 .wm file and 2 .xmcd files.)
L7Mechanisms Field Trip to MIT Museum
L8Mechanisms (Forces in 2D Mechanisms) (PDF - 1.0 MB)DFPath Generation - Mathcad (MCD)
Path Generation - Excel (XLS)
Vise Grips Model (WM)
L9Mechanisms (3D Mechanisms) (PDF)DFMathcad® files: HTM about a Point, HTM about a Vector, 3D Leg Mechanism (ZIP) (The ZIP file contains: 3 .mcd files.)
L10Journal Bearings (PDF)DFMcPherson Strut (XMCD - 1.8 MB)
L11Rolling Element Bearings (PDF)AS
L12BeltsDF
L13CamsDF(ZIP) (The ZIP file contains: 3 .xmcd files.)
L14Bolted JointsDF(XMCD)
L15FastenersAS
L16Optics Modeling; Calibration; Machine Error PropagationGuest LecturerAmazon logo Handout: Frey, D. "Error Budgeting." Chapter 10 in Robotics and Automation Handbook. Edited by W. H. C. Bassetti. Boca Raton, FL: CRC Press, 2004. ISBN: 9780849318047.
L17BatteriesDF
L18Electric Motors (PDF)DF
L19ActuatorsDF
L20HydraulicsAS
L21MicrocontrollersDF
L22SensorsDF
L23Final Project Clinic
L24Course Summary / Feedback




Assignments

Special software is required to use some of the files in this section: .zip and .xmcd.


AssignmentsSupporting Files
Homework 1 - Gears (PDF)
Homework 2 - Gears (PDF)
Homework 3 - Kinematic Analysis and Synthesis (PDF)
Homework 4 - Mechanisms: Analysis, Synthesis, Forces (PDF)Mathcad® Files (ZIP) (The ZIP file contains: hw4_soln_1.xmcd and hw4_soln_2.xmcd.)
Homework 5 - 3D Analysis of Forces (PDF)
Homework 6 - 3D Mechanism Synthesis, Journal Bearings, and Rolling Element Bearings (PDF)
Homework 7 - Design and Manufacturing (PDF)Data File (TXT)
Homework 8 - Bolted Joints (PDF)




Projects

Project Goals

The team project is a central experience in this course, in which students apply electro-mechanical design principles for a variety of machine elements. Teams of 3 to 5 people will work on a project of their choice (from a list of suggested topics), and be limited to a $500 budget. The project requirements include:



Some Project Ideas

The following project ideas were introduced in the slides for Lecture 1 (PDF)



List of Students' Projects

Students chose the following projects to work on during the term:





Study Materials

This page presents some study materials for the two exams.

Concept Questions for Exam 1 (PDF)

Concept Questions for Exam 2 (PDF)




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