Course Number:  MECH 2120
Course Title:   Kinematics and Dynamics of Machines
Credit Hours:  4
Prerequisites:  MATH2630, MECH2110
Co requisites:   None

Coordinators:
Dan B. Marghitu, Ross 109, phone: 844-3369, office hours: 01:00-02:00 p.m.TR.
Eliza Banu, TA, Ross Hall 349, phone: 844-3403, email: banueli@auburn.edu
Kevin Siniard, TA, Ross Hall, email: kjs0005@auburn.edu

Objectives:
Upon completion of this course, the student will be able to:
1. Characterize and describe the motion of a rigid body and a system of rigid bodies.
2. Identify and describe the forces acting on a rigid body and a system of rigid bodies.
3. Construct free body diagrams of rigid bodies in motion.
4. Construct equations relating the motion of the bodies to the forces acting on the system.  Solve  the resulting equations.
5. Use computer software (Working Model, MATLAB/Mathematica) as a tool for the study of mechanisms.
6. Design gears and epicyclic gear trains.

Tentative Schedule:

1. INTRODUCTION  figures (pdf) (1 classes)  Solutions (pdf) Lecture (pdf)

2. FUNDAMENTALS  figures (pdf) (4 classes)  Solutions (pdf)  Lecture (pdf)
Homework 1  (pdf) solutions (pdf) due: Jan 24 (use Blackboard)

3. POSITION ANALYSIS  figures (pdf) (6 classes)   Solutions (pdf) 
Lecture (pdf)  MATLAB examples (pdf)  MATLAB files: Program 1, Program 2
Homework 2: MATLAB (pdf)  due: Feb 5 (use Blackboard)
Homework 3: position (pdf)  solutions (pdf) due: Feb 7 (use Blackboard)

4. VELOCITY AND ACCELERATION ANALYSIS  figures (pdf) (12 classes) Solutions (pdf)
Lecture Rigid Body Kinematics(pdf)  Examples: I. slider-crank (pdf)  II.  R-TRR (pdf)
I. Problem R-RRT(pdf)    Problem R-RRR-RRT (1.4.4) (pdf)   
II. Problem R-RTR(pdf)   Problem R-RTR-RTR (pdf)
Homework 4: Problems 1, 2, (pdf) 3, 4 (pdf) due: Feb 19 (use Blackboard)
Homework 5: Acceleration of a point  that moves relative to a rigid body (pdf) due: Feb 21 (use Blackboard)
Homework 6: Problems 5, 6 (pdf)  due: Feb 28 (use Blackboard) solutions  P5   P6  (pdf)
Homework 7: Problems 7, 8 (pdf)  due: March 4 (use Blackboard) solutions  P7   P8  (pdf)

5. CONTOUR EQUATIONS FOR MECHANISMS  figures (pdf) (2 classes)  Solutions (pdf)

6. FORCE ANALYSIS   figures (pdf) (14 classes) Solutions (pdf)
Lecture Force Analysis (pdf)   figures (pdf)  table (pdf)
Homework 8: Accelerations of CM, mass moments of inertia (pdf) due: March 25 (use Blackboard) solutions
Homeworks 9-10: Force analysis (pdf)  due: April 1  (use Blackboard)
Example Problem R-RTR (pdf)
Homework 11: Problems 6.3-6.6 (pdf) due: April 14 (use Blackboard)
Homeworks:  Joint reaction forces (pdf)  figures (pdf)  solutions

 7. DYNAMICS   figures (pdf)
[Direct Dynamics (pdf)]  Appendix 2 (Mathematica)
 Problem R-RRT (pdf)    Problem R-RTR (pdf)    HW: Problem R-RTR_I
Direct Dynamics: text (pdf)  figures (pdf)  Appendix 1(program: pdf  mathematica)
Pendulum Programs: Mathematica (pdf  and Mathematica)  Matlab (pdf)  ( R.m and R_program.m)

Homework 12: Pendulum figure  (pdf)         (Program (mathematica))
Homework 13: Problem1 (pdf)
Homework 14:  Problem 2, Problem 3, Problem 4, Problem 22 (PDF)

Rigid Body Dynamics  Dr. Nels H. Madsen
Example 1. Pendulum (HTML) -  mathematica program(pdf) HTML-format
Example 2.   Example 3.   Example 4.   Example 5.   Example 6.   Example 7.   Example 8.

NEWTON'S LAWS OF MOTION  (AUDIO)
 Newton's Three Laws of Motion

8. MECHANISMS WITH GEARS (pdf) (3 classes)

Tests (3 classes)


Laboratory projects:  

PART I: WORKING MODEL

Mechanism analysis with Working Model  figures (pdf)

Gear analysis (pdf)   Gear analysis with Working Model (pdf)

PART II: MECHANISM ANALYSIS WITH MATLAB

Position Analysis with MATLAB   figures (pdf)  MATLAB files: Program 1, Program 2, Program 3, Program 4, Program 5, Program 6, Program 7, Program 8  (pdf)

Velocity and Acceleration Analysis with MATLAB    figures   (pdf) MATLAB files:   Program 1,   Program 2,   Program 3,   Program 4,   Program 5,   Program 6,   Program 7,   Program 8

Dynamic Force Analysis with MATLAB    figures  (pdf)  MATLAB files: Program 1, Program 2, Program 3, Program 4, Program 5, Program 6,  Program 7

Direct Dynamics (Newton-Euler eom) with MATLAB (pdf)  MATLAB files:  Program 1,  Program  2,  R.m,   Program 3,  Program 4,  Program 5,  Program 6,  Program 7,  Program 8,  RR.m,  Rrobot.m,  RRrobot.m

FIGURES  and  TABLES (Figs. 1 - 20 ) (pdf)

MECHANISM ANALYSIS WITH MATHEMATICA
Mechanisms analysis with Mathematica  figures  programs  (pdf)
Mechanism analysis with packages  figures  programs  (pdf)

Textbook: instructor's notes (please see the AU Access Blackboard)
References:
J. L. Meriam and L. G. Kraige, Engineering Mechanics: Dynamics, John Wiley & Sons, New York, 1997.
R.L. Norton, Design of Machinery, McGraw-Hill, New York, 1999.
D.B. Marghitu, Kinematics Chains and Machine Components Design, Elsevier, Amsterdam, 2005
D.B. Marghitu and M.J. Crocker, Analytical Elements of Mechanisms, Cambridge University Press, 2001.
C. E. Wilson and J. P. Sadler, Kinematics and Dynamics of Machinery, Harper Collins College Publishers, 1991.

APPLICATIONS

WB00850_.GIF (324 bytes)

FIGURES  and  TABLES (Figs. 1 - 20 ) (pdf)

WB00850_.GIF (324 bytes)

VIDEO (RealPlayer):  R-RTR   R-RTR1    R-RTR-RRR(fig3)    R-RTR-RTR(fig5)    R-RTR-RRT(fig13)    R-RTR-RTR    R-RTR-RTR

WB00850_.GIF (324 bytes)

Extra Homeworks:
Problems 1.2.1, 1.2.4, 1.2.6, 1.2.7, 1.2.9, 1.2.10
Problems 1.3.5, 1.3.6, 1.3.10
Problems 1.4.5, 1.4.9, 1.4.13 - velocities and accelerations
Problems 1.4.10, 1.4.12, 1.4.21 - velocities and accelerations
Problems  1.6.2, 1.6.2(mathematica), 1.6.3, 1.6.4 - joint forces
Problems 1.6.8, 1.6.9, 1.6.12, 1.6.13 - joint forces

WB00850_.GIF (324 bytes)

Position Analysis (pdf)      [sample  (pdf )  Mathematica files: Program 1,  Program 2,  Program 3 ]

WB00850_.GIF (324 bytes)

Velocity and Acceleration Analysis (pdf)
I. DERIVATIVE  METHOD: text (pdf)   program (Mathematica)    program1  (Mathematica)
II. ALGEBRAIC METHOD:  text (pdf)   program (Mathematica) 
III. CONTOUR METHOD:  text (pdf)   program (Mathematica)

WB00850_.GIF (324 bytes)

Dynamic Force Analysis (pdf)    sample (pdf)
ProgramDyad (Mathematica)
ProgramContour (Mathematica)   

Rigid Body Kinematics  Dr. Nels H. Madsen
Example 1.   Example 2.   Example 3.   Example 4.   Example 5.   Example 6.

Structural analysis: structural diagram, contour diagram, dyads (pdf)

Mathematica Programs
Position analysis: R-RRT mechanism (pdf)
Position analysis: R-RTR-RRT (pdf)
Velocity and acceleration analysis: R-RTR-RRT (pdf)
R-TRR  (position, velocity, acceleration) (pdf)


Problem R-RTR-RRT (P.9.9)  position analysis;  velocity and acceleration analysis (method I and method II - contour ) (pdf)

Problems (complete set) (pdf)
 
Dynamic Force Analysis Example   FBD of individual links   FBD of dyads    Contour method
Force analysis: R-RTR mechanism (input data)    solutions:  fbdcontourdyad
Direct Dynamics (NEWTON- EULER eom)  (pdf)    Appendix 2 (Mathematica)

WB00850_.GIF (324 bytes)

Newton-Euler equations - Double Pendulum (pdf)
Double Pendulum  -  Mathematica program (pdf)

WB00850_.GIF (324 bytes)

Problems(pdf)
Moments of inertia
Homework:  Section 6.6: Find the joint forces using individual links


A practical introduction to Mathematica
 
Grading and Evaluation Procedures
Prerequisite: (first or second week): 5%
Exam I  : 15%
Exam II : 15%
Comprehensive final exam: 35%
Laboratory project, homeworks, quizzes (B.M.E Program Homework Presentation Standard): 30%

Accessibility
It is the policy of Auburn University to provide accessibility to its programs and activities, and reasonable accommodation for persons defined as having a disability under Section 504 of the Rehabilitation Act of 1973, as amended, and the Americans with Disabilities Act of 1990.  Students who need special accommodations should make an appointment to see the instructor as soon as possible or contact the Students with Disabilities Program office at (334) 844-5943 (Voice/TT).
 

by Dan B. Marghitu
 

AG00111_.GIF (1635 bytes) Dan Marghitu's home page