Course Number:  MECH 2120 


Course Title:   Kinematics and Dynamics of Machines 


Credit Hours:  4 


Prerequisites:  MATH2630, MECH2110 


Co requisites:   None

 

Coordinators: 
Dan B. Marghitu

 

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)  chapter1(pdf)

2. FUNDAMENTALS  figures (pdf) (4 classes)  Solutions (pdf)  Lecture (pdf)  chapter2(pdf)
Exercise 1  (pdf) solutions (pdf)

3. POSITION ANALYSIS  figures (pdf) (6 classes)   Solutions (pdf) 
Lecture (pdf)  MATLAB examples (pdf)  MATLAB files: Program 1, Program 2
Exercise 2: MATLAB (pdf)
Exercise 3: position (pdf)  solutions (pdf)

4. VELOCITY AND ACCELERATION ANALYSIS  figures (pdf) (12 classes) Solutions (pdf)   chapter4(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)
Exercise 4: Problems 1, 2, (pdf) 3, 4 (pdf)
Exercise 5: Acceleration of a point  that moves relative to a rigid body (pdf)
Exercise 6: Problems 5, 6 (pdf)  solutions  P5   P6  (pdf)
Exercise 7: Problems 7, 8 (pdf)  solutions  P7   P8  (pdf)

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

6. FORCE ANALYSIS   figures (pdf) (14 classes) Solutions (pdf)  chapter6(pdf)
Lecture Force Analysis (pdf)   figures (pdf)  table (pdf)
Exercise 8: Accelerations of CM, mass moments of inertia (pdf)  solutions
Exercise 9: Force analysis (pdf)
Example Problem R-RTR (pdf)
Exercise 10-11: Problems 6.3-6.6 (pdf)
Exercise:  Joint reaction forces (pdf)  figures (pdf)  solutions
 Problem R-RRT (pdf)    Problem R-RTR (pdf)    HW: Problem R-RTR_I

 7. DYNAMICS   figures (pdf)
[Direct Dynamics (pdf)]  Appendix 2 (Mathematica)
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)
Exercise 12: Pendulum (pdf)         (Program (mathematica))
Exercise 13: Problems (pdf)  
        P1- Bar on the wall MATLAB Solution
        P3 - MATLAB Solution
Exercise 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
Understanding Newton's Laws of Motion

Ordinary Differential Equations (pdf)

8. MECHANISMS WITH GEARS (pdf) (3 classes)
Exercise: Gear Trains (solutions: Problem 1 Problem 4 Problem 5)

 

Tests (3 classes)

Exam 2 solutions: Problem 1 Problem 2


 

Video Problems at  ftp://ftp.eng.auburn.edu/pub/marghdb or smb://marghdb@lotus/ftp/marghdb (for MAC)


Laboratory projects:  

 

PART I: WORKING MODEL

Mechanism analysis with Working Model  figures

Gear analysis

Gear analysis with Working Model

 

 

PART II: MECHANISM ANALYSIS WITH MATLAB

Position Analysis with MATLAB

Velocity and Acceleration Analysis with MATLAB  

Dynamic Force Analysis with MATLAB   

Direct Dynamics (Newton-Euler eom) with MATLAB

 

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

 

Textbook: 
J. L. Meriam and L. G. Kraige, Engineering Mechanics: Dynamics, John Wiley & Sons, New York
instructor's notes (please see the AU Access Blackboard)
References: 
R.L. Norton, Design of Machinery, McGraw-Hill, New York, 1999
D.B. Marghitu, Mechanisms and Robots Analysis with MATLAB, Springer, 2009
D.B. Marghitu, Kinematics Chains and Machine Components Design, Elsevier, Amsterdam, 2005
C. E. Wilson and J. P. Sadler, Kinematics and Dynamics of Machinery, Harper Collins College Publishers, 1991
eCourses - University of Oklahoma: http://ecourses.ou.edu/home.htm

 

APPLICATIONS

 

FIGURES  and  TABLES (Figs. 1 - 15 ) (pdf)

 

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

 

Exercises:
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

 

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

 

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)

 

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  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)

 

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





Problems(pdf) 
Moments of inertia
Exercise: Find the joint forces using individual links


 

A practical introduction to Mathematica

 

Grading and Evaluation Procedures

Prerequisite: (first or second week): 3%

Exam I  : 15%

Exam II : 15%

Comprehensive final exam: 30%

Laboratory project, quizzes (each quiz 2%), homework: 37%

Grading Scale: A=100-90% B=90-80% C=80-70% D=70-60% F<60%

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).