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 2Exercise 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)  solutionsExercise 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 SolutionExercise 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 MotionUnderstanding 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 or smb://marghdb@lotus/ftp/marghdb (for MAC)

Laboratory projects:  



Mechanism analysis with Working Model  figures

Gear analysis

Gear analysis with Working Model




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 MATHEMATICAMechanisms 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 Yorkinstructor's notes (please see the AU Access Blackboard)References: R.L. Norton, Design of Machinery, McGraw-Hill, New York, 1999D.B. Marghitu, Mechanisms and Robots Analysis with MATLAB, Springer, 2009D.B. Marghitu, Kinematics Chains and Machine Components Design, Elsevier, Amsterdam, 2005C. E. Wilson and J. P. Sadler, Kinematics and Dynamics of Machinery, Harper Collins College Publishers, 1991eCourses - University of Oklahoma:




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, 1.2.10Problems 1.3.5, 1.3.6, 1.3.10Problems 1.4.5, 1.4.9, 1.4.13 - velocities and accelerationsProblems 1.4.10, 1.4.12, 1.4.21 - velocities and accelerationsProblems  1.6.2, 1.6.2(mathematica), 1.6.3, 1.6.4 - joint forcesProblems 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 ProgramsPosition 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 inertiaExercise: 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).