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

Dan B. Marghitu, 2418G Wiggins Hall, phone: 844-3335, office hours: 01:00-02:00 p.m. TR.

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 (Solidworks, 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 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)

hw1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Video Problems at or smb://marghdb@lotus/ftp/marghdb (for MAC)

Laboratory projects:  


Mechanism analysis with Working Model  figures (pdf)

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


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 6Program 7

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

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

Mechanisms analysis with Mathematica  figures  programs  (pdf)
Mechanism analysis with packages  figures  programs  (pdf)

J. L. Meriam and L. G. Kraige, Engineering Mechanics: Dynamics, John Wiley & Sons, New York
instructor's notes (please see AU Canvas)
R.C. Hibbeler, Engineering Mechanics: Dynamics, 12/E, Prentice Hall, 2010
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:


WB00850_.GIF (324 bytes)

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

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 1Program 2Program 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  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

WB00850_.GIF (324 bytes)

Moments of inertia
Exercise: Find the joint forces using individual links

A practical introduction to Mathematica

 Makeup Work  Makeup for hour exams will be given only for valid University excused absences. Makeup quizzes will not be given. Instead, excused absence on quiz days will be treated as if no quiz were given. Any work missed due to an unexcused absence will receive a grade of Zero. If an hour exam is missed due to valid excuse you must contact me by email within 48 hours after the start time of the missed exam to make arrangements for makeup. For the purposes of this class, a University Excuse must be issued by Engineering Student Services in Shelby.

Accessibility  It is the policy of Auburn University to provide accessibility to it’s 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 have a documented disability and need special accommodations should make an appointment to see me as soon as possible.

Contingency  If normal class and/or lab activities are disrupted due to illness, emergency, or crisis situation (such as an H1N1 flu outbreak), the syllabus and other course plans and assignments may be modified to allow completion of the course. If this occurs, an addendum to your syllabus and/or course assignments will replace the original materials.


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