MAAE 3004: Dynamics of Machinery

Kinematic and dynamic analysis of mechanisms and machines. Mechanism force analysis. Static and dynamic balancing. Kinematic and dynamic analysis of cams. Free and forced vibration of single-degree-of-freedom systems. Introduction to multibody dynamics.


Lecture Outline

  • Week 1 – Introduction: Definitions; geometrical categorization of mechanisms; mobility; kinematic inversion; Grashof’s law.
  • Week 2 – Displacement Analysis: Introduction; graphical solution of vector equations.
  • Week 3 – Velocity Analysis: Definitions; velocity polygons; apparent linear velocity of a point; apparent angular velocity; instant  centres of velocity.
  • Weeks 4 & 5 – Acceleration Analysis:> Linear acceleration; angular acceleration; acceleration difference vector;acceleration polygons; apparent acceleration; instant centres.
  • Week 6 – Force Analysis of Mechanisms: Preliminaries; forces acting on links; graphical analysis and superposition; analytical force balance and matrix solution.
  • Week 7 – Force Balancing: Introduction; balancing of machinery; balancing of rotating shafts; analysis of rotor balancing.
  • Weeks 8 & 9 – Free Vibration of SDOF Systems: Basic concepts; undamped translational system; Rayleigh’s energy method; free vibration with viscous damping.
  • Weeks 9 & 10 – Harmonically Excited Vibration: Equation of motion; undamped response; magnification factor; damped response; energy dissipation.
  • Week 11 – Cams: Kinematics of cams:  definition and classification; displacement diagrams; cam profile design. Dynamics of cams: rigid cam systems.
  • Week 12 – Multibody Dynamics: Definitions; system description; kinematics and dynamics; software.


  • J.J. Uicker, Jr., G.R. Pennock, and J.E. Shigley. Theory of Machines and
  • Mechanisms, 4th edition, Oxford University Press, 2011.

Suggested Supplemental References(on reserve at McOdrum Library):

  • F.P. Beer, E.R. Johnston Jr., and W.E. Clausen. Vector Mechanics for Engineers – Dynamics, 7th edition,    McGraw-Hill Inc.
  • H.H. Mabie and C.F. Reinholz. Mechanisms and Dynamics of Machinery, 4th edition, Wiley.
  • G.H. Martin. Kinematics and Dynamics of Machines, 2nd edition, McGraw-Hill.
  • W.T. Thomson and M. D. Dahleh. Theory of Vibration with Application, 5th edition, Prentice-Hall.

Course Notes and Assignments:

Posted on WebCT

Drawing Instruments:

Students will require the elements of a geometry set to perform graphical kinematic analysis.  This includes: ruler, protractor, compass, 45-45-90 degree triangle, 30-60-90 degree triangle.

Course Evaluation:

  • Midterm Examination (Closed book): 30%
  • Final Examination (formula sheets will be provided): 70%