2021-2022 / MECA0031-2

Kinematics and dynamics of mechanisms


30h Th, 20h Pr, 40h Proj.

Number of credits

 Master of Science (MSc) in Aerospace Engineering5 crédits 
 Master of Science (MSc) in Biomedical Engineering5 crédits 
 Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)5 crédits 
 Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)5 crédits 


Olivier Bruls

Language(s) of instruction

English language

Organisation and examination

Teaching in the second semester


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

In this course, the student will get familiar with engineering techniques that are used for the design of articulated systems, with applications in the fields of automotive design (power train, suspension), airplane design (flaps, landing gears), space technologies (deployable structures), biomedical engineering (biomechanics of the musculo-skeletal system), robotics and wind turbines.

  • Introduction : historical remarks, fields of application, topology of a mechanism, degrees of freedom, generalized coordinates
  • Kinematics: rigid body (finite rotations, computation of positions velocities and accelerations), multibody systems, formulation using absolute coordinates
  • Dynamics: d'Alembert and Hamilton principles, rigid-body dynamics, treatment of kinematic constraints (constraint elimination technique, Lagrange multiplier method), finite element method for multibody systems
  • Flexible systems: discrete elastic systems, nonlinear finite element method (strain measures, spatial discretization, bar element, beam element), super-element technique (corotational formulation, modal reduction)
  • Numerical methods: time integration algorithms for ordinary differential equations and differential-algebraic equations
  • Introduction to the dynamics of mechatronic systems: coupled modelling of a mechanism and its control system (sensors, actuators, controllers)
  • Application to problems from automotive design, aeronautics, space technology and biomedical engineering.

Learning outcomes of the learning unit

  • Basic theoretical concepts in multibody system dynamics
  • Understanding analysis and simulation methods that are used for the simulation of multibody systems
  • Utilization of a simulation software in order to solve practical engineering problems

Prerequisite knowledge and skills

  • Linear algebra
  • Numerical methods
  • Classical mechanics
  • Solid mechanics
  • Finite element method
  • MATLAB or Python programming
  • Basic use of NX/SIMCENTER 3D

Planned learning activities and teaching methods

Exercises sessions. Sessions on computer (introduction to SIMCENTER/SAMCEF/MECANO). Practical work by groups of two students (use of MATLAB and SIMCENTER/SAMCEF/MECANO software).

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Additional information:

The course includes

  • lectures
  • exercise sessions
  • laboratory sessions for an introduction to the SAMCEF/MECANO software
  • Two practical works to be prepared in groups of two students using MATLAB (or Python) and SIMCENTER/SAMCEF/MECANO. Sessions will be organized for the follow-up.

Recommended or required readings

  • Lecture notes will be available at the "Centrale des cours".
  • Reference book: M. Géradin, A. Cardona, Flexible Multibody Dynamics - A Finite Element Approach, John Wiley and Sons, Chichester, 2001.

Assessment methods and criteria

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions ) AND oral exam

Written work / report

Additional information:

Two elements are considered for the evaluation

  • the theory exam (oral and written, 60%). In case of distant organization for sanitary reasons, the theory exam is only oral.
  • the practical works (40%)

Work placement(s)

Organizational remarks

For the practical works, students are invited to get MATLAB and SIMCENTER 3D.


Olivier Brüls: o.bruls@uliege.be
Nayan Levaux: Nayan.Levaux@uliege.be