Welcome to Advanced Modelling of Mechanical Systems

Description: An increasing demand for designing reliable and high-performance mechanical systems such as hydraulic cranes, wind turbines or robotic systems requires in-depth understanding of dynamic behavior of the systems, which can be achieved by modeling and simulation at the system level.

The course is aimed to provide fundamental theories and methods for the modeling and simulation of mechanical systems. The course deals with the formulation and solutions of dynamic equations of multibody systems. Both rigid and flexible systems in planar and spatial movements will be considered.

The topics will include kinematic analysis with constraints, analytical dynamics, and numerical integration of the equation of motion. The dynamic modeling of flexible multibody systems will be introduced. Dynamic modeling with MSC Adams is demonstrated with their applications in industry in the workshop.


Knowledge of linear algebra, rigid body kinematic and dynamics, ordinary differential equations

Criteria for assessment:

The assessment will be based upon the written report


The course consists of three full-day lectures and a half-day workshop:

Day 1 (01/10) Kinematic description of rigid bodies

Open and closed-loop mechanisms
Constraint equations
Rigid body orientation and rotation matrix
Position, velocity and acceleration analysis
Other kinds of kinematic analysis

Day 2 (02/10) Dynamic modeling of rigid multibody systems

Newton-Euler equation
Lagrange equations
Numerical implementation
Formulations with improved performance
Recursive Newton-Euler formulation of robots

Day 3 (03/10) Introduction of flexible system dynamics

Kinematics of flexible body
Description of deformation
Constraint equations and governing equations of motion
Modeling of flexible multibody systems
Numerical examples

Day 4 (04/10): Workshop on dynamic modeling with MSc.Adams

Overview of MSC Software
Introduction to Adams
Overview of the capabilities of Adams with examples
Follow-along hands-on exercise

Organizer: Shaoping Bai, e-mail: shb@m-tech.aau.dk; Michael Skipper Andersen, e-mail: msa@m-tech.aau.dk

Lecturers: Aki Mikkola, Professor, Lappeenranta University of Technology, Finland; Shaoping Bai, Associate Professor, Aalborg University; Michael Skipper Andersen, Associate Professor, Aalborg University; Fredrik Sjögren, MSC.Software Sweden AB (TBC)

ECTS: 3.0

Time: 1-4 October 2019
Place: Aalborg University

Number of seats: 30

Deadline: 16 September 2019

Important information concerning PhD courses
We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registration.