Flexible Multibody System Analysis for Control Purposes - Course Material

The course material will be provided in two ways. Part of the material listed on this page can be downloaded (PDF format). The lecture notes (see below) that are only provided in hardcopy to all registered course participants. Some other material will also be provided in hardcopy (as indicated below), so there is no need to print the PDF document.

Lecture notes

The Course overview (CO) gives an overview of the topics covered in this course. It can be downloaded, but it has also been provided in the hardcopy course material.

The lecture notes on "Dynamics of Machines and Mechanisms" (DoM) by Jonker cover most of the theoretical background addressed in this course. These notes are only provided in hardcopy to all registered course participants.
For participants who want to read more background information, additional books on relevant subjects are:

oMechanics of Materials, J.M.Gere and S.P.Timoshenko, ISBN 0-278-00040-1

oEngineering Mechanics Dynamics, R.C.Hibbeler, ISBN 978-0-13-203809-6

oEngineering Mechanics Statics & Dynamics Principles, A.Bedford and W.Fowler, ISBN 0-13-008209-

A tutorial on “Prototype modelling of mechanical systems (PM)” can be found on this page. It is accompanied with input files for use with the SPACAR software. The tutorial has been provided in hardcopy.

The manual of the SPACAR toolbox for Matlab/Simulink (SP) can be downloaded, but it has also been provided in the hardcopy course material.

The linearisation papers (LP) covering the perturbation method and subsequent modal analysis are:
Wa-701 (LP-1): J.B. Jonker and R.G.K.M. Aarts, A perturbation method for dynamic analysis and simulation of flexible manipulators, Multibody Systems Dynamics (ISSN 1384-5640) 6 (3) pp. 245-266 (2001).
Wa-751 (LP-2): Ronald G.K.M. Aarts and J.B. Jonker, Efficient dynamic simulation of flexible link manipulators with PID control, DETC’01, 2001 ASME Design Engineering Technical Conferences, Ed. D.T.Mook and B.Balachandran, Pittsburgh, Pennsylvania, September 9-12, 2001.

The paper (ES) on the extended input-output representation for control synthesis in multbody system dynamics:
Wa-1162 (ES): J.B. Jonker, R.G.K.M. Aarts, J. van Dijk, A linearized input-output representation of flexible multibody systems for control synthesis, Multibody System Dynamics (ISSN 1384-5640) 21 (2) pp. 99-122 (2009).

Two papers on “Modeling and mechatronica design of mechanisms with flexible joints”:
Paper (M4M) on the design of an active encoderhead and
Paper (M4M2) on the design of a tilting mirror system.


All slides used during the course will be available in PDF format. As soon as they can be downloaded, the link below will be activated:

Slides CO accompanying the course overview.

Slides DoM about the theory presented by Prof. Jonker.

Slides SP about the SPACAR software package.

Slides LP about the linearised equations of motion for simulations with the perturbation method.

Slides ES on the extended input-output representation.

Slides M4M and slides M4M2 on Modeling and mechatronica design.


The exercises can be downloaded once the links are activated:

Exercise 1 for weeks 2 and 3.

Exercise 2 and Matlab files for weeks 4 and 5.

Exercise 3 for weeks 7 and 8.