Musculoskeletal modeling by multibody biomechanics

This Ph.D. course introduces techniques for modeling of musculoskeletal systems based on multibody dynamics. Unlike most courses in the field, this one takes a bottom-up approach beginning with kinematics of open and closed chains and ending with analysis of complex and anatomically realistic models. The course uses the AnyBody Modeling System throughout and also contains an introduction to this system.

  • This course is open to all Ph.D. students from all universities and free of charge.
  • The course is also open to industrial participants at the charge of 4000 DKK.
  • University afffiliates who are not PhD students, i.e. post docs and such, are welcome to sign up and can participate for free, but in case the course is overbooked, priority will be given to PhD students.

News flash!

The signup for this course has been an overwhelming success, and we have received more than twice as many requests to particpate as we can accommodate. We have therefore succeeded to find a sponsor to repeat the originally planned course. This means that the plan now is:

  • Course #1: April 23 - 27, 2012 (signup now closed)
  • Course #2: May 7 - 11, 2012 (signup is open)

Please notice that the two courses are identical. Course #2 is simply a repetition of #1.

Most of those who have already signed up for for course #1 will be accommodated. You will receive a confirmation soon. A few of the last signups for course #1 cannot be accommodated, but you have the option to sign up for course #2 and you will be given priority if you do so.

Venue and organization

The course is hosted by the Department of Mechanical and Manufacturing Engineering, Aalborg University.

The course is organized by:

Signup for course #1 is now closed. To sign up for course #2 please use this link and select the appropriate course from the list.

Please direct questions to John Rasmussen: jr(at)m-tech(dot)aau(dot)dk


  • Please download and familiarize yourself with the material listed for each topic in the list below.
  • Please bring a Laptop computer capable of running Windows applications. It is most preferable if the laptop also has Matlab installed. We can unfortunately not provide Matlab licenses to the course participants.
  • If you come from a country outside mainland Europe, please bring the necessary conversion plugs. Danish sockets are generally compatible with German plugs. Our voltage is 230 V.
  • Please download and install the newest version of the AnyBody Modeling System before the course. The software can be downloaded from However, please do not request a license for AnyBody. A license will be provided at the course.

Course contents

Day and time Venue Topic   Literature
9am - 4pm
Fibigerstræde 16,
room 1-101

Kinematics (Michael Skipper Andersen)

  1. Degrees of freedom and constraints
  2. Open and closed chains
  3. Forward and inverse kinematics
  4. The Cartesian formulation
  5. Defining and analyzing simple kinematic models in AnyBody


  1. Introduction: p. 35-42.
  2. General kinematic analysis: p. 42-50 (focus on the method of appended driving constraints).
  3. Planar kinematics: p. 77-86 (before 4.2.3)
  4. Spatial kinematics: p. 187-200
  5. Euler parameters: p. 153-157 (before 6.1.2), p. 158 - 164 (before 6.1.5) and p. 172 - 173.
  6. Euler and Bryant angles: p. 347-352.
9am - 4pm
Fibigerstræde 16,
room 1-101

Kinetics (John Rasmussen)

  1. Dynamic equilibrium equations
  2. Forward and inverse dynamics
  3. Statically determinate and indeterminate systems
  4. Simple kinetic analysis in AnyBody


Erdemir et al. (password-protected)

Damsgaard (chapter 3)

Slides for Tuesday and Wednesday

9am - 4pm
Fibigerstræde 16,
room 1-101

Muscle systems (John Rasmussen)

  1. Physiological properties, redundancy, muscle cooperation and antagonism
  2. Muscle models
  3. Optimality principles and physiology
  4. Definition and analysis of simple muscle systems in AnyBody



Rasmussen et al. (password-protected)

Holmberg & Klarbring (password-protected)

SimpleLeg demo model

Lombard demo model

3D antagonist model

9am - 4pm
Fibigerstræde 16,
room 1-101

Development of real models (Mark de Zee)

  • Validation
  • Calibration
  • Generic versus person-specific model
  • Real model development cases in AnyBody

Advanced kinematics (Michael Skipper Andersen)

  • The concept of kinematic measures
  • Advanced joints and interesting combinations of constraints
  • Kinematic redundancy


9am - 4pm
Fibigerstræde 16,
room 1-101

Development of real models (Mark de Zee, continued)

  • Validation continued
  • Model sensitivity to parameters

Introduction of assignment (Michael Skipper Andersen)

  1. Motion capture
  2. Driving AnyBody models with mocap data
  3. Parameter estimation from kinematics


Course assignment. Has to be completed and sent to for graduation of the course. Deadline: May 11th (course #1) and May 25th (course #2).


Participants are expected to organize their own accommodation. We recommend the following options:

  • Danhostel Aalborg. This is located at the opposite end of the city from the University, but there are convenient bus connections.
  • Cabinn Hotel Aalborg. New and centrally located hotel with inexpensive rooms. The rooms are rather small.
  • Prinsen Hotel. This is an older but very convenient and inexpensive hotel close to the center of the city.
  • Scandic Hotel Aalborg. This is a nice, mid-range hotel within walking distance from the university campus but about 4 km from the city center. It is very conveneintly located for drivers.


The exact location of each lecture is listed in the table above. Please find a map of the campus here. All lectures are in the the building Fibigerstræde 16 as shown on the map. If you have trouble finding the place, please call John Rasmussen at 45 2089 8350 as you approach the university.


Lunch can be bought in the university canteen next to the course venue. Inexpensive and very large pizzas are available from Bella Italia just across the small pond from the course venue and made-to-order sandwiches can be bought in the sandwich shop next to the pizzaria.