Description: Multibody Dynamics A is an introductory course in applied dynamics of mechanical systems. The emphasis is on the usage of multibody dynamics software. We want you to learn enough about dynamics in 3D that you will be able to use a standard multibody dynamics software package correctly, appreciate the limitations, and say some sensible things about the model at hand.

In the course you will learn about the fundamentals of Multibody Dynamics: the description of the orientation of a rigid body in space, the Newton-Euler equations of motion for a 3D rigid body, how to add constraints to the equations of motion, and how to solve such a system of coupled equations. You will spend most of the time (80%) in doing the lab assignments. These assignment consists of a number of practical problems that have to be worked out with the software package ADAMS. Your findings are to be put down in a Lab Report.

Goal: By the end of the course you be able to make a complex model of realistic 3D mechanical system and draw some conclusions from the dynamical analysis.

Grading: The written exam is of the open book type and has the form of a questionnaire about the findings as written down in your lab report. The report serves as reference material for your exam. At the end of the exam the questionnaire together with the Lab Report are to be handed over, The final grading is 50% on the report and 50% on the written exam.

News

Hand-Outs
- The course Contents.
- The Laboratory Assignments.
- A short Introduction to ADAMS (1,169 KB).
- Tire and Road files for assignment#5:  16r26_new.tir, 18r38_new.tir, FlatRoad.rdf.
- Transparencies for Lecture2 .
- Transparencies for Lecture3 .
- Transparencies for Lecture5 .
- An example of a written exam t20062006eng.pdf

- Only for those who are interested in doing an alternative assignment #5, dynamics of bicycle:
wb1310labassignNew5, bicycle600c, bicycle700c, FlatRoad, MeijaardPapadopoulosRuinaSchwab2007

Office Hours
Arend L. Schwab, a.l.schwab@tudelft.nl, Monday, 14-16 h., room 8B-4-22.

Teaching Assistant
Alexander Steenhoek,  a.m.steenhoek@tudelft.nl

Lab Hours
PC-room 8A-1: Tue 13-17 h.

Week 1

Tuesday, April 7, 2009, 10:45-12:30 u, room A.

• Introduction.
  

Short introduction to the Multibody Dynamics-A course. Showed as an example the modeling of a bicycle to investigate the inherent stability of the system and how-to-steer a bicycle. Some of the material I showed can be found on my website under bicycle dynamics or at www.bicycle.tudelft.nl

Week 2

Tuesday, April 14, 2009, 10:45-12:30 u, room A.

• Newton-Euler eqn's of motion for a rigid body in space.

Talked about Newton and Euler, and presented the Newton-Euler equations of motion for a rigid body in space. Talked about the Inertia tensor Ic, which changes due to the change in orientation of the body.  As an example I calculated the torques applied at the bicycle wheel from assignment 2. First wrong and then right. Finally you should look at a nice derivation of the Newton-Euler equations of motion by means of the linear and angular momentum balance. See my transparencies for Lecture2 .

Week 3

Tuesday, April 21, 2009, 10:45-12:30 u, room A.

• How to describe the Orientation of a Rigid Body in Space.

Discussed the need to describe orientation in space for a rigid body. Talked a little bit about orientation in 1D 2D, 3D and 4D. Came up with the idea of orientation is a sequence of rotations about axes in different planes. Discussed the recipe for Euler Angles and showed a materialization of Euler Angles by means of "can's" in sequence. Showed, by experiment, that EA are not vectors, they do not obey the commutative law v1+v2=v2+v1. Derived the rotation matrix R in terms of EA. Derived the expressions for the angular velocities in terms of the Euler angles (phi,chi,psi) and the rate of change of the Euler angles. From these we can find the inverse and the integrate the rate of chance of the Euler angles in order to get the new orientation of the body. Unfortunately this inverse shows a singularity at sin(chi)=0, which I explained in a physical way by means of the "can's". The first can and the last can are in series, therefore the individual rate of changes of the two angles, phi and chi, can not be resolved. I also discussed some useful literature on Multibody Dynamics, where most books are present at the TUDelft library. If not, please contact me. My transparencies for Lecture3 .

Maybreak, next lecture in two weeks.

Week 4

Tuesday, May 12, 2009, 10:45-12:30 u, room A.

• Modeling of mechanical systems.

Today I talked about the third assignments. We discussed the modeling of the overhead crane and why the container moves. Then we investigated the motion of an asymmetric loaded container, and addressed the question if it will rotate or not.

Week 5

Tuesday, May 19, 2009, 10:45-12:30 u, room A.

• Coupled Differential and Algebraic Equations (DAE's).

First I talked the insides of ADAMS or how ADAMS works, that is: how does ADAMS set up and solve the equations of motion? I demonstrated the method on a simple 2D pendulum. Derived the coupled differential and algebraic equations and discussed the the general approach for 3D multibody dynamics systems. See my notes on lecture5.
Next I talked about assignment #4, the Governer. I discussed some aspects of the model; how to find the equilibrium angle at constant rpm. I showed some pages from "Higher Mechanics", by Horace Lamb, Cambridge University Press, 1920, which shows that in the absence of damping a centrifugal governor is unstable. This complies with the results you get for moderate damping.

Week 6

Tuesday, May 26, 2009, 10:45-12:30 u, room A.

• Modeling of mechanical systems.

I talked about assignment #5, a Tractor put to the moose test. This was the last lecture.

June 2: No Lecture.

Finally:

See you all at the written exam, and please don't forget to bring a copy of your lab report to the exam. This will serve as reference material and you have to hand in the copy together with your written exam.

This is an example of a written exam: t20062006eng.pdf

SUCCES!