Course syllabus

Course-PM

MMA092 Rigid body dynamics lp2 HT20 (7.5 hp)

Course is offered by the department of Mechanics and Maritime Sciences, division of Dynamics

Contact details

Teachers

Håkan Johansson, e-mail: hakan.johansson@chalmers.se (examiner)

Petri Piiroinen, e-mail: petri.piiroinen@chalmers.se

Björn Pålsson, e-mail: bjorn.palsson@chalmers.se (computer sessions)

Department

Mechanics and Maritime Sciences, Div Dynamics.

Visit: Hörsalsvägen 7A, Floor 3

To contact: Use email or visit us (Håkan, Petri and Björn have office in same corridor). Don't use chat or inside-canvas messaging as it is not as frequently read.

Course purpose

Many mechanical systems, such as cars and robots, exhibit a much more complicated, three-dimensional motion than those treated in basic courses in mechanics. Many degrees-of-freedom, complicated constraints, three-dimensional rotations, coupled oscillations, and stability problems are among the complications that may occur. This course gives the tools needed to analyse such problems. Apart from analytical methods, also software for simulating complicated dynamical systems is introduced. The course includes a large, more real world project, which uses both analytical methods and software.

Schedule

TimEdit

Course literature

• Boström: Rigid body dynamics (compendium)
  • This book will be printed and can be collected at M2 dept free of charge. Will also be posted as pdf on this site.
• Shabana: Dynamics of Multibody Systems (e-book)
  • This book is available as e-book via Chalmers Library
• M.M. Japp: Formulas in mechanics
  • The sheet of formulas will be distributed together with written exam (if so). Will also be posted as pdf on this site.

Course design

The scheduled teaching activities involves a number of combined lectures and exercises (L) and computer class (with teacher in room or online to answer questions), see course summary below or the calendar. A major part of the course is the work with hand-ins, which includes numerical and analytical solution of a set of dynamics problems, illustrating course topics.

Lectures (chapter in Boström compendium)

Lecture	Teacher	Topic	Boström	Self-study problems	Shabana
L1	Håkan	Introduction, Particle dynamics	1.1-5	1.4, 1.7, 1.9	1.2-3
L2	Håkan	System of particles	1.5-6	1.15	1.2-3
L3	Håkan	Planar motion kinetics (Newton formulation)	4.5	4.5, 4.6	1.4
L4	Håkan	Planar motion kinetics (Lagrange formulation)	5.1-2	5.4, 5.6, 5.10	1.6, 3.1-3.4
L5	Petri	Rotating coordinate frames, Angular velocity and acceleration	2.1-2	2.1	2
L6	Petri	Rigid body kinematic, constraints	3.1-4	3.1, 3.3, 3.4, 3.6, 3.9	2, 1.6, 3.1
L7	Petri	Relative motion	2.2-3	2.4, 2.7, 2.9	2.5
L8	Håkan	Newton's laws for rigid bodies	4.1-3	4.9, 4.10, 4.12, 4.15
L9	Håkan	Newton's laws for rigid bodies (special cases)	4.4-7	4.17, 4.18, 4.19
L10	Håkan&Petri	Lagrange's equations for multibody system; Modeling human gait	5.1-2	5.2, 5.11	3
L11	Håkan	Linearizations, oscillations, modal analysis	5.2-5.3, 6	6.2, 6.8, 6.9,  6.10	3
L12	Håkan	Course summary and outlook

Changes made since the last occasion

The lectures and examination has been changed to work with distance learning. In particular, the written exam is replaced by hand-ins and online individual oral presentation. Moreover, the problem-solving sessions have been incorporated into the lectures.

Learning objectives and syllabus

After completion of the course the student should be able to

- Use advanced kinematics, such as generalized coordinates, rotation matrices, relative motion, Euler angles, and various constraints (joints, rolling, etc).

- Apply Newton's and Lagrange's equations of motion to mechanical systems composed of particles and rigid bodies.

- Calculate eigenfrequencies and modal vectors for mechanical systems characterized by linearized equations of motion.

- Work with commercial software for mechanical systems in simple cases.

- Apply the learned skills to a complex mechanical problem, such as a car suspension or a robot, and show this ability by working with such a problem both analytically and with software.

Link to the syllabus on Studieportalen (please note that examination form has changed).

Study plan

If the course is a joint course (Chalmers and Göteborgs Universitet) you should link to both syllabus (Chalmers and Göteborgs Universitet).

Examination form

The examination of the course consists of a set of hand-ins with both analytical and simulation tasks.

Hand-in	Deadline	Mandatory part	Supplementary part
A1	Week 3	yes	0 p
A2	Week 4	yes	2 p
A3	Week 5	yes	2 p
A4	Week 6 (Tuesday)	yes	2 p
A5	Week 7	no	4 p

 

The hand-in work contains a basic parts required to pass the course and supplementary parts. Completing supplementary parts gives maximum 10 points. The project work is 5 assignments A1-A5. A1 has only a mandatory part; A2-A4 has one mandatory part and 2 point each, while A5 has 4 points. The assignments are made available on Mondays week 2-6, and to be submitted Wednesday the following week (except A4, which is due on the Tuesday). The assignments are to be done and submitted individually.

 

The hand-ins will be corrected, and errors in the mandatory part will require re-submission. After A4, there will be an individual presentation where each students meet teacher online and discuss the mandatory parts of the assignments. Completing the mandatory parts of assignments and the individual presentation will give grade 3 in the course.

 

In order to get a grade 4 or 5 in the course, at least 5 or 9 points (with at least 2 points on A5), respectively, is needed. Moreover, after A5, there will be an additional individual presentation where students meet teacher and discuss the supplementary parts of the assignments.