Course syllabus

Course-PM

MMA092 Rigid body dynamics lp2 HT19 (7.5 hp)

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

Contact details

Examiner, lectures

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

Problem-solving sessions, project

Björn Pålsson, e-mail: bjorn.palsson@chalmers.se

Department

Mechanics and Maritime Sciences, Div Dynamics.

Visit: Hörsalsvägen 7A, Floor 3

To contact: Use email or visit us (Håkan and Björn have office next to each other). 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

TimeEdit

Course literature

• Boström: Rigid body dynamics (compendium)
  • This book will be printed and distributed 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 the exam. Will also be posted as pdf on this site.

Course design

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

Lectures (chapter in Boström compendium)

Lecture	Topic	Boström	Shabana
L1-2	Introduction, Particle dynamics	1.1-5	1.2-3
L3	System of particles	1.5-6	1.2-3
L4	Planar motion kinetics (Newton formulation)	4.5	1.4
L5	Guest lecture; Lagrangian mechanics	5.1-2	1.6, 3.1-3.4
L6	Rotating coordinate frames, Angular velocity and acceleration	2.1-2	2
L7	Rigid body kinematics	3.1-2	2
L8	Rigid body kinematic, constraints	3.3-4	1.6, 3.1
L9	Relative motion	2.2-3	2.5
L10	Newton's laws for rigid bodies	4.1-3
L11	Newton's laws for rigid bodies (special cases)	4.4-7
L12	Lagrange's equations for multibody system	5.1-2	3
L13	Lagrange's equations, linearizations	5.2-5.3	3
L14	Coupled oscillations, modal analysis	6.1-2
L15	Course summary and outlook

L5 starts with a guest lecture  (45 mins) by Prof Jussi Sopanen, Lappeenranta university (LUT) "Real-time multibody simulation of mobile working machines in product development and user training."

 

	Problem solved	Recommended self-study
P1	Adams intro;1.8, 1.12, 1.16	1.4, 1.7, 1.9, 1.15
P2 (45 mins)	4.2, 5.1	4.6, 5.6
P3	4.3, 5.3, 5.5, 5.12	4.5, 5.4, 5.10
P4	3.2, 3.5, 3.7, 3.10	3.1, 3.3, 3.4, 3.6, 3.9
P5	2.8, 2.10, 2.11, 4.1	2.1, 2.4, 2.7, 2.9
P6	4.7, 4.11, 4.13	4.9, 4.10, 4.12, 4.15
P7	4.5, 4.16, 4.21	4.17, 4.18, 4.19
P8	5.7, 5.8, 5.9	5.2, 5.11
P9	6.1, 6.4, 6.7, 6.11	6.2, 6.8, 6.9, 6.10
P10 (3x45mins)	Solution of old exam

 

 

Changes made since the last occasion

The lectures have been revised and the format for project using ADAMS has been changed to several smaller problems rather than one big.

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.

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 two parts: Project work and a written exam.

 

The project work contains a basic parts required to pass the course and supplementary parts. Completing supplementary parts gives maximum 5 bonus points to the final exam. The project work is 5 assignments A1-A5. A1 has only a mandatory part; A2-A4 has one mandatory part and 1 bonus point each, while A5 has 2 bonus points. The assignments are made available on Mondays week 2-6, and to be submitted Wednesday the following week (except A5, which is due on the Thursday). The assignments are to be done and submitted individually.

 

The written exam consists of four problems of the type solved on the problem-solving sessions and within the project work. Each problem on the exam can give a maximum of 5 points. Bonus points from the supplementary part of the project work are added. The course grade is determined as:

Points (incl. bonus)	8-12	13-17	18-25
Grade	3	4	5

 

No aids may be brought to the exam, however, the formula sheet ''M.M. Japp: Formulas in mechanics'' will be distributed together with the exam. Note that calculators are not used on the exam.

 

For times and places of exams, see the Student Portal.

 

Please note that the exam must be written in English according to Chalmers rules.