Kinematic Geometry of Robot Mechanisms

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34011 - GCR, Course 2011-2012

Course data

• Course code: 34011-GCR.
• Prerequisites: Entry level courses in linear algebra, mechanics, and a working knowledge of some computer language. Here's a summary of the main concepts needed from such courses.
• Official course name: The official course name is "Geometria Computacional en Robòtica (GCR)". The course contents has evolved in precedent years, and the title of this page better describes the current course structure. Actions are being made to adapt the official course name to the title of this page.
• Academic year: 2011-2012 (Previous academic years: 2010-2011, 2009-2010, 2008-2009).
• Master programme: Master in Automatic Control and Robotics.
• Semester: Second.
• ECTS Credits: 5.
• Teaching language: Catalan mainly. Spanish and English sometimes. Our university provides a comprehensive range of Catalan courses for beginners to advanced learners, which are supported with self-learning resources and language exchange services. More resources can be found on the Intercat web site.
• Professors in charge: Lluís Ros, Pablo Jiménez, Montse Manubens, and Oriol Bohigas.
• Unit: Institut de Robòtica i Informàtica Industrial.
• Room: We meet on monday from 10:00 to 12:00, and thursday from 10:00 to 11:00, at aula Master.
• Consultation hours: Friday from 12:30 to 13:00 (Pablo Jimenez), and from 15:00 to 15:30 (Lluís Ros).

Please see these hints on using the wiki space.

Presentation and objective

This course is devoted to the statics and instantaneous kinematics of robot mechanisms, a basic set of tools for the analysis and control of manipulation devices, such as serial or parallel manipulators, cable-driven robots, or multi-fingered hands.

Traditionally, the theories of statics and instantaneous kinematics have been learned separately in mechanical engineering courses. However, they proceed alongside one another, the important principle of reciprocity linking them together. Using this principle, and the homogeneous representation of forces and velocities as screw vectors, this course aims at studying the two subjects in a unified manner. In this way, the kinetostatic analysis of robots becomes computationally much simpler, the conclusions derived much richer, and the techniques turn out to be applicable to arbitrary mechanisms. Overall, a global picture of the behaviour of manipulation devices in and out a singular configuration is gained.

Although the presented techniques were well established by the end of the 19th century, with the work of Robert Ball, Felix Klein, James C. Maxwell, Luigi Cremona, Jean Bernouilli, Hermann Grassmann, Arthur Cayley, Julius Plücker, and others, the subject, yet important, has remained largely unnoticed by the Robotics Community, where the rigorous study of statics and instantaneous kinematics is apparently receding. An additional goal of this course is to help reversing this trend.

Learning methodology

The subject will be worked out in classical theory and problem sessions mainly. Depending on the evolution of the course, a number of seminar sessions might be programmed too. In such sessions, the active participation of the assistants is a fundamental aspect, and the professor's task is, essentially, to direct the session, presenting and setting the topics in a context, and coordinating the debate and the discussion among the students.

Grading

Grading is mainly based on a final examination. The final mark will also take into account the student's participation in class or in this wiki space (contributions to the debate of the topics, questions raised, and their resolution).

The final exam will have two parts:

• Part I: Two problems, similar to those solved in exercise sessions.

• Part II: Ten questions with multiple-choice answers.

Here there are some examples of such problems and questions:

• Exam 2011: Problems, questions.

• Exam 2010: Problems, questions.

• Exam 2009: Questions.

If the group of students is not large, the final exam might be oral. In that case, the exam will consist of a first block of conceptual questions, and a second block of questions regarding the exercises solved in class.

Schedule, readings and exercises

The course is structured into several modules. Modules 1 to 5 mainly follow the book by Joseph Duffy, "Statics and Kinematics with Applications to Robotics", Cambridge University Press, 1996. Module 6 loosely follows material that can be found in the book by Joseph K. Davidson and Kenneth H. Hunt. "Robots and Screw Theory: Applications of Kinematics and Statics to Robotics". Oxford University Press, 2004. However, some of the modules contain additional material not covered in such books. In any case, we will try to make all of the course contents available on-line, either in the form of slides (that the student should complement with class notes), or detailed lecture notes.

The following schedule (and the related pages and documents) is subject to change. Please watch this page and all its sub-pages if you want to be notified by e-mail about any changes introduced.

Module 0: Introduction

Course presentation: 1 hour, on February 13 (PDF slides, PPT slides)

Module 1: Mobility and displacement analysis

Theory: 2 hours, on February 13 and 16 (PDF slides, PPT slides, note, Theo Jansen's linkage, FAQ)

Exercises: 1 hour, on February 23.

Module 2: Statics

Theory: 4 hours, on February 20 and 27 (Lecture notes in PDF, FAQ)

Exercises: 3 hours, On March 1, 8, and 15.

Module 3: Instantaneous kinematics

Theory: 4 hours, on March 5 and 12 (PDF Slides, FAQ)

Exercises: 3 hours, on March 22, 29, and April 12.

Module 4: Series-parallel dualities on planar robots

Theory: 8 hours (FAQ)

Principle of Virtual Power: 2 hours, on March 19 (PDF Slides).

Reciprocity: 1 hour, on March 26 (Lecture notes in PDF).

Static analysis of the 3R manipulator: 1 hour, on March 26 (Lecture notes in PDF).

The duality diagram of a serial manipulator: 2 hours, on April 16 (Lecture notes in PDF).

Kinematic analysis and duality diagram of a parallel manipulator: 2 hours, on April 23 (Lecture notes in PDF).

Exercises: 4 hours, on April 19, 26, and May 3, 10.

Module 5: Introduction to hybrid control of force and position

Theory: 4 hours, on April 30 and May 7 (Lecture notes in PDF).

Exercises: 1.5 hours, on May 17, 24.

Module 6: General twists and wrenches and kinetostatic analysis of spatial manipulators

Theory: 4 hours, on May 14 and 21

Index and introduction (Lecture notes in PDF)

Part A: General wrenches and Poinsot's theorem (Lecture notes in PDF)

Part B: General twists and Chasles' theorem (Lecture notes in PDF)

Part C: Kinetostatics of general serial and parallel manipulators (Lecture notes in PDF))

Appendix: Couples as force systems (Lecture notes in PDF)

Terminology

Here's a free translation to Catalan, of the principal English words used for the main concepts of the course.

Bibliography

Course main book:

• Joseph Duffy. "Statics and Kinematics with Applications to Robotics". Cambridge University Press, 1996. Book partially available from Google Books. Here's a review of this book by J.-P. Merlet, appeared in The International Journal of Robotics Research, Vol. 16, No. 3, page 410, June 1997. Please see also this errata file compiled by the course members, and this table of notation used in the book.

Recommended material for further study:

• Joseph K. Davidson and Kenneth H. Hunt. "Robots and Screw Theory: Applications of Kinematics and Statics to Robotics". Oxford University Press, 2004. Book partially available in Google books. Here's a review of this book by G. Pennock, appeared in the ASME Journal of Mechanical Design, Vol. 126, pp. 763-764, July 2004.

• Gilbert Strang. "The fundamental theorem of Linear Algebra". The American Mathematical Monthly, Vol. 100, No. 9 (Nov. 1993), pp. 848-855.

• Gilbert Strang. Introduction to Linear Algebra, 4th edition. Wellesley-Cambridge Press, 2009.

• The excellent video lectures associated with the previous book.

• Felix Klein. "Elementary Mathematics from an Advanced Standpoint". Dover 2004.

• Kenneth H. Hunt. "Kinematic Geometry of Mechanisms". Oxford Science Publications 1978.

• Robert Stawell Ball. "A Treatise on the Theory of Screws". Cambridge University Press. Reprinted in 1998, from the first 1900 edition.

Links

• Wiki pages of previous years: Course 2010-2011 Course 2009-2010, Course 2008-2009.
• Academic calendar of master courses at UPC.
• Timetable of all master courses (February-June Semester).
• Teacher's space (Access restricted to teachers only).