Robotics Group

International Summer School

Screw-Theory Based Methods in Robotics

August 22-30, 2009
University of Genoa, Italy

We wish to thank all participants, the lecturers, and our volunteers.
You all contributed to a successful summer school.
Please keep in touch and stay tuned for the next Summer Screws.

Università di Genova














The applications of the theory of screws are based on the combined representation of angular and linear velocity, or similarly force and moment, as one element of a six-dimensional vector space.

The importance of screw theory in robotics is widely recognised, in principle. In practice, almost nowhere is it taught to mechanical-engineering students and few know how to use it. Yet, in a variety of areas of robotics, methods and formalisms based on the use of screw geometry and algebra have shown to be superior to other techniques and have led to significant advances. These include the development of fast and efficient dynamics algorithms, discoveries in the nature of robot compliance and mechanism singularity, and the invention of numerous parallel mechanisms.

The instructors in the summer school are the authors of many of these results. They will teach the participants to apply existing techniques and to develop new ones in their own research. The basic theoretical notions will be introduced in a rigorous manner, but the emphasis will be on applications, with examples and exercises.



The school is intended for graduate students and young researchers in robotics. Participants are expected from both academia and industry.

It is strongly recommended that attendees have their own portable computers, preferably with Matlab and Maple. Alternative equivalent software can also be used.

Some experience with (and availability of) 3D CAD software would be helpful but not required.

Software and computer access can be provided to a limited number of participants upon request.



You can download the Program here.

The material addresses subjects sufficiently fundamental to be within the desirable competence of any mechanical roboticist, and in each area advanced screw-theory based methods have been used to great advantage.

Basic vector-space properties of twists and wrenches: physical interpretation of the linear operations; linear dependence and independence, subspaces; bases and coordinates. (Lecturer: Dimiter Zlatanov)

Scalar products, dual spaces, reciprocity. Constraint and freedom in mechanisms. Constraint analysis. Type synthesis of single-loop mechanisms and parallel manipulators. (Lecturers: Xianwen Kong and Dimiter Zlatanov)

Velocity and singularity analysis of parallel and interconnected-chain mechanisms. Derivation of input-output velocity equations and singularity conditions. (Lecturers: Matteo Zoppi and Dimiter Zlatanov)
Mappings between screw spaces, stiffness and inertia. Structure of robot compliance. Eigenvalue problems and eigenscrews. Synthesis with springs. (Lecturer: Harvey Lipkin)
6D formulation of the dynamics of individual rigid bodies and rigid-body systems. Equations of motion. Dynamics algorithms. (Lecturer: Roy Featherstone)



Dimiter Zlatanov has used screw theory in the singularity and mobility analysis of mechanisms. He is the inventor of one of the first-known 4-dof parallel mechanisms and has presented courses and talks on screw-based methods in various universities.

Xianwen Kong is the inventor of numerous parallel mechanisms and the co-author of the book Type synthesis of parallel mechanisms. His results have been based on methods from screw-system theory.

Matteo Zoppi has developed screw-theoretical techniques for the derivation and application of velocity equations for complex-chain manipulators. He is also the inventor of a number of mechanisms.

Harvey Lipkin has worked more than any one on applying screw-theoretical methods in different areas of robotics and mechanisms, such as hybrid control, compliance, vibrations, and dynamics. He has taught various aspects of screw theory and supervised graduate students in the use of such methods.

Roy Featherstone is the inventor of the Articulated-Body Dynamics Algorithm, and the author of the books Robot Dynamics Algorithms and Rigid Body Dynamics Algorithms. His ground-breaking work in dynamics has relied on a screw-theoretical formalism for the formulation of the equations of motion.




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