Abstract
A lattice of geometries is presented and compared for representing some geometrical aspects of the kinematic design of robot systems and subsystems Three geometries (set theory, topology and projective geometry) are briefly explored in more detail in the context of three geometric configurations in robotics (robot groupings, robot connectivities and robot motion sensor patterns).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Alexandroff P, (1961), Elementary Concepts of Topology (Dover Publications, New York)
Birkhoff G, MacLane S, (1965), A Survey of Modern Algebra (MacMillan, New York)
Brooks R A, (1999), Cambrian Intelligence (MIT Press)
Coxeter H S M, (1993), The Real Projective Plane (Springer-Verlag, Berlin)
Harvey I, Husbands P, Cliff D, Thomson A and Jakobi N, (1996), “Evolutionary Robotics at Sussex”, in Proc. ISRAM 96: Int. Symp. on Robotics & Manufacturing, Montpelier, France
Hausner M, (1965), A Vector Space Approach to Geometry (Dover Publications, New York)
Klein F, (1939), Elementary Mathematics from an Advanced Standpoint (two volumes) (Noble) (Dover, New York edition, 1948)
Kreyszig E, (1959), Differential Geometry, (University of Toronto Press, Toronto) (Dover, New York edition, 1991)
Meserve B E, (1955), Fundamental Concepts of Geometry (Dover, New York edition, 1983)
Modenov P S and Parkhomenko A S, (1965a), Geometric Transformations, Volume 1: Euclidean and Affine Transformations (Academic Press, New York)
Modenov P S and Parkhomenko A S, (1965b), Geometric Transformations, Volume 2: Projective Transformations (Academic Press, New York)
Porteous I R, (1969), Topological Geometry (Van Nostrand Reinhold, London)
Rindler W, (1966), Special Relativity (Oliver and Boyd)
Weyl H, (1939), The Classical Groups, (Princeton, New Jersey)
Wilson R J, (1996), Introduction to Graph Theory (Longman)
Yale P B, (1968), Geometry and Symmetry (Holden-Day, San Francisco) (Dover, New York edition, 1988).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 CISM, Udine
About this chapter
Cite this chapter
Rooney, J. (2006). Geometric Configuration in Robot Kinematic Design. In: Zielińska, T., Zieliński, C. (eds) Romansy 16. CISM Courses and Lectures, vol 487. Springer, Vienna. https://doi.org/10.1007/3-211-38927-X_9
Download citation
DOI: https://doi.org/10.1007/3-211-38927-X_9
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-36064-4
Online ISBN: 978-3-211-38927-0
eBook Packages: EngineeringEngineering (R0)