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Erschienen in:
Introduction Kapitel lesen Erstes Kapitel lesen

2008 | OriginalPaper | Buchkapitel

2. Kinematics

verfasst von : Kenneth Waldron, Prof, James Schmiedeler, Prof

Erschienen in: Springer Handbook of Robotics

Verlag: Springer Berlin Heidelberg

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Abstract

Kinematics pertains to the motion of bodies in a robotic mechanism without regard to the forces/torques that cause the motion. Since robotic mechanisms are by their very essence designed for motion, kinematics is the most fundamental aspect of robot design, analysis, control, and simulation. The robotics community has focused on efficiently applying different representations of position and orientation and their derivatives with respect to time to solve foundational kinematics problems.
This chapter will present the most useful representations of the position and orientation of a body in space, the kinematics of the joints most commonly found in robotic mechanisms, and a convenient convention for representing the geometry of robotic mechanisms. These representational tools will be applied to compute the workspace, the forward and inverse kinematics, the forward and inverse instantaneous kinematics, and the static wrench transmission of a robotic mechanism. For brevity, the focus will be on algorithms applicable to open-chain mechanisms.
The goal of this chapter is to provide the reader with general tools in tabulated form and a broader overview of algorithms that can be applied together to solve kinematics problems pertaining to a particular robotic mechanism.

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Vorheriges Kapitel Introduction
Nächstes Kapitel Dynamics
Literatur
1.1.
W. R. Hamilton: On quaternions, or on a new system of imaginaries in algebra, Philos. Mag. 18, installments July 1844 - April 1850, ed. by D. E. Wilkins (2000)
1.2.
E.B. Wilson: Vector Analysis (Dover, New York 1960), based upon the lectures of J. W. Gibbs, (reprint of the second edn. published by Charles Scribnerʼs Sons, 1909)
1.3.
H. Grassman: Die Wissenschaft der extensiven Grösse oder die Ausdehnungslehre (Wigand, Leipzig 1844)
1.4.
J.M. McCarthy: Introduction to Theoretical Kinematics (MIT Press, Cambridge 1990)
1.5.
W.K. Clifford: Preliminary sketch of bi-quarternions, Proc. London Math. Soc., Vol. 4 (1873) pp. 381–395
1.6.
A. P. Kotelnikov: Screw calculus and some applications to geometry and mechanics, Annal. Imp. Univ. Kazan (1895)
1.7.
E. Study: Geometrie der Dynamen (Teubner, Leipzig 1901)
1.8.
G.S. Chirikjian, A.B. Kyatkin: Engineering Applications of Noncommutative Harmonic Analysis (CRC, Boca Raton 2001)MATH
1.9.
R. von Mises: Anwendungen der Motorrechnung, Z. Angew. Math. Mech. 4(3), 193–213 (1924)CrossRef
1.10.
J.E. Baker, I.A. Parkin: Fundamentals of Screw Motion: Seminal Papers by Michel Chasles and Olinde Rodrigues (School of Information Technologies, The University of Sydney, Sydney 2003), translated from O. Rodrigues: Des lois géométriques qui régissent les déplacements dʼun système dans lʼespace, J. Math. Pures Applicqu. Liouville 5, 380–440 (1840)
1.11.
R.S. Ball: A Treatise on the Theory of Screws (Cambridge Univ Press, Cambridge 1998)MATH
1.12.
J.K. Davidson, K.H. Hunt: Robots and Screw Theory: Applications of Kinematics and Statics to Robotics (Oxford Univ Press, Oxford 2004)MATH
1.13.
K.H. Hunt: Kinematic Geometry of Mechanisms (Clarendon, Oxford 1978)MATH
1.14.
J.R. Phillips: Freedom in Machinery: Volume 1. Introducing Screw Theory (Cambridge Univ Press, Cambridge 1984)
1.15.
J.R. Phillips: Freedom in Machinery: Volume 2. Screw Theory Exemplified (Cambridge Univ Press, Cambridge 1990)
1.16.
G.S. Chirikjian: Rigid-body kinematics. In: Robotics and Automation Handbook, ed. by T. Kurfess (CRC, Boca Raton 2005), Chapt. 2
1.17.
R.M. Murray, Z. Li, S.S. Sastry: A Mathematical Introduction to Robotic Manipulation (CRC, Boca Raton 1994)MATH
1.18.
A. Karger, J. Novak: Space Kinematics and Lie Groups (Routledge, New York 1985)
1.19.
R. von Mises: Motorrechnung, ein neues Hilfsmittel in der Mechanik, Z. Angew. Math. Mech. 2(2), 155–181 (1924), [transl. J. E. Baker, K. Wohlhart, Inst. for Mechanics, T. U. Graz (1996)]CrossRef
1.20.
J.D. Everett: On a new method in statics and kinematics, Mess. Math. 45, 36–37 (1875)
1.21.
R. Featherstone: Rigid Body Dynamics Algorithms (Kluwer Academic, Boston 2007)
1.22.
F. Reuleaux: Kinematics of Machinery (Dover, New York 1963), (reprint of Theoretische Kinematik, 1875, in German).
1.23.
K.J. Waldron: A method of studying joint geometry, Mechan. Machine Theory 7, 347–353 (1972)CrossRef
1.24.
T.R. Kane, D.A. Levinson: Dynamics, Theory and Applications (McGraw-Hill, New York 1985)
1.25.
J.L. Lagrange: Oeuvres de Lagrange (Gauthier-Villars, Paris 1773)
1.26.
J. Denavit, R.S. Hartenberg: A kinematic notation for lower-pair mechanisms based on matrices, J. Appl. Mech. 22, 215–221 (1955)MATHMathSciNet
1.27.
W. Khalil, E. Dombre: Modeling, Identification and Control of Robots (Taylor Francis, New York 2002)
1.28.
K.J. Waldron: A study of overconstrained linkage geometry by solution of closure equations, Part I: a method of study, Mech. Machine Theory 8(1), 95–104 (1973)CrossRef
1.29.
R. Paul: Robot Manipulators: Mathematics, Programming and Control (MIT Press, Cambridge 1982)
1.30.
J.J. Craig: Introduction to Robotics: Mechanics and Control (Addison-Wesley, Reading 1986)
1.31.
K.J. Waldron, A. Kumar: The Dextrous workspace, ASME Mech. Conf. (Los Angeles 1980), ASME paper No. 80-DETC-108
1.32.
R. Vijaykumar, K.J. Waldron, M.J. Tsai: Geometric optimization of manipulator structures for working volume and dexterity, Int. J. Robot. Res. 5(2), 91–103 (1986)CrossRef
1.33.
J. Duffy: Analysis of Mechanisms and Robot Manipulators (Wiley, New York 1980)
1.34.
D. Pieper: The Kinematics of Manipulators Under Computer Control. Ph.D. Thesis (Stanford University, Stanford 1968)
1.35.
C.S.G. Lee: Robot arm kinematics, dynamics, and control, Computer 15(12), 62–80 (1982)CrossRef
1.36.
M.T. Mason: Mechanics of Robotic Manipulation (MIT Press, Cambridge 2001)
1.37.
H.Y. Lee, C.G. Liang: A new vector theory for the analysis of spatial mechanisms, Mechan. Machine Theory 23(3), 209–217 (1988)CrossRef
1.38.
R. Manseur, K.L. Doty: A robot manipulator with 16 real inverse kinematic solutions, Int. J. Robot. Res. 8(5), 75–79 (1989)CrossRef
1.39.
M. Raghavan, B. Roth: Kinematic analysis of the 6R manipulator of general geometry, 5th Int. Symp. Robot. Res. (1990)
1.40.
D. Manocha, J. Canny: Real Time Inverse Kinematics for General 6R Manipulators Tech. rep. (University of California, Berkeley 1992)
1.41.
B. Buchberger: Applications of Gröbner bases in non-linear computational geometry. In: Trends in Computer Algebra, Lect. Notes Comput. Sci., Vol. 296, ed. by R. Janen (Springer, Berlin 1989) pp. 52–80
1.42.
P. Kovacs: Minimum degree solutions for the inverse kinematics problem by application of the Buchberger algorithm. In: Advances in Robot Kinematics, ed. by S. Stifter, J. Lenarcic (Springer, New York 1991) pp. 326–334
1.43.
L.W. Tsai, A.P. Morgan: Solving the kinematics of the most general six- and five-degree-of-freedom manipulators by continuation methods, ASME J. Mechan. Transmission Autom. Design 107, 189–195 (1985)CrossRef
1.44.
C.W. Wampler, A.P. Morgan, A.J. Sommese: Numerical continuation methods for solving polynomial systems arising in kinematics, ASME J. Mech. Des. 112, 59–68 (1990)CrossRef
1.45.
R. Manseur, K.L. Doty: Fast inverse kinematics of 5-revolute-axis robot manipulators, Mechan. Machine Theory 27(5), 587–597 (1992)CrossRef
1.46.
S.C.A. Thomopoulos, R.Y.J. Tam: An iterative solution to the inverse kinematics of robotic manipulators, Mechan. Machine Theory 26(4), 359–373 (1991)CrossRef
1.47.
J.J. Uicker Jr., J. Denavit, R.S. Hartenberg: An interactive method for the displacement analysis of spatial mechanisms, J. Appl. Mech. 31, 309–314 (1964)MATH
1.48.
J. Zhao, N. Badler: Inverse kinematics positioning using nonlinear programming for highly articulated figures, Trans. Comput. Graph. 13(4), 313–336 (1994)CrossRef
1.49.
D.E. Whitney: Resolved motion rate control of manipulators and human prostheses, IEEE Trans. Man Mach. Syst. 10, 47–63 (1969)CrossRef
1.50.
H. Cheng, K. Gupta: A study of robot inverse kinematics based upon the solution of differential equations, J. Robot. Syst. 8(2), 115–175 (1991)CrossRef
1.51.
L. Sciavicco, B. Siciliano: Modeling and Control of Robot Manipulators (Springer, London 2000)
1.52.
R.S. Rao, A. Asaithambi, S.K. Agrawal: Inverse Kinematic Solution of Robot Manipulators Using Interval Analysis, ASME J. Mech. Des. 120(1), 147–150 (1998)CrossRef
1.53.
C.W. Wampler: Manipulator inverse kinematic solutions based on vector formulations and damped least squares methods, IEEE Trans. Syst. Man Cybern. 16, 93–101 (1986)CrossRefMATH
1.54.
D.E. Orin, W.W. Schrader: Efficient computation of the jacobian for robot manipulators, Int. J. Robot. Res. 3(4), 66–75 (1984)CrossRef
1.55.
D. E. Whitney: The mathematics of coordinated control of prosthetic arms and manipulators J. Dynamic Sys. Meas. Contr. 122, 303–309 (1972)
1.56.
R.P. Paul, B.E. Shimano, G. Mayer: Kinematic control equations for simple manipulators, IEEE Trans. Syst. Man Cybern. SMC-11(6), 339–455 (1981)
1.57.
R.P. Paul, C.N. Stephenson: Kinematics of robot wrists, Int. J. Robot. Res. 20(1), 31–38 (1983)CrossRef
1.58.
R.P. Paul, H. Zhang: Computationally efficient kinematics for manipulators with spherical wrists based on the homogeneous transformation representation, Int. J. Robot. Res. 5(2), 32–44 (1986)CrossRef
1.59.
H. Asada, J.J.E. Slotine: Robot Analysis and Control (Wiley, New York 1986)
1.60.
F.L. Lewis, C.T. Abdallah, D.M. Dawson: Control of Robot Manipulators (Macmillan, New York 1993)
1.61.
R.J. Schilling: Fundamentals of Robotics: Analysis and Control (Prentice-Hall, Englewood Cliffs 1990)
1.62.
M.W. Spong, M. Vidyasagar: Robot Dynamics and Control (Wiley, New York 1989)
1.63.
T. Yoshikawa: Foundations of Robotics (MIT Press, Cambridge 1990)
Metadaten
Titel
Kinematics
verfasst von
Kenneth Waldron, Prof
James Schmiedeler, Prof
Copyright-Jahr
2008
Buch
Springer Handbook of Robotics

Print ISBN: 978-3-540-23957-4

Electronic ISBN: 978-3-540-30301-5

Copyright-Jahr: 2008

DOI
https://doi.org/10.1007/978-3-540-30301-5_2

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