The mathematical properties associated with the exponential rotation matrices are reviewed. By means of two typical mechanism examples, it is demonstrated that these properties constitute a versatile analytical tool, which can be used effectively in kinematic studies on spatial mechanical systems involving position, velocity, acceleration, and singularity analyses.
Issue Section:
Research Papers
1.
Bahar
, L. Y.
, 1970, “Direct Determination of Finite Rotation Operators
,” J. Franklin Inst.
0016-0032, 298
(5
), pp. 401
–404
.2.
Özgören
, M. K.
, 1976, “Optimization of Manipulator Motions
,” Proceedings Second CISM-IFTOMM Symposium on Theory and Practice of Robots and Manipulators
, Warsaw
, Poland
, pp. 27
–36
.3.
Bottema
, O.
, and Roth
, B.
, 1979, Theoretical Kinematics
, North-Holland
, Netherlands
, Chaps. 2 and 13.4.
Brockett
, R. W.
, 1984, “Robotic Manipulators and the Product of Exponential Formula
,” Proceedings of International Symposium on Mathematical Theory of Networks and Systems
, Berlin
, Germany
, pp. 120
–127
.5.
Özgören
, M. K.
, 1987, “Application of Exponential Rotation Matrices to the Kinematic Analysis of Manipulators
,” Proceedings Seventh World Congress on the Theory of Machines and Mechanisms
, Sevilla
, Spain
, pp. 1187
–1190
.6.
Özgören
, M. K.
, 1994, “Some Remarks on Rotation Sequences and Associated Angular Velocities
,” Mech. Mach. Theory
0094-114X, 29
, pp. 933
–940
.7.
Özgören
, M. K.
, 1999, “Kinematic Analysis of a Manipulator With its Position and Velocity Related Singular Configurations
,” Mech. Mach. Theory
0094-114X, 34
, pp. 1075
–1101
.8.
Özgören
, M. K.
, 1999, “Kinematic Analysis of Spatial Mechanisms using Exponential Rotation Matrices
,” Proceedings of Tenth World Congress on the Theory of Machines and Mechanisms
, Oulu
, Finland
, pp. 711
–716
.9.
Balkan
, T.
, Özgören
, M. K.
, Arıkan
, M. A. S.
, and Baykurt
, H. M.
, 2000, “A Method of Inverse Kinematic Solution Including Singular and Multiple Configurations for a Class of Robotic Manipulators
,” Mech. Mach. Theory
0094-114X, 35
, pp. 1221
–1236
.10.
Balkan
, T.
, Özgören
, M. K.
, Arıkan
, M. A. S.
, and Baykurt
, H. M.
, 2001, “A Kinematic Structure-Based Classification and Compact Kinematic Equations for Six-dof Industrial Robotic Manipulators
,” Mech. Mach. Theory
0094-114X, 36
, pp. 817
–832
.11.
Özgören
, M. K.
, 2002, “Topological Analysis of 6-Joint Serial Manipulators and Their Inverse Kinematic Solutions
,” Mech. Mach. Theory
0094-114X, 37
, pp. 511
–546
.12.
Murray
, R. N.
, Li
, Z.
, and Sastry
, S. S.
, 1994, A Mathematical Introduction to Robotic Manipulation
, CRC
, London
, Chap. 2.13.
Selig
, J. M.
, 1996, Geometrical Methods in Robotics
, Springer-Verlag
, New York
, Chap. 4.14.
Hervé
, J. M.
, 1982, “Intrinsic Formulation of Problems of Geometry and Kinematics of Mechanisms
,” Mech. Mach. Theory
0094-114X, 17
, pp. 179
–184
.15.
Hervé
, J. M.
, 1999, “The Lie Group of Rigid Body Displacements, a Fundamental Tool for Mechanism Design
,” Mech. Mach. Theory
0094-114X, 34
, pp. 719
–730
.16.
Denavit
, J.
, and Hartenberg
, R. S.
, 1955, “A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices
,” ASME J. Appl. Mech.
0021-8936, 23
, pp. 215
–221
.17.
Griffis
, M.
, and Duffy
, J.
, 1989, “A Forward Displacement Analysis of a Class of Stewart Platforms
,” J. Rob. Syst.
0741-2223, 6
, pp. 703
–720
.18.
Raghavan
, M.
, and Roth
, B.
, 1993, “Inverse Kinematics of the General 6R Manipulator and Related Linkages
,” ASME J. Mech. Des.
1050-0472, 115
, pp. 502
–508
.19.
Lee
, H. Y.
, and Reinholtz
, C. F.
, 1996, “Inverse Kinematics of Serial-Chain Manipulators
,” ASME J. Mech. Des.
1050-0472, 118
, pp. 396
–404
.20.
Nielsen
, J.
, and Roth
, B.
, 1999, “On the Kinematic Analysis of Robotic Mechanisms
,” Int. J. Robot. Res.
0278-3649, 18
, pp. 1147
–1160
.21.
Erdem
, B. E.
, 1996, “Analysis and Control of Manipulators at Singular Positions
,” M.Sc. thesis, Middle East Technical University, Ankara.22.
Mavroidis
, C.
, and Roth
, B.
, 1995, “Method to Determine Uncertain Configurations of 6-R Manipulators
,” Proceedings of Ninth World Congress on the Theory of Machines and Mechanisms
, Milano
, Italy
, pp. 1987
–1992
.23.
Paul
, B.
, 1979, Kinematics and Dynamics of Planar Machinery
, Prentice-Hall, Englewood Cliffs
, NJ, USA
, Chap. 8.Copyright © 2007
by American Society of Mechanical Engineers
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