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Geometric characterization of the workspace of non-orthogonal rotation axes
1. | DFKI GmbH, Robotics Innovation Center, Robert-Hooke-Straße 1, 28359 Bremen, Germany |
References:
[1] |
B. Alpern, L. Carter, M. Grayson and C. Pelkie, Orientation maps: Techniques for visualizing rotations (a consumer's guide), in VIS '93: Proceedings of the 4th conference on Visualization, (1993), 183-188. |
[2] |
S. Bai and J. Angeles, A unified input-output analysis of four-bar linkages, Mechanism and Machine Theory, 43 (2008), 240-251.
doi: 10.1016/j.mechmachtheory.2007.01.002. |
[3] |
O. A. Bauchau and L. Trainelli, The Vectorial Parameterization of Rotation, Nonlinear Dynamics, 32 (2003), 71-92.
doi: 10.1023/A:1024265401576. |
[4] |
B. Bongardt, Sheth-Uicker Convention Revisited - A Normal Form for Specifying Mechanisms, Technical report, RIC, DFKI, 2012. |
[5] |
P. B. Davenport, Rotations about nonorthogonal axes, AIAA Journal, 11 (1973), 853-857. |
[6] |
L. Dorst, D. Fontijne and S. Mann, Geometric Algebra - An Object-Oriented Approach to Geometry, Morgan Kaufmann Series in Computer Graphics, Morgan Kaufmann, 2007. |
[7] |
F. Freudenstein, Approximate synthesis of four-bar linkages, Transaction ASME, 77 (1955), 853-861. |
[8] |
K. C. Gupta, Kinematic analysis of manipulators using the zero reference position description, International Journal of Robotics Research, 5 (1986), 5-13.
doi: 10.1177/027836498600500202. |
[9] |
A. J. Hanson, Visualizing Quaternions, Morgan Kaufmann, 2007.
doi: 10.1145/1281500.1281634. |
[10] |
M. J. D. Hayes, K. Parsa and J. Angeles, The effect of data-set cardinality on the design and structural errors of four-bar function-generators, in 10th World Congress on the Theory of Machines and Mechanisms, (1999), 437-442. |
[11] |
M. Husty, E. Ottaviano and M. Ceccarelli, A Geometrical characterization of workspace singularities in 3r manipulators, in Advances in Robot Kinematics: Analysis and Design, (2008), 411-418.
doi: 10.1007/978-1-4020-8600-7_43. |
[12] |
M. L. Husty, M. Pfurner and H.-P. Schröcker, A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator, Mechanism and Machine Theory, 42 (2007), 66-81.
doi: 10.1016/j.mechmachtheory.2006.02.001. |
[13] |
F. Klein, Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis,, 1932., ().
|
[14] |
J. B. Kuipers, Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality, Princeton University Press, 2002. |
[15] |
Z. Liu and J. Angeles, Least-square optimization of planar and spherical four-bar function generator under mobility constraints, Journal of Mechanical Design, 114 (1992), 569-573.
doi: 10.1115/1.2917045. |
[16] |
C. D. Mladenova and I. M. Mladenov, Vector decomposition of finite rotations, Reports on Mathematical Physics, 68 (2011), 107-117.
doi: 10.1016/S0034-4877(11)60030-X. |
[17] |
R. M. Murray, S. S. Sastry and L. Zexiang, A Mathematical Introduction to Robotic Manipulation, CRC Press, 1994. |
[18] |
R. P. Paul and C. N. Stevenson, Kinematics of robot wrists, International Journal of Robotics Research, 2 (1983), 31-38.
doi: 10.1177/027836498300200103. |
[19] |
M. Pfurner, Analysis of Spatial Serial Manipulators Using Kinematic Mapping, PhD thesis, University of Innsbruck, Austria, 2006. |
[20] |
G. Piovan and F. Bullo, On coordinate-free rotation decomposition: Euler angles about arbitrary axes, IEEE Transactions on Robotics, 28 (2012), 728-733.
doi: 10.1109/TRO.2012.2184951. |
[21] |
J. M. Selig, Geometric Fundamentals of Robotics, 2nd ed., Springer, New York, 2005. |
[22] |
J. R. Shewchuk, Lecture Notes on Geometric Robustness,, 2009., ().
|
[23] |
M. D. Shuster and F. L. Markley, Generalization of the euler angles, The Journal of the Astronautical Sciences, 51 (2003), 123-132. |
[24] |
J. Stillwell, Naive Lie Theory, Undergraduate Texts in Mathematics, Springer, 2008.
doi: 10.1007/978-0-387-78214-0. |
[25] |
A. T. Yang and F. Freudenstein, Application of dual-number quaternion algebra to the analysis of spatial mechanisms, Journal of Applied Mechanics, 31 (1964), 300-308.
doi: 10.1115/1.3629601. |
show all references
References:
[1] |
B. Alpern, L. Carter, M. Grayson and C. Pelkie, Orientation maps: Techniques for visualizing rotations (a consumer's guide), in VIS '93: Proceedings of the 4th conference on Visualization, (1993), 183-188. |
[2] |
S. Bai and J. Angeles, A unified input-output analysis of four-bar linkages, Mechanism and Machine Theory, 43 (2008), 240-251.
doi: 10.1016/j.mechmachtheory.2007.01.002. |
[3] |
O. A. Bauchau and L. Trainelli, The Vectorial Parameterization of Rotation, Nonlinear Dynamics, 32 (2003), 71-92.
doi: 10.1023/A:1024265401576. |
[4] |
B. Bongardt, Sheth-Uicker Convention Revisited - A Normal Form for Specifying Mechanisms, Technical report, RIC, DFKI, 2012. |
[5] |
P. B. Davenport, Rotations about nonorthogonal axes, AIAA Journal, 11 (1973), 853-857. |
[6] |
L. Dorst, D. Fontijne and S. Mann, Geometric Algebra - An Object-Oriented Approach to Geometry, Morgan Kaufmann Series in Computer Graphics, Morgan Kaufmann, 2007. |
[7] |
F. Freudenstein, Approximate synthesis of four-bar linkages, Transaction ASME, 77 (1955), 853-861. |
[8] |
K. C. Gupta, Kinematic analysis of manipulators using the zero reference position description, International Journal of Robotics Research, 5 (1986), 5-13.
doi: 10.1177/027836498600500202. |
[9] |
A. J. Hanson, Visualizing Quaternions, Morgan Kaufmann, 2007.
doi: 10.1145/1281500.1281634. |
[10] |
M. J. D. Hayes, K. Parsa and J. Angeles, The effect of data-set cardinality on the design and structural errors of four-bar function-generators, in 10th World Congress on the Theory of Machines and Mechanisms, (1999), 437-442. |
[11] |
M. Husty, E. Ottaviano and M. Ceccarelli, A Geometrical characterization of workspace singularities in 3r manipulators, in Advances in Robot Kinematics: Analysis and Design, (2008), 411-418.
doi: 10.1007/978-1-4020-8600-7_43. |
[12] |
M. L. Husty, M. Pfurner and H.-P. Schröcker, A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator, Mechanism and Machine Theory, 42 (2007), 66-81.
doi: 10.1016/j.mechmachtheory.2006.02.001. |
[13] |
F. Klein, Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis,, 1932., ().
|
[14] |
J. B. Kuipers, Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality, Princeton University Press, 2002. |
[15] |
Z. Liu and J. Angeles, Least-square optimization of planar and spherical four-bar function generator under mobility constraints, Journal of Mechanical Design, 114 (1992), 569-573.
doi: 10.1115/1.2917045. |
[16] |
C. D. Mladenova and I. M. Mladenov, Vector decomposition of finite rotations, Reports on Mathematical Physics, 68 (2011), 107-117.
doi: 10.1016/S0034-4877(11)60030-X. |
[17] |
R. M. Murray, S. S. Sastry and L. Zexiang, A Mathematical Introduction to Robotic Manipulation, CRC Press, 1994. |
[18] |
R. P. Paul and C. N. Stevenson, Kinematics of robot wrists, International Journal of Robotics Research, 2 (1983), 31-38.
doi: 10.1177/027836498300200103. |
[19] |
M. Pfurner, Analysis of Spatial Serial Manipulators Using Kinematic Mapping, PhD thesis, University of Innsbruck, Austria, 2006. |
[20] |
G. Piovan and F. Bullo, On coordinate-free rotation decomposition: Euler angles about arbitrary axes, IEEE Transactions on Robotics, 28 (2012), 728-733.
doi: 10.1109/TRO.2012.2184951. |
[21] |
J. M. Selig, Geometric Fundamentals of Robotics, 2nd ed., Springer, New York, 2005. |
[22] |
J. R. Shewchuk, Lecture Notes on Geometric Robustness,, 2009., ().
|
[23] |
M. D. Shuster and F. L. Markley, Generalization of the euler angles, The Journal of the Astronautical Sciences, 51 (2003), 123-132. |
[24] |
J. Stillwell, Naive Lie Theory, Undergraduate Texts in Mathematics, Springer, 2008.
doi: 10.1007/978-0-387-78214-0. |
[25] |
A. T. Yang and F. Freudenstein, Application of dual-number quaternion algebra to the analysis of spatial mechanisms, Journal of Applied Mechanics, 31 (1964), 300-308.
doi: 10.1115/1.3629601. |
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