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Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

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Dual Quaternions as a Tool for Rigid Body Motion Analysis: A Tutorial with an Application to Biomechanics

Ettore Pennestrì
  • Dipartimento di Ingegneria Meccanica, Università Roma Tor Vergata via del Politecnico, 1, 00133 Roma, Italy
/ Pier Valentini
  • Dipartimento di Ingegneria Meccanica, Università Roma Tor Vergata via del Politecnico, 1, 00133 Roma, Italy
Published Online: 2010-10-18 | DOI: https://doi.org/10.2478/v10180-010-0010-2

Dual Quaternions as a Tool for Rigid Body Motion Analysis: A Tutorial with an Application to Biomechanics

Dual quaternions and dual quaternion interpolation are powerful mathematical tools for the spatial analysis of rigid body motions. In this paper, after a review of some basic results and formulas, it will be presented an attempt to use these tools for the the kinematic modeling of human joints. In particular, the kinematic parameters extracted from experimentally acquired data are compared with those theoretically computed from dual quaternions rigid body motion interpolation.

Kwaterniony dualne jako narzędzie analizy ruchu ciał sztywnych. Przykład zastosowań w biomechanice

Kwaterniony dualne i interpolacja z użyciem kwaternionów dualnych stanowią silne narzędzia matematycznye wykorzystywane analizy ruchu przestrzennego ciał sztywnych. W artykule przedstawiono przegląd podstawowych wzorów i wyników, a następnie zaprezentowano próbę użycia tych narzędzi do modelowania kinematyki stawów w ciele człowieka. W szczególności, parametry kinematyczne wyznaczone na podstawie danych eksperymentalnych porównano z wyliczonymi teoretycznie na podstawie interpolacji ruchu ciał sztywnych z użyciem kwaternionów dualnych.

Keywords: biomechanics; dual quaternion interpolation; human motion

  • M. Hiller, C. Woernle, A unified representation of spatial displacements. Mechanism and Machine Theory, 19, 477-486, 1984.

  • J.S. Dai, An historical review of the theoretical development of rigid body displacements from Rodrigues parameters to the finite twist. Mechanism and Machine Theory, 41, 41-52, 2006.

  • L. Chèze, and J. Dimnet, Three-Dimensional Analysis of Human Movement, chapter Modeling Human Body Motions by the Techniques Known to Robotics, 177-200. Human Kinetics, 1995.

  • V. M. Zatsiorsky, Kinematics of Human Motion, Human Kinetics, 1998.

  • M. McCarthy, Introduction to theoretical kinematics. The MIT Press, 1990.

  • B. Jüttler, Visualization of moving objects using dual quaternion curves. Computers & Graphics, 18(3), 315-326, 1994. [Crossref]

  • A. McAulay, Octonions - A Development of Clifford's Bi-Quaternions. Cambridge University Press, 1898.

  • A. T. Yang, Application of Quaternion Algebra and Dual Numbers to the Analysis of Spatial Mechanisms. PhD thesis, Columbia University, 1963.

  • E. Pennestrì, R. Stefanelli, Linear algebra and numerical algorithms using dual numbers. Multibody System Dynamics, 18, 323-344, 2007. [Web of Science]

  • E. Pennestrì, and P.P. Valentini, Linear dual algebra algorithms and their Application to Kinematics. In C.L. Bottasso, editor, Multibody Dynamics Computational Methods and Applications, Vol. 12, Springer Verlag, 2008.

  • K.R. Etzel, and J.M. McCarthy, Spatial motion interpolation in an image space of so(4). In Proceedings of The 1996 ASME Design Engineering Technical Conference and Computers in Engineering Conference, 96-DETC/MECH-1164, 1996.

  • L. Kavan, and S. Collins, and C. O'Sullivan, and J. Zara, Dual Quaternions for Rigid Transformation Blending. Technical Report TCD-CS-2006-46, The University of Dublin, Trinity College, 2006.

  • L. Kavan, and S. Collins, and Zara, and C. O'Sullivan, Geometric Skinning with Approximate Dual Quaternion Blending. ACM Transaction on Graphics, 27, 105, 2008. [Web of Science]

  • K.K. Teu, and W. Kim, Estimation of the axis of a screw motion from noisy data—A new method based on Plücker lines. Journal of Biomechanics, 39, 2857-2862, 2006.

  • A. Page, and V. Mata, and J.V. Hoyos, and R. Porcar, Experimental determination of instantaneous screw axis in human motion. Error analysis. Mechanism and Machine Theory Mechanism and Machine Theory, 42, 429-441, 2007. [Web of Science]

  • H. H. Cheng, Computation of dual numbers in the extended finite dual plane. In Proc. of the 1993 ASME Design Automation Conference, 73-80, Sept. 19-22, 1993.

  • H. H. Cheng, Programming with dual numbers and its applications in mechanisms design. Engineering with Computers, 10(4), 212-229, 1994.

  • K. Wohlhart, Motor Tensor Calculus. In J. P. Merlet and B. Ravani, editors, Computational Kinematics 93-102. Kluwer Academic Publishers, 1995.

About the article

Published Online: 2010-10-18

Published in Print: 2010-01-01

Citation Information: Archive of Mechanical Engineering, ISSN (Print) 0004-0738, DOI: https://doi.org/10.2478/v10180-010-0010-2. Export Citation

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