Abstract
In 1978, Hunt found a set of vector subspaces of screws that guarantee ‘full-cycle mobility’ of linkages and exhibit remarkable properties. They are subalgebras of the Lie algebra se(3) of the Euclidean group and they are at the basis of most families of mechanisms with special motion capabilities. This paper proves the existence of screw systems that, though not being subalgebras of se(3), still exhibit important properties for full-cycle motions, namely the invariance of both the space dimension and the pitch of the principal screws. Such systems are named persistent and they are believed to play an important role in both mobility analysis and mechanism synthesis.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
O. Khatib. Dynamic control of manipulators in operational space. In Sixth CISM-IFToMM Congress on Theory of Machines and Mechanisms, pp. 1128–1131 (1983).
P. Baerlocher and R. Boulic. An inverse kinematics architecture enforcing an arbitrary number of strict priority levels. Visual Computer, 20(6), 402–417 (2004).
L. Sentis. Synthesis and control of whole-body behaviors in humanoid systems. PhD thesis, Stanford University (2007).
Jaeheung Park. Control strategies for robots in contact. PhD thesis, Stanford University (2006).
Ph. Sardain and G. Bessonnet. Forces acting on a biped robot. Center of pressure – zero moment point. IEEE Transactions on Systems, Man, and Cybernetics, Part A, 34(5), 630–637 (2004).
S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, and H. Hirukawa. Biped walking pattern generation by using preview control of zero-moment point. In Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003).
K. Harada, H. Hirukawa, F. Kanehiro, K. Fujiwara, K. Kaneko, S. Kajita, and M. Nakamura. Dynamical balance of a humanoid robot grasping an environment. In Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, pp. 1167–1173 (2004).
P.-B. Wieber. Constrained dynamics and parametrized control in biped walking. In Proceedings International Symposium on Mathematical Theory of Networks and Systems, Perpignan (2000).
P.-B. Wieber. On the stability of walking systems. In Proceedings International Workshop on Humanoid and Human Friendly Robotics (2002).
F.-T. Cheng, T.H. Chen, and Y.-Y. Sun. Efficient algorithm for resolving manipulator redundancy – The compact QP method. In Proceedings of the 1992 IEEE International Conference on Robotics and Automation, Nice, France (1992).
Y. Abe, M. da Silva, and J. Popovic. Multiobjective control with frictional contacts. In Proceedings Symposium on Computer Animation (SCA) (2007).
C. Collette, A. Micaelli, C. Andriot, and P. Lemerle. Dynamic balance control of humanoids for multiple grasps and non coplanar frictional contacts. In Proceedings of Humanoids ’07 (2007).
S. Barthélemy, P. Bidaud, and A. Micaeli. Contrôle de l’équilibre des humains virtuels, chapter 2. École des Mines de Paris (2009).
G. Metta, G. Sandini, D. Vernon, L. Natale, and F. Nori. The iCub humanoid robot: an open platform for research in embodied cognition. In Permis: Performance Metrics for Intelligent Systems Workshop, Washington DC, USA, August (2008).
J. Yuan. Closed-loop manipulator control using quaternion feedback. IEEE Journal of Robotics and Automation, 4(4), 434–440 (1988).
S. Barthélemy and A. Micaelli. Arboris for Matlab.
J. Löfberg. Yalmip: A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan (2004).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this paper
Cite this paper
Carricato, M., Martínez, J.M.R. (2010). Persistent Screw Systems. In: Lenarcic, J., Stanisic, M. (eds) Advances in Robot Kinematics: Motion in Man and Machine. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9262-5_20
Download citation
DOI: https://doi.org/10.1007/978-90-481-9262-5_20
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9261-8
Online ISBN: 978-90-481-9262-5
eBook Packages: EngineeringEngineering (R0)