Abstract
The subalgebras of the Lie algebra se(3) of the Euclidean group are at the basis of most families of mechanisms with special motion capabilities. Recently, it was shown that, by conveniently composing subalgebra generators, persistent screw systems (PSSs) may be obtained. PSSs are not subalgebras of se(3), but they still exhibit remarkable invariant properties. For this reason, they may play an important role in both mobility analysis and mechanism design. This paper presents all generators of PSSs of dimension 4.
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
Notes
- 1.
Though A is generated here by a chain of serially-connected screws, this is not a necessary requisite.
- 2.
A ∗ and B ∗ are, respectively, tangent spaces at the identity to quotient manifolds of the subgroups associated with A n and B m by the subgroup associated with I h [5].
References
Carricato, M., Rico Martínez, J.M.: Persistent screw systems. In: Lenarčič J., Stanišic̀, M.M. (eds.) Advances in Robot Kinematics: Motion in Man and Machine, pp. 185–194. Springer, Dordrecht (2010)
Carricato, M., Rico Martínez, J.M.: Persistent screw systems of dimension three. In: Proc. of 13th World Congress in Mechanism and Machine Science, pp. 1–12, Paper No. A7_430. Guanajuato, Mexico (2011)
Gibson, C.G., Hunt, K.H.: Geometry of screw systems—2, classification of screw systems. Mech. Mach. Theory 25(1), 11–27 (1990)
Hunt, K.H.: Kinematic Geometry of Mechanisms. Clarendon, Oxford (1978)
Meng, J., Liu, G., Li, Z.: A geometric theory for analysis and synthesis of sub-6 dof parallel manipulators. IEEE Trans. Robot. 23(4), 625–649 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Carricato, M. (2012). Persistent Screw Systems of Dimension Four. In: Lenarcic, J., Husty, M. (eds) Latest Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4620-6_19
Download citation
DOI: https://doi.org/10.1007/978-94-007-4620-6_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4619-0
Online ISBN: 978-94-007-4620-6
eBook Packages: EngineeringEngineering (R0)