Abstract
It is well known that a general displacement of a rigid body may be regarded as a finite twisting motion upon an axis in space. Such a twist axis may be treated as a screw when a measure of pitch appropriate to finite twists is used. The author has recently shown that when the displacement of a specialised, axi-symmetric, body is considered, each of the infinity of finite twist screws which are then available for the displacement is a linear combination of just two of their number.
This result is here exploited to derive parameters of the finite twist axis for displacement of a generally shaped body.
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
Angeles, J., “Automatic Computation of the Screw Parameters of Rigid Body Motions. Part I: Finitely-Separated Positions.”, Trans. ASME, J. Dynamic Systems, Measurement and Control, Vol. 108, pp. 32–38, 1986a.
Angeles, J., “Automatic Computation of the Screw Parameters of Rigid Body Motions. Part II: Infinitesimally-Separated Positions.”, Trans. ASME, J. Dynamic Systems, Measurement and Control, Vol. 108, pp. 39–43, 1986b.
Bottema, O., “On a set of displacements in space”, Journal of Engineering for Industry, Trans. ASME Series B, Vol. 95, pp. 451–454, May 1973.
Chasles, M., “Note sur les proprietes generales du Systeme de deux corps…”, Bull. Sci.Math. Ferrusac, Vol. 14, pp. 321–326, 1830.
Hunt, K.H., “Kinematic Geometry of Mechanisms”, Clarendon Press, Oxford 1978.
Hunt, K.H., “Manipulating a Body through a Finite screw Displacement”, Proceedings of the 7th World Congress, IFToMM, Sevilla Spain, Sept 1987, Pergamon Press 1987, pp. 187–191, 1987.
Parkin, I.A., “Co-ordinate Transformations of Screws with Applications to Screw Systems and Finite Twists”, Technical Report TR 342, Basser Dept. of Computer Science, University of Sydney, May 1988.
Parkin, I.A., “A Third Conformation with the Screw Systems: Finite Twist Displacements of a Directed Line and Point”, Technical Report TR 351, Basser Dept. of Computer Science, University of Sydney, October 1989.
Phillips, Jack, “Freedom in Machinery”, Vol. 1, Cambridge University Press, 1984.
Phillips, J.R., and Zhang, W.X., “The Screw Triangle and the Cylindroid”, Proceedings of the 7th World Congress, IFToMM, Sevilla Spain, Sept 1987, Pergamon Press, 1987, pp. 179–182, 1987.
Phillips, Jack, “Freedom in Machinery”, Vol. 2, Cambridge University Press, 1990.
Sticher, F., “On the Finite Screw Axis Cylindroid”, Mech. Mach. Theory, Vol. 24, No. 3, pp. 143–155, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Wien
About this paper
Cite this paper
Parkin, I.A. (1991). On Determining Parameters of the Twist-Axis for the Finite Displacement of a Body. In: Stifter, S., Lenarčič, J. (eds) Advances in Robot Kinematics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4433-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-7091-4433-6_9
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82302-6
Online ISBN: 978-3-7091-4433-6
eBook Packages: Springer Book Archive