Abstract
This paper deals with the comparison between the line geometries of point and line displacements. The central concept is that two linear complexes of different pitches are associated to a displacement screw. One is pertaining to point displacements, while the other to line displacements. Similarities between the two linear complexes in their construction, elements, properties, and relations to the displacement screw are investigated. This study shows that all of the recently developed theorems and properties in the line geometry of line displacements resemble those in the well-developed line geometry of point displacements. The results provided in this paper can help bridge the gap between point and line displacements in both theoretical treatments and practical applications.
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References
Study, E., Von den Bewegungen und Umlegungen, Mathematische Annalen, 39, 1891, pp. 441–564.
Bottema, O., and Roth, B., Theoretical Kinematics, North-Holland Publishing Company, Amsterdam, 1979.
Huang C., Kuo W., and Ravani B., On the Linear Line Complex and Helicoidal Vector Field Associated with Homologous Lines of a Finite Displacement, 12th IFToMM World Congress, Besançon, France, June 18–21, 2007.
Huang C., Kuo W., and Ravani B., On the Regulus Associated with the Displacement of a Line, Proceedings of the 2007 ASME International Design Engineering Technical Conferences and Computer and Information in Engineering Conference, Las Vegas, USA, September 4–7, 2007.
Phillips, J., Freedom in Machinery, Volumes 1 and 2, Cambridge University Press, Cambridge, 1984, 1990.
Hunt, K. H., Kinematic Geometry of Mechanisms, Claredon, Oxford, 1978.
Pottmann H., and Wallner J., Computational Line Geometry, Springer-Verlag, Berlin, 2001.
Tsai, L. W., and Roth, B., Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis, ASME Journal of Engineering for Industry, Vol. 95(B), 1973, pp. 603–611.
Huang, C., and Wang, J. C., The Finite Screw System Associated with the Displacement of a Line, Journal of Mechanical Design, Trans. ASME, Vol. 125, 2003, pp. 105–109.
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Huang, C. (2009). A Comparison Between Line Geometries of Point and Line Displacements. In: Ceccarelli, M. (eds) Proceedings of EUCOMES 08. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8915-2_8
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DOI: https://doi.org/10.1007/978-1-4020-8915-2_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8914-5
Online ISBN: 978-1-4020-8915-2
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