Abstract
It is well established that finite displacement screws effective for the (incompletely specified) relocation of a body with symmetries form linearly combined sets if they are of a sin-screw form Ŝ = sin 1/2ĝq ŝ, characterised by pitch P s = 1/2 σ/tan 1/2θ. This paper shows that screws of indefinitely many other functional forms may be derived, each with a correspondingly distinct definition of pitch, which in the same kinematical situations will also form sets of screws that are linearly combined with dual coefficients. As example, screws of form ŝ = sin ĝqŝ, of pitch ŝ = d/tan θ, are evaluated that describe displacement of a point-line.
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References
Bottema, O. and Roth, B., Theoretical Kinematics, North-Holland Publishing Company, Amsterdam (1979). Reprinted Dover, New York (1990).
Huang, C. and Roth, B., Analytic expressions for the finite screw systems. Mechanism and Machine Theory 29, 207-222 (1994).
Huang, C. and Wang, J-C., The finite screw system associated with the displacement of a line. Journal of Mechanical Design, Trans. ASME 125, 105-109 (2003).
Huang, C., Kuo, W. and Ravani, B., On the linear line complex and helicoidal vector field as-sociated with homologous lines of a finite displacement. In Proceedings 12th IFToMM World Congress on the Theory of Machines and Mechanisms, Besançon, France, Paper CK541, pp. 6 (2007).
Hunt, K.H., Kinematic Geometry of Mechanisms. Clarendon Press, Oxford (1990).
Hunt, K.H. and Parkin, I.A., Finite displacements of points, planes and lines via screw theory. Mechanism and Machine Theory 30, 177-192 (1995).
Parkin, I.A., A third conformation with the screw systems: finite twist displacements of a directed line and point. Mechanism and Machine Theory 27, 177-188 (1992).
Parkin, I.A., The role of body symmetry in determining screws for finite displacement of a rigid body. In Proceedings NATO ASI on Computational Methods in Mechanisms Vol. 2, Varna, Bulgaria, June 16-28, pp. 145-154 (1997).
Parkin, I.A., Linear systems of tan-screws for finite displacement of a rigid body with sym-metries. In Proceedings Sixth International Workshop on Advances in Robot Kinematics, Strobl, Austria, June-July, J. Lenar či č and M.L. Husty (Eds.), Kluwer Academic Publishers, pp. 317-326 (1998).
Parkin, I.A., The screws for finite displacement of a rigid body expressed in terms of its sym-metry screws. In Proceedings of CK2005, International Workshop on Computational Kin-ematics, Cassino, Italy, May, Paper 08CK2005, pp. 15 (2005).
Yang, A.T., Calculus of screws. In Basic Questions of Design Theory, W.R. Spillers (Ed.), Elsevier, New York, pp. 265-281 (1974).
Zhang, Y. and Ting, K-L., On the basis screws and screw systems of point-line and line displacements. Journal of Mechanical Design, Trans. ASME 126, 56-62 (2004).
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Parkin, I.A. (2008). Alternative Forms for Displacement Screws and Their Pitches. In: Lenarčič, J., Wenger, P. (eds) Advances in Robot Kinematics: Analysis and Design. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8600-7_21
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DOI: https://doi.org/10.1007/978-1-4020-8600-7_21
Publisher Name: Springer, Dordrecht
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