Abstract
It has been known for some time 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 \( \hat S = sin\hat \theta \hat s \), characterised by pitch P S = σ/ tanθ. (ŝ, ∣ŝ∣ = 1, is the unit line of the Mozzi-Chasles screw-axis and \( \hat \theta = \theta + \varepsilon \sigma \) is the dual half-angle of the displacement.) This paper shows that screws of a tan-screw form, \( \hat T = tan\hat \theta \hat s \), characterised by pitch P T = 2σ/ sin 2θ, enjoy the same properties of linear combination.
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Parkin, I.A. (1998). Linear Systems of Tan-Screws for Finite Displacement of a Rigid Body with Symmetries. In: Lenarčič, J., Husty, M.L. (eds) Advances in Robot Kinematics: Analysis and Control. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9064-8_32
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DOI: https://doi.org/10.1007/978-94-015-9064-8_32
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