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A remarkable 8R-mechanism. (English) Zbl 07608760

Holderbaum, William (ed.) et al., 2nd IMA conference on mathematics of robotics. Selected papers, online from Manchester, UK, September 8–10, 2021. Cham: Springer. Springer Proc. Adv. Robot. 21, 107-114 (2022).
Summary: We present some observations on a closed 8R-mechanism with the remarkable property that locking one of its joints in any configuration (of a suitable two-dimensional component of the configuration space) restricts the mechanism to a one-dimensional motion where automatically every other joint is locked as well. Equivalently, at any configuration, the four joints of even index and the four joints of odd index form respective Bennett mechanisms. The mechanism is constructed from a bivariate quaternion polynomial of bidegree (2, 2) which allows two factorisations with linear univariate factors. So far, only isolated examples are known.
For the entire collection see [Zbl 1491.68018].

MSC:

68T40 Artificial intelligence for robotics
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[1] Hegedüs, G.; Schicho, J.; Schröcker, HP, Factorization of rational curves in the Study quadric and revolute linkages, Mech. Mach. Theory, 69, 1, 142-152 (2013) · doi:10.1016/j.mechmachtheory.2013.05.010
[2] Hegedüs, G., Schicho, J., Schröcker, H.P.: Four-pose synthesis of angle-symmetric 6R linkages. ASME J. Mech. Robot. 7(4), 041006 (2015)
[3] Kong, X.; Jin, Y., Type synthesis of 3-DOF multi-mode translational/spherical parallel mechanisms with lockable joints, Mech. Mach. Theory, 96, 323-333 (2016) · doi:10.1016/j.mechmachtheory.2015.04.019
[4] Kong, X.; Pfurner, M., Type synthesis and reconfiguration analysis of a class of variable-DOF single-loop mechanisms, Mech. Mach. Theory, 85, 116-128 (2015) · doi:10.1016/j.mechmachtheory.2014.10.011
[5] Lercher, J., Scharler, D.F., Schröcker, H.P., Siegele, J.: Factorization of quaternionic polynomials of bi-degree (n,1), ArXiv 2011, 01744 (submitted for publication, 2020)
[6] Lercher, J., Schröcker, H.P.: A multiplication technique for the factorization of bivariate quaternionic polynomials. ArXiv 2105, 08500, submitted for publication 2021 · Zbl 1497.16027
[7] Li, Z.; Schicho, J., Classification of angle-symmetric 6R linkages, Mech. Mach. Theory, 70, 372-379 (2013) · doi:10.1016/j.mechmachtheory.2013.08.002
[8] Liu, K., Yu, J., Kong, X.: Synthesis of multi-mode single-loop Bennett-based mechanisms using factorization of motion polynomials. Mech. Mach. Theory 155, 104110 (2021)
[9] Lynch, KM; Park, FC, Modern Robotics. Mechanics, Planning, and Control (2017), Cambridge: Cambridge University Press, Cambridge
[10] Pfurner, M.; Kong, X.; Huang, C., Complete kinematic analysis of single-loop multiple-mode 7-link mechanisms based on Bennett and over constrained RPRP mechanisms, Mech. Mach. Theory, 73, 117-129 (2014) · doi:10.1016/j.mechmachtheory.2013.10.012
[11] Pottmann, H., Wallner, J.: Computational Line Geometry. In: Mathematics and Visualization, Springer, Berlin (2010). doi:10.1007/978-3-642-04018-4_1 2nd printing · Zbl 1175.51014
[12] Schicho, J., The multiple conical surfaces, Beitr. Algebra Geom., 42, 1, 71-87 (2001) · Zbl 0987.14005
[13] Skopenkov, M., Krasauskas, R.: Surfaces containing two circles through each point. Math. Ann. 373, 1299-1327 (2018). doi:10.1007/s00208-018-1739-z · Zbl 1416.51003
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