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Lercher, Johanna; Scharler, Daniel F.; Schröcker, Hans-Peter

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

Keywords:

quaternions; dual quaternions; bivariate polynomial; factorisation; Bennett mechanism
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\textit{J. Lercher} et al., Springer Proc. Adv. Robot. 21, 107--114 (2022; Zbl 07608760)
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