Abstract
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.
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Notes
- 1.
Strictly speaking, it parametrises one component of the mechanism’s configuration space. We don’t know if other components do exist or not.
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Lercher, J., Scharler, D.F., Schröcker, HP. (2022). A Remarkable 8R-Mechanism. In: Holderbaum, W., Selig, J.M. (eds) 2nd IMA Conference on Mathematics of Robotics. IMA 2020. Springer Proceedings in Advanced Robotics, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-91352-6_11
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DOI: https://doi.org/10.1007/978-3-030-91352-6_11
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