Abstract
This paper presents a controlled tying approach for knots using fixtures and simple pulling motions applied to the ends of string. Each fixture is specific to a particular knot; the paper gives a design process that allows a suitable fixture to be designed for an input knot. Knot tying is separated into two phases. In the first phase, a fixture is used to loosely arrange the string around a set of rods, with the required topology of the given knot. In the second phase, the string is pulled taut and slid along the rods (the tightening fixture ) in a direction such that the cross-sections of the rods get closer together, allowing controlled tightening. Successful tying is shown for two interesting cases: a “double coin” knot design, and the top of a shoelace knot.
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Notes
- 1.
Some initial videos demonstrating the arrangement of several knots and tightening of the shoelace unknot can be found at http://www.cs.dartmouth.edu/~harrisonwfw/knotTying.html.
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Acknowledgments
Discussions with Yuliy Baryshnikov were instrumental in the development of four-piece fixtures. We also would like to thank Yu-Han Lyu, Jordan Kunzika, and George Boateng for helpful discussion and feedback. This work was supported by NSF grant IIS-1217447.
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Wang, W., Bell, M.P., Balkcom, D. (2015). Towards Arranging and Tightening Knots and Unknots with Fixtures. In: Akin, H., Amato, N., Isler, V., van der Stappen, A. (eds) Algorithmic Foundations of Robotics XI. Springer Tracts in Advanced Robotics, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-16595-0_39
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