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Title: Knotty Knits are Tangles on Tori
In this paper we outline a topological framework for constructing 2-periodic knitted stitches and an algebra for joining stitches together to form more complicated textiles. Our topological framework can be constructed from certain topological “moves" which correspond to “operations" that knitters make when they create a stitch. In knitting, unlike Jacquard weaves, a set of n loops may be combined in topologically nontrivial ways to create n stitches. We define a swatch as a mathematical construction that captures the topological manipulations a hand knitter makes. Swatches can capture the topology of all possible 2-periodic knitted motifs: standard patterns such as garter and ribbing, cables in which stitches connect one row of loops to a permutation of those same loops on the next row much like operators of a braid group, and lace or pieces with shaping which use increases and decreases to disrupt the underlying square lattice of stitches.  more » « less
Award ID(s):
1847172
NSF-PAR ID:
10230429
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Proceedings of Bridges 2020
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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Metrics of interest were peak-to-peak displacement (mm), stiffness (N/mm), ultimate failure load (N) and failure mode. Data are presented as averages and standard deviations. A Wilcoxon signed-rank test was used to evaluate the groups for time to complete stitch and biomechanical performance. Statistical significance was set at P = .05. RESULTS SECTION: In Group 1, the time to complete the whip stitch was not significantly different between User 1 and User 3, where the average completion time was 1 min 13 sec. Similarly, there were no differences between Users when performing the WhipLock (Group 2) with an average time of 1 min 49 sec. In Group 3 (whip stitch), User 2 took 1 min 48 sec to complete the whip stitch, whereas User 4 took 1 min 25 sec (p=.033). The time to complete the WhipLock stitch (Group 4) was significantly different, where User 2 took 3 min and 44 sec, while User 4 only took 2 min 3 sec (p=.002). 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