Knot twisting

These are required to make threads, i.e. the final drawing, twisting and winding of cotton. Such motors must possess very smooth acceleration to eliminate breakage of threads. They are recommended to have a starting torque of 150-200% of T, and a pull-out torque of 200-275% of with a mean acceleration torque ol 150-175%. A normal acceleration time of 5-10 seconds is recommended. Faster acceleration may cause more breakages, while a slower acceleration may result in snarls and knots in the yarn as a result of insufficient tension. 

Helicity is defined as a qualitative measurement of how a topological configuration is linked, knotted, or twisted. If A is the vector potential of electromagnetism, the quantity then defines magnetic helicity. In order to obtain a nonnull value for K, the condition A (V A) /- 0 must be verified in the volume... 

Figure 6. The Mobius strip approach (three half-twists) to a trefoil knot.

A directed knot synthesis relying upon the Mobius strip principle was conceived by Schill and coworkers [41-50] who synthesized the doubly bridged tetraamino-p-benzoquinone 9. Connection of three such molecules by long chains should give the molecular ladder 10, precursor of the three half-twist-containing Mobius strip 11 (Figure 8). 

Our template synthesis of knots implies that the target molecules are obtained as cationic dicopper(I) complexes. Therefore we considered the possibility of interconverting both enantiomers into a pair of diastereomeric salts [137, 138] by combining them with an optically active anion. Binaphthyl phosphate (BNP") [139] drew our attention because its chirality arises from the binaphthyl core, which is twisted. This helical structure is of the same type as that of die copper double helix, precursor of the knot. Besides, both compounds are aromatic and, thus, we could expect some potentially helpful stacking interactions [87],... 

A 180 ° twist would correspond to a Mobius strip which could form a single large ring a 540 ° twist would yield a trifold knot and 720 ° twist a double treaded catenane. 

Human hair is made of protofibrils, which are twisted bundles of the coiled protein alpha-keratin. Alpha-keratin is so strong and flexible that a human hair can be tied in a knot without breaking. 

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