From Knot Atlas
Thanks to our link with LinKnot, on Windows systems KnotTheory` accepts graphical knot input.
(For In see Setup)
As in the section Using the LinKnot package, the first step is to add LinKnot to the Mathematica search path. This path will likely be different on your computer.
Thus for example, the input line
pops a blank window on which a knot or a link can be drawn with mouse clicks. At first pass all crossings are drawn as "new over old", but a further click on any given crossing will flip it.
A right click followed by selecting "quit" will then determine the Gauss code of the knot or link just drawn and return it to Mathematica:
K is now perfectly usable within KnotTheory`: