Hi Derek and Dave,
I agree that it would be an excellent idea to get started - how about naming the parts, actions, chiral versions, etc., of a simple knot or hitch? A good friend of mine has been reading these posts (Hi Jimmy!) and he thought that an overhand knot would be a good start and I will throw in the half hitch as the next one - can we come up with some way of defining those structures?
My suggestion for the overhand knot, FWIW, is this:
Overhand Knot: A crossed and tucked turn in a line (CrTkTn) starting from either side of the line. When started with the turn on the right-hand side of the SPart, with the WEnd ending on the RH side of the line, the result is a RH/Cr/Tk/Tn. Similarly when starting on the LH side, the result is a LH/Cr/Tk/Tn. When tightened, hard to release. Acts as a stopper knot or terminal to a line to prevent fraying. Base for some decorative knots (list?). Also known as: (long list)
To clarify some terms, in a general section, applying to all knots (this needs to be MUCH larger!) we need something like this:
Orientation: All transitions, intersections, and actions are as seen from the knotter; X-axis positive away from Knotter; Y-axis positive towards knotter's head, Z-axis positive to right of knotter, starting at 0 at waist level or thereabouts; RH - on or toward the knotter's right side, LH - on or toward the knotter's left side.
SPart: The standing part of the line, about which the working end rotates or on which the working end does work; generally the part of a line that takes the load.
WEnd: The working end of the line, that part which moves in forming the knot.
Line: A flexible structure capable of supporting an undefined load other than its self-weight, manufactured from organic fibers or inorganic wire, fiber or crystalline material.
Tighten: The action of pulling the WEnd and/or the SPart of a line such that the structure closes on itself or on the object about which it is turned or tied.
Transition: The change seen after a line has been maneuvered into place.
Intersection: The meeting of a line or strands with another line or strands.
Action: Physical motion of part of the line (or loop?)
Turn: The transition of a line, along its own axis, through 360 degrees, beginning waist level, positive X and negative Y, with X-axis positive away from the knotter, Y-axis positive to the knotter's head.
Crossed: An intersection of two lines or parts of the same line, loop or other structure, such that the two parts are in contact but not passing one through the other.
Tuck/Tucked: The action of passing a line or loop over and under the same piece of line, so as to rotate the tucked part by 360 degrees around the X-axis using the Y-axis and Z-axis.
Tied/Tying: The action of maneuvering the parts of a knot so as to bring the parts together to form a functional object in the line.
Knot: A structure formed in line so as to perform a function, create a decorative object, join elements together or (?)
There is plenty still to do, perhaps too, a lot of simplification, but this may form a starting point - your thoughts?
SquareRigger