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05-29-2014
10:53 AM

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05-29-2014
10:53 AM

Modelling a Reef Knot

Hello,

I have, unfortunately, a requirement to model a Reef Knot (or Square Knot, as you might know it) again.

In the past, I have made a couple of wiggly curves orthogonal to each other and intersected them and run a VSS along them to create each half loop. A few mirrors and you have a passable looking knot. It takes a lot of tweaking and fiddling to get it looking presentable, though. Then there was the added complication that I was required to model a Slip-Reef Knot - one with a loop on one side that you could pull to undo the knot, a bit like a shoelace.

Is there an equation (or equations) to define such a knot? The nice thing about the equation approach would be that it took less work to make it look good and it would also scale nicely. That way, it would be done once and for all and I wouldn't have to repeat all the tweaking every time.

I'm sure someone out there has sorted this out.

Currently using WF4, M220, but I would imagine the principle applies equally well to any version. Bear in mind that I won't be able to open your solutions created in Creo 2.0, though...

Cheers,

John

Solved! Go to Solution.

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05-30-2014
08:48 AM

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05-30-2014
08:48 AM

I made it.

X=.45*cos(t)+.25*cos(-t)-.45*cos(-3*t)

y=.45*sin(t)+.25*sin(-t)-.45*sin(-3*t)

z=0.2*sin(5*t)

11 REPLIES 11

05-29-2014
11:38 AM

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05-29-2014
11:38 AM

If anyone would have it, it would be http://mathworld.wolfram.com/SquareKnot.html

It doesn't look like anything useful for modeling, though the topology is OK.

05-29-2014
02:36 PM

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05-29-2014
02:36 PM

Fun problem. It should be just a matter of parameterizing the knot and plugging the equations into a datum curve by equation.

That being said, I have no idea how one might go about parameterizing a knot.

The guy who made this website does. He has parametric equations for a granny knot which is similar to a reef knot.

http://paulbourke.net/geometry/knots/

I plugged the following into a datum curve:

x = -22*cos(t) - 128*sin(t) - 44*cos(3*t) - 78*sin(3*t)

y = -10*cos(2*t) - 27*sin(2*t) + 38*cos(4*t) + 46*sin(4*t)

z = 70*cos(3*t) - 40*sin(3*t)

And with a sweep I got this:

Maybe you can tweak these equations to form a reef knot. I might work on this later.

05-29-2014
07:37 PM

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05-29-2014
07:37 PM

05-30-2014
08:48 AM

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05-30-2014
08:48 AM

I made it.

X=.45*cos(t)+.25*cos(-t)-.45*cos(-3*t)

y=.45*sin(t)+.25*sin(-t)-.45*sin(-3*t)

z=0.2*sin(5*t)

05-30-2014
11:22 AM

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05-30-2014
11:22 AM

Whoa, cool!

Done by "curve by equation" I take it?

05-30-2014
01:49 PM

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05-30-2014
01:49 PM

Frank, yes curve by equation.

It's not a big thing, I think I just had more successful google searching.

05-30-2014
03:00 PM

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05-30-2014
03:00 PM

Figured. I thought this would be cool to use for a coiled wire rope model.....

05-30-2014
04:06 PM

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05-30-2014
04:06 PM

yeah it would, hopefully someone will work on that, I dont really have the time at the moment.

05-30-2014
11:24 AM

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05-30-2014
11:24 AM

Nice work Matt!

05-29-2014
10:49 PM

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05-29-2014
10:49 PM

Search for "Instructional Knot Tying Animations (Blender)" and view in wonder.

No doubt it's not trivial work, but still amazing.

05-30-2014
03:49 AM

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05-30-2014
03:49 AM

Amazing, indeed.