Again Catenary

Hi all,

in this simple definition I started from a line, subdivided into X parts and thenI used it to generate a catenary.

How can I generate an interpolation curve between the particle output?

Another question (and most important): is there a way to have a spring without extensions, so to be rigid? For example if I start from a polyline with 10 equal segments, after the "relaxation" I find different values lenght; in this way my chain is not unflexible as for Hooke's law.

Thanks so much

Lio

Attachments:

Catena_03.3dm, 23 KB
Catena_03.ghx, 215 KB

Replies to This Discussion

Permalink Reply by Victor Leung on April 28, 2011 at 9:54am

First Question quick answer,

If you plug the subdivided points into the Geometry Input in correct order, you will get the geometry output which can be connected in correct sequence.

Second Question,

Not sure if a very high stiffness would do the job?

Because the small line segments is not restrained to bend, to it will still perform the catenary.

Cheers

Victor

Permalink Reply by Lio on May 2, 2011 at 4:04am

Hi Victor,

thanks for your reply but I can't figure out how to order the particles output so that the interpolation curve can work. Can you show me your suggestion?

Again I can't have rigid segment even if I put very high value of stiffness: is there any chance to have indeformable lines?

Last geometrical question: between two points pass infinte catenaries depending of their lenght; if I revolve this infinity of catenary along an horizontal axes, I obtain a catenoid.

Which one among this infinity, generates the minimal area surface (which is also a minimal surface)?

Thanks again

Lio

Permalink Reply by Daniel Piker on May 2, 2011 at 5:00am

Regarding the rigid segments - if you make the stiffness high enough, you can get the lines to keep their length to whatever degree of precision you need.

The attached example shows Kangaroo hanging a chain while keeping the length of the segments identical to their original length to within a factor of 0.0000000001

You can keep increasing the stiffness even more if you like (you'll need to decrease the timestep proportionately, so the more accurate you go, the slower it will get). Eventually I guess you will run into floating point precision issues, but I can't imagine any practical reason why you'd ever need that level of accuracy.

That said, I am working on something to allow the user to more easily specify springs of effectively infinite stiffness and have it solve without having to do all this fiddling about with timesteps.

Attachments:

stiff_catenary.ghx, 197 KB

Permalink Reply by Lio on May 2, 2011 at 6:10am

Hi Daniel,

thanks very much for your reply. Changing also the timestep all it works perfectly, and the accuracy of 0.001 is more then enough!

Last question, do you know how (given two points) to select among the infinity of catenaries passing through them, the catenary which will create the catenoid with minimal area?

Thanks again

Lio

Permalink Reply by Lio on May 19, 2011 at 4:50am

In this little example I made a comparison between a real catenary (measured) and the simulation in Kangaroo, and the result is very impressive.

I would like to make some comparisons like this also with minimal surfaces and I would like to use soap films models like Frei Otto did. Do you know any book that describes his workflow?

Bye

Lio

Attachments: