# Modelling a flexible strip

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## Modelling a flexible strip

 Does anybody here know how to model a flexible strip with rigidly held ends? I.e. the maths to generate the curve. It's a bit like modelling a catenary, but instead of being defined by gravity and tension, the main force is the strip trying to be straight and not bent.I crudely modelled the polypropylene strips I used in Mendel90 using arcs but I need a more accurate model for my new machine. _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: Modelling a flexible strip

 Administrator > On Dec 1, 2017, at 10:20 AM, nop head <[hidden email]> wrote: > > Does anybody here know how to model a flexible strip with rigidly held ends? I.e. the maths to generate the curve. It's a bit like modelling a catenary, but instead of being defined by gravity and tension, the main force is the strip trying to be straight and not bent. > This sounds very much like what Beziér curves were originally meant to be used for.  -Marius _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: Modelling a flexible strip

 Yes, a flexible strip was called a spline: https://en.wikipedia.org/wiki/Flat_splineOn 1 December 2017 at 10:45, Marius Kintel wrote:> On Dec 1, 2017, at 10:20 AM, nop head <[hidden email]> wrote: > > Does anybody here know how to model a flexible strip with rigidly held ends? I.e. the maths to generate the curve. It's a bit like modelling a catenary, but instead of being defined by gravity and tension, the main force is the strip trying to be straight and not bent. > This sounds very much like what Beziér curves were originally meant to be used for.  -Marius _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: Modelling a flexible strip

 you'd need something to constrain the total length of the sline thought wouldn't you? On 01/12/17 16:02, doug moen wrote: Yes, a flexible strip was called a spline: https://en.wikipedia.org/wiki/Flat_spline On 1 December 2017 at 10:45, Marius Kintel wrote: > On Dec 1, 2017, at 10:20 AM, nop head <[hidden email]> wrote: > > Does anybody here know how to model a flexible strip with rigidly held ends? I.e. the maths to generate the curve. It's a bit like modelling a catenary, but instead of being defined by gravity and tension, the main force is the strip trying to be straight and not bent. > This sounds very much like what Beziér curves were originally meant to be used for.  -Marius _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org ```_______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org ``` _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: Modelling a flexible strip

 Thanks for the pointers. I think what I need is a minimum energy spline with a fixed length.Playing with a Bezier spline using this tool https://www.desmos.com/calculator/cahqdxeshd , I get something that looks about right using four control points. The end points are obviously where my ends are. The next points in seem to define tangents to the curve at is ends. These can be on a line through the mounting plane. I.e. through the planes the ends are clamped to. To get the length correct I can move those two points equally away from the ends points until it is long enough. Since there seems to be no easy way to calculate the length of a Bezier curve I would need to compute it by recursive splitting the curve until it converges. Then do a search moving the two points.I have no idea if a Bezier spline is minimum energy or not.On 1 December 2017 at 16:49, Chris Camacho wrote: you'd need something to constrain the total length of the sline thought wouldn't you? On 01/12/17 16:02, doug moen wrote: Yes, a flexible strip was called a spline: https://en.wikipedia.org/wiki/Flat_spline On 1 December 2017 at 10:45, Marius Kintel wrote: > On Dec 1, 2017, at 10:20 AM, nop head <[hidden email]> wrote: > > Does anybody here know how to model a flexible strip with rigidly held ends? I.e. the maths to generate the curve. It's a bit like modelling a catenary, but instead of being defined by gravity and tension, the main force is the strip trying to be straight and not bent. > This sounds very much like what Beziér curves were originally meant to be used for.  -Marius _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org ```_______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org ``` _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: Modelling a flexible strip

 In reply to this post by nophead May be a lot more complex then the flat splines. See:2017-12-01 13:20 GMT-02:00 nop head :Does anybody here know how to model a flexible strip with rigidly held ends? I.e. the maths to generate the curve. It's a bit like modelling a catenary, but instead of being defined by gravity and tension, the main force is the strip trying to be straight and not bent.I crudely modelled the polypropylene strips I used in Mendel90 using arcs but I need a more accurate model for my new machine. _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: Modelling a flexible strip

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## Re: Modelling a flexible strip

 On 2017-12-05 23:01, nop head wrote: > Yes it is a bit tight, which is why I modelled it. The problem is it > needs to not hit the shelf below that covers the electronics. It only > cycles once per build so I think I will get away with it. I have used > ribbons on X and Y that move millions of times in a build. Nice video, although the cable deformation is somewhat unrealistic. If knowing the true shape was critical, it would require non-linear finite element analysis. Someone mentioned a catenary, but this cable is much stiffer than a catenary (essentially no bending stiffness). The problem is quite similar to analyzing flexible risers used on the offshore industry. Non-negligible bending stiffness, large deformations, boundary conditions at the ends. Still the simplified approximation was quite ok for a demo. Carsten Arnholm _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: Modelling a flexible strip

 Yes I suspect the bend radius would be a bit bigger in real life, closer to an arc. The cable is ribbon, so not stiff at all but I bend it around a 0.8mm thick polypropylene strip to distribute the bending. It is the strip I am trying to model. It works like a cable chain for ribbon but is a lot more compact and cheaper. Without it ribbon tends to bend too much at the attachment points.The model needs to predict the length to make the strip as that goes on the BOM. The length should be as long as possible without hitting the bottom as it would buckle if it did. Using Bezier my guess is it is a bit shorter than it could be. If it is not too much that will be OK but if it is grossly wrong then the strip is tighter than it needs to be so is not good for cable life.When I get home I will mock it up and see if it is accurate enough. If not I will try to work out a minimum energy solution using finite elements. It is after all drawn with 100 finite elements so I can easily calculate the bend at each joint. The tricky bit is moving the joints to minimise the energy.On 7 December 2017 at 10:31, wrote:On 2017-12-05 23:01, nop head wrote: Yes it is a bit tight, which is why I modelled it. The problem is it needs to not hit the shelf below that covers the electronics. It only cycles once per build so I think I will get away with it. I have used ribbons on X and Y that move millions of times in a build. Nice video, although the cable deformation is somewhat unrealistic. If knowing the true shape was critical, it would require non-linear finite element analysis. Someone mentioned a catenary, but this cable is much stiffer than a catenary (essentially no bending stiffness). The problem is quite similar to analyzing flexible risers used on the offshore industry. Non-negligible bending stiffness, large deformations, boundary conditions at the ends. Still the simplified approximation was quite ok for a demo. Carsten Arnholm _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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