Aha! Yes, your function seems much more useful. I would call yours a "tesselation_hinge" since it tessellates the child object. I can think more about how to make yours a little more general. > One more comment: I don't think it is a good idea to crop the shape to > constrain it to a rectangle [length, width]. The bounding boxes of shape1 > of my code overlaps each other along a row. > If you ar talking about the cropping of my hinge to the outline of the circle: While I obviously misunderstood what you were asking for, that is one reason I thought (what I thought was) your proposal was a little odd. However, I found that while the hinges at the edges do get cut off, causing edge effects, this can be fixed by increasing the "hinges_across_length". If for some reason this makes the hinge too rigid, then "d" can be decreased. On Fri, Aug 26, 2016 at 11:22 AM, Ronaldo Persiano <rcmpersiano@gmail.com> wrote: > One more comment: I don't think it is a good idea to crop the shape to > constrain it to a rectangle [length, width]. The bounding boxes of shape1 > of my code overlaps each other along a row. > > > > _______________________________________________ > OpenSCAD mailing list > Discuss@lists.openscad.org > http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org > >

I meant it is not a good idea to crop the children inside the hinge module. It would be users responsibility to define cutting shapes that produce sensible results. 2016-08-26 12:35 GMT-03:00 Ari Diacou <ari.diacou@gmail.com>: > > If you ar talking about the cropping of my hinge to the outline of the > circle: While I obviously misunderstood what you were asking for, that is > one reason I thought (what I thought was) your proposal was a little odd. > However, I found that while the hinges at the edges do get cut off, causing > edge effects, this can be fixed by increasing the "hinges_across_length". > If for some reason this makes the hinge too rigid, then "d" can be > decreased. >

You guys might want to look at a technology called “Industrial Origami” Just my $0.02, Jean-Paul N1JPL > On Aug 26, 2016, at 12:51 PM, Ronaldo Persiano <rcmpersiano@gmail.com> wrote: > > I meant it is not a good idea to crop the children inside the hinge module. It would be users responsibility to define cutting shapes that produce sensible results. > > 2016-08-26 12:35 GMT-03:00 Ari Diacou <ari.diacou@gmail.com>: > > If you ar talking about the cropping of my hinge to the outline of the circle: While I obviously misunderstood what you were asking for, that is one reason I thought (what I thought was) your proposal was a little odd. However, I found that while the hinges at the edges do get cut off, causing edge effects, this can be fixed by increasing the "hinges_across_length". If for some reason this makes the hinge too rigid, then "d" can be decreased. > > > _______________________________________________ > OpenSCAD mailing list > Discuss@lists.openscad.org > http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org

Okay, last one ( I think). I have implemented Ronaldo's suggestion to have a tessellation module that acts on a child object. It can be found at http://www.thingiverse.com/thing:1745322 or below: //Living Hinge //Ari M Diacou //Metis Industries //August 2016 //Thanks to Ronaldo Persiano for the inspiration for add_hinge() and tesselation_hinge() ////Uncomment lines to see Examples (all flat for DXF exporting) ///////////////////////////// Hinge() /////////////////////////////////////// //hinge(); //hinge(d=6); //hinge(length=20, size[0]=39,d=6,hinge_length=2.5,hinges_across_length=2,minimum_thinness=3); //hinge(length=30, size[0]=20,d=2,hinge_length=2.5,hinges_across_length=2,minimum_thinness=3,center=true); //hinge(length=20, size[0]=40,d=3,hinge_length=4,hinges_across_length=0,minimum_thinness=1); //linear_extrude(height=5) hinge(length=20, size[0]=40,d=6,hinge_length=2.5,hinges_across_length=2,minimum_thinness=3); //////////////////////////// Add_Hinge() //////////////////////////////////// //add_hinge(size[0]=20,length=size[1],center=true) square([3*size[1],size[1]-1],center=true); //add_hinge(size[0]=20,length=90) translate([5,0]) circle(d=90); //add_hinge(size[0]=30,length=90,hinges_across_length=3) circle(d=90); //add_hinge(size[0]=30,length=90,hinges_across_length=3,center=false) circle(d=90); //add_hinge(size[0]=30,length=90,hinges_across_length=3,minimum_thinness=.1) circle(d=90); //////////////////////////// Tesselate() //////////////////////////////////// //tesselate(num=[3,6], size=[3,2],padding=[.1,.1],type="hex") rotate(30) circle($fn=6); //tesselate(num=[3,6], size=[2,1],padding=[.4,.1],type="tri") translate([-.1,-.1]) text("T",valign="center",halign="center"); //tesselate(num=[6,6], size=[2,.7071],padding=[0.01,.01],type="tri") translate([0,.25]) rotate(30) circle($fn=3); //tesselate(num=[8,6], size=[2,1],padding=[.6,.1],type="tri") translate([-.1,-.1]) rotate(25) text("y",valign="center",halign="center"); //tesselate(num=[6,8], size=[1.5,1],padding=[.6,.1],type="hex") translate([-.1,-.1]) text("+",valign="center",halign="center"); //////////////////////// Tesselation_Hinge() //////////////////////////////// tesselation_hinge(num=[6,8], size=[9,6],padding=[.6,.1],type="hex") translate([-.1,-.1]) text("+",valign="center",halign="center"); //tesselation_hinge(size=[4,5],num=[3,6],padding=[.1,.4],type="hex") translate([-.8,-.5])square(); //running bond bricks //tesselation_hinge(size=[4,5],num=[4,5],padding=[.1,.1],type="tri") translate([0,.28])rotate(30) circle($fn=3); //tesselation_hinge(size=[4,5],num=[4,5],padding=[.7,.1],type="tri") translate([-.1,-.1]) rotate(5) text("t",valign="center",halign="center"); //tesselation_hinge(num=[3,6], size=[3,6],padding=[.4,.1],type="tri") translate([-.1,-.1]) text("T",valign="center",halign="center"); //tesselation_hinge(size=[6,6],num=[6,6],padding=[.2,.2],type="hex") rotate(30) circle($fn=6); /////////////////////////////// Functions ///////////////////////////////////// module hinge(size=[20,30],d=3,minimum_thinness=3,hinge_length=3,hinges_across_length=2,center=false){ //size[1] = the y dimension of the hinge, parallel to the laser cuts //size[0] = the x dimension of the hinge, transverse to laser cuts //d=the distance between parallel laser cuts //What is the minimum distance that two parallel lines can be apart before the laser does something catastrophic? E.g. setting uncontrollable fire to the work piece. This is "minimum_thinness" //hinge_length=the distance between 2 colinear laser cuts //hinges_across_length=the number of hinges across the size[1] of the hinge //center is a boolean value, if true, place the center of the rectangle at the origin, if false, put the bottom left corner at the origin (just like square() and cube()) ep=.00101;//epsilon, a small number,=1.01 micron, a hack (for OpenSCAD 2015.03) used to make square()'s which look like lines (which OpenSCAD doesn't support). Hopefully, your laser has a function which says something like "ignore cuts less than THRESHOLD apart", set that to anything greater than ep. adjust=center?-[size[0],size[1]]/2:[0,0];//a vector for adjusting the center position th=d/2<minimum_thinness?ep:d/2;//If the distance between lines is less than the minimum thickness, just make linear cuts, specifically, set the size[0]=th=thickness of the squares to ep, which is just above 1 micron (for 1=1mm slicers) n=floor(size[0]/d); m=floor(abs(hinges_across_length)); echo(str("Number of hinges (m)=",m)); //input cleaning, ensures m ϵ {non-negative integers} echo(str("Suggested filename: Living Hinge-",size[1],"x",size[0],"mm-h=",m,"x",hinge_length,"-th=",th)); echo(str("The distance between parallel laser cuts (d) is: ",d," mm.")); //the size[1] of the short lines short=(size[1]-m*hinge_length)/(m+1); //the size[1] of the long lines long=(size[1]-(m+1)*hinge_length)/(m); echo(str("There should be n=",n," links in the hinge.")); translate(adjust) difference(){ square([size[0],size[1]],center=false); if(m==0) //In the special case where |hinges_across_length|<1, the hinge should look like: // | --------------------------------------| // |-------------------------------------- | // | --------------------------------------| // |-------------------------------------- | for(i=[0:n]) translate([i*d,(pow(-1,i))*hinge_length]) // (-1)^i,{iϵZ} = {-1,+1,-1,+1,...} square([th,size[1]]); else //A hinge with hinges_across_length=2 should look like: // |------------ ------------ ------------| // | ----------------- ----------------- | // |------------ ------------ ------------| // | ----------------- ----------------- | for(i=[0:n]){ //Iterating across x translate([i*d*1,0]){ //Do the x translation seperate from the y translations if(i%2==1) //For odd columns for(j=[0:m-1]){ translate([0,hinge_length+j*(long+hinge_length)]) square([th,long]); } if(i%2==0) //For even columns for(j=[0:m]){ translate([0,j*(short+hinge_length)]) square([th,short]); } } } } } module add_hinge(size=[20,30],d=3,minimum_thinness=3,hinge_length=3,hinges_across_length=2,center=true){ //add_hinge() modifies another 2D object, by adding a hinge which is centered on the origin (by default, this can be changed to false, so that the bottom left corner of the hinge is at the origin. It uses the same parameters as hinge(). //First, difference() a rectangle the size of the hinge from the child object (makes a hole for the hinge //Second, union() a hinge with First (puts the hinge in the hole) //Third, intersection() the child object with Second (cuts off any extra hinge that sticks out past the child object) intersection(){ children(); union(){ hinge(size=size,d=d,minimum_thinness=minimum_thinness,hinge_length=hinge_length,hinges_across_length=hinges_across_length,center=center); difference(){ children(); square([size[0],size[1]],center=center); } } } } module tesselate(num=[1,1],size=[1,1],padding=[0,0],type="square"){ //Tesselate acts on a child object, and tesselates it, in a sqaure, triagular or hexagonal array. //num is [the number of objects in x, the number of objects in y] //size is [the size of each "cell" in x, the size of each "cell" in y] //padding is how much should be subtracted from the "cell" size to get the object size. This is absolute, not proportional, i.e. padding of .1 means each object is 0.1mm smaller than the cell, not 10% or 90% the size of the cell. //type is the type of array. There are exactly 3 types of regular polyhedron tesselations, square (normal graph paper), hexagonal (hex tiles, e.g. Civilization 5, or bricks in "running bond"), and triangular (this particular code uses a 180 degree rotation in z instead of a reflection in the xz-plane index = (type=="h"||type=="hex"||type=="hexagon"||type=="hexagonal") ? 1 : (type=="t"||type=="tri"||type=="triangle"||type=="triangular") ? 2 : 0;//index converts the text of type into a numbered index. I didn't want to slow down computation time by having if statements or conditionals, so I calculate transforamtions for all 3, make an array of them, and then use index to pick the appropriate one. sq=[[1,0],[0,1]]; hex=[[1,0],[.5,.75]]; tri=[[.5,0],[0,1]]; //These are the unit vectors for each of the array types. Map=[sq,hex,tri][index]; for(j=[0:num[1]-1]) //Iterate in y for(i=[0:num[0]-1]){ //Iterate in x translation=[(i+.5)*Map[0]*size[0]+(j+.5)*Map[1]*size[1],[(i+.5)*(size[0]*Map[0][0])+Map[1][0]*size[0]*(j%2),(j+.5)*(size[1]*Map[1][1])],(i+.5)*Map[0]*size[0]+(j+.5)*Map[1]*size[1]][index]; //What is the vector that describes the position of each object in the array? rot=[0,0,180*((i+j)%2)][index]; //Only triangular arrays need a rotation translate(translation) rotate(rot) resize(size-padding) children(); } } module tesselation_hinge(num=[1,1],size=[1,1],padding=[0,0],type="square"){ //Tesselation hinge takes the difference of a square(size) and a tesselate(). //size as used in this function is the size of the hinge, not the size of each object (like in tesselate()) the size of the objects are dynamically adjusted based on num and padding, and of course, the size of the hinge. //num, padding and type have all the same meanings as they do in tesselate(). index = (type=="h"||type=="hex"||type=="hexagon"||type=="hexagonal") ? 1 : (type=="t"||type=="tri"||type=="triangle"||type=="triangular") ? 2 : 0; sq=[[1,0],[0,1]]; hex=[[1,0],[.5,.75]]; tri=[[.5,0],[0,1]]; Map=[sq,hex,tri][index]; //These parameters need to be re-declared because when calling tesselate(), the size of each object needs to be recalculated based on the size of each cell. These parameters must be the same in both functions. difference(){ square(size); tesselate(num=num,size=[size[0]/num[0]/Map[0][0],size[1]/num[1]/Map[1][1]],padding=padding,type=type) children(); } } On Fri, Aug 26, 2016 at 12:51 PM, Ronaldo Persiano <rcmpersiano@gmail.com> wrote: > I meant it is not a good idea to crop the children inside the hinge > module. It would be users responsibility to define cutting shapes that > produce sensible results. > > 2016-08-26 12:35 GMT-03:00 Ari Diacou <ari.diacou@gmail.com>: > >> >> If you ar talking about the cropping of my hinge to the outline of the >> circle: While I obviously misunderstood what you were asking for, that is >> one reason I thought (what I thought was) your proposal was a little odd. >> However, I found that while the hinges at the edges do get cut off, causing >> edge effects, this can be fixed by increasing the "hinges_across_length". >> If for some reason this makes the hinge too rigid, then "d" can be >> decreased. >> > > > > _______________________________________________ > OpenSCAD mailing list > Discuss@lists.openscad.org > http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org > >

Nice work, Ari! And very well documented. I have been caught by your hinge question. So, I could not wait your solution and have written mine own. Comparing it with yours I realized that we have used different tiling (or tesselation) approaches. <http://forum.openscad.org/file/n18295/Hinge_tiling.png> That is my code where I included the above patterns, four of them I found at ponoko site and two I designed myself. Hope you like it: living_hinges2.scad <http://forum.openscad.org/file/n18295/living_hinges2.scad> As you can see, I don't make any change to the patterns (children()) except translation to the tilling position and flipping. The tile dimensions, arguments of hinge module, may be different from the pattern dimensions so they are able to overlap like in the "diamonds" above. I think that the standard hinge pattern (the one you use in your hinge module) is probably the more adequate to the function. Other patterns may have some value, like diamonds and bowling pins. The others have more decorative appeal but they seem to be either fragile or less flexible for a living hinge. I don't have a laser cutting service nearby to try them. Any way, it was fun to play with them. -- View this message in context: http://forum.openscad.org/Living-Hinges-tp18217p18295.html Sent from the OpenSCAD mailing list archive at Nabble.com.

Has this been tried with printed plastic? ----- Admin - PM me if you need anything, or if I've done something stupid... Unless specifically shown otherwise above, my contribution is in the Public Domain; to the extent possible under law, I have waived all copyright and related or neighbouring rights to this work. Obviously inclusion of works of previous authors is not included in the above. The TPP is no simple “trade agreement.” Fight it! http://www.ourfairdeal.org/ time is running out! -- View this message in context: http://forum.openscad.org/Living-Hinges-tp18217p18301.html Sent from the OpenSCAD mailing list archive at Nabble.com.

         - Michele

On 09-01-2016 11:29 PM, MichaelAtOz wrote: > Has this been tried with printed plastic? > > What, living hinges? Yes, I print them in polypropylene. They work just as well as commercial ones. - Michele

nice work. I found one hinge design that flexes in both directions. Only example I found. its here: http://lab.kofaktor.hr/en/portfolio/super-flexible-laser-cut-plywood/ -- View this message in context: http://forum.openscad.org/Living-Hinges-tp18217p18303.html Sent from the OpenSCAD mailing list archive at Nabble.com.

Great design, Neon22! I was looking for something like that. Thank you. At a first look of that design, I saw lots of interlocked swastikas. After that it reminded me the Hilbert curve. I coded the pattern for the design and found the hinge() parameters to reproduce it: <http://forum.openscad.org/file/n18313/koFACTORlab_flex.png> > module koFACTORlab_flex(a=20,b,kerf=0.5) { > c = b==undef ? a : b/2; > p = [[-1,2],[-1,4],[1,4],[1,0],[-3,0], > [-3,-4],[1,-4],[1,-2],[-1,-2] > ]*[[a,0],[0,c]]/5; > q = [[0,3],[0,1],[-2,1],[-2,5],[2,5], > [2,9],[-2,9],[-2,7],[0,7] > ]*[[a,0],[0,c]]/5; > for(i=[1:len(p)-1]) line(p[i-1],p[i],kerf); > for(i=[1:len(q)-1]) line(q[i-1],q[i],kerf); > } > size = 20; // each square size > kerf = 0.5; > hinge(horRepeat=5, vertRepeat=3, patWidth=size, patHeight=2*size, > border=20, align=size) > translate([size/8,0]) koFACTORlab_flex(a=size,kerf=kerf); -- View this message in context: http://forum.openscad.org/Living-Hinges-tp18217p18313.html Sent from the OpenSCAD mailing list archive at Nabble.com.

This looking very good. Consider this pattern also if you like http://www.thingiverse.com/thing:304177 -- View this message in context: http://forum.openscad.org/Living-Hinges-tp18217p18333.html Sent from the OpenSCAD mailing list archive at Nabble.com.