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enter image description here

Asked to draw a quadrilateral with sides 3, 4, 5 and 6, one might create what's shown above, using the tools available in, say geogebra. A moment's reflection indicates that the requirement would be met if CD 'connected to' AD to make this a concave figure.

I have been searching for software that would enable its user to move BC and AC in such a way that remained attached to AB yet CD's length was a constant four.

Instrumenpoche seems a possibility; however, my French in poor. I would be willing to put in the effort if it appeared that it might be able to do this.

Incidentally, this is not a graphing problem, and I haven't been able to make geogebra do it.

Bill
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    The r/geogebra subreddit may be a better place for this question. It's the "official" community for help with the GeoGebra software. – Blue Jan 16 '24 at 20:42
  • Is something like this what you have in mind? I've set it so that C,D are fixed and the lengths of AB, BC, CD, AD remain fixed; this leaves one degree of freedom left which I've given to A. – Semiclassical Jan 16 '24 at 21:15
  • @Semiclassical: Thanks. Something like that, yes, except that the lengths of all four sides must be fixed. – Bill Jan 17 '24 at 18:04
  • @Bill the sides AB, BC, CD, AD do have fixed length in the above. (That said, I seem to have set them as 4,5,4,3 respectively. So AB should be 6 instead.) – Semiclassical Jan 17 '24 at 18:30
  • @Semiclassical: Something odd is happening: I have just visited the drawing once again; I can move vertex D so that the length of CD varies over a wide range. – Bill Jan 17 '24 at 18:38
  • I see what you mean. If you ignore that and focus on A instead it works fine, but that’s not ideal. In any case, though, there’s actually already Geogebra applets out there for four-bar linkages. See for instance: https://www.geogebra.org/m/BueCG9ch. (There’s a few others if that isn’t to your taste.) – Semiclassical Jan 17 '24 at 18:40
  • @Semiclassical: I'm glad you see what I mean! – Bill Jan 17 '24 at 18:43

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Somewhat like in this sketch?

enter image description here

Ignore the given circle through D.

Line or link CD including end points remains fixed in length while A and B move to positions A' and B' on circles (blue, yellow) with centers D,C respectively.

4-bar mechanism.

Narasimham
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  • Thank you, yes, this is what I mean. Can you suggest software that enables its user to animate this mechanism? – Bill Jan 17 '24 at 18:08
  • One can set up vectors along the 3 movable links. The shorter link AD rotates full 360 degrees, BC undergoes oscillations. The connecting rod AB has instantaneous rotation around intersection point of AD and BC. – Narasimham Jan 18 '24 at 21:06