Hart's A-frame revisited

After the CICM conference in Hagenberg, Austria, we had some fresh discussions with Chris Sangwin, one of the speakers of the didactics workshop. Chris was one of the most prominent persons who motivated my work last year on planar mechanical linkages, most importantly by his book How round is your circle?.
So, Chris gave me some feedback on a recent paper (which was written with my son, Benedek, together, by me), and he suggested improving the Lego model of Hart's A-frame in order to have full movement instead of just a 4 cm long one. He sent me some concrete plans as well, and finally I managed to build an improved version of the original Lego linkage. Now it produces a 7 cm long straight line. Luckily, this new version can also be built from the same set, the only extension is a new type of pen refill (an A2 type; other ballpoint standards may also be acceptable, but for the best result an A2 type should be used).

 

Note the non-linear motion that can be produced by flipping the linkage at one of its extents. GeoGebra can also find this non-linear component by computing the locus equation curve. If you have a fast enough computer, you can give it a try. Otherwise, you can see this screenshot only, but you can still have an impression:

The LocusEquation command in GeoGebra presents an algebraic output that is sometimes a "bit more" than the real locus should be. In the present case, after doing some further steps with Maple (namely, absolute factorization of the output), it turns out that the non-linear motion can be described with the algebraic equation x^4*y^2-16*x^3*y^2+(2*y^4-96*y^2+2304)x^2+(-16*y^4+1280*y^2-18432)x+y^6+160*y^4/9-2816*y^2+36864=0. (I leave this in the shown form to make it possible for the reader to copy and paste it into some mathematics tool, including GeoGebra.)
Absolute factorization is a nice thing. If you don't have access to Maple, you may still try Singular's absfact library.