In this section we will find a suitable modification on a given linkage for achieving a desired movement. In other words, we will automatically discover geometry theorems by using GeoGebra ART.

Chebyshev's 4 bar linkage can be further improved to result in even better approximations of a straight line. For example, Roberts' mechanism yields such a result. In general it is also possible to do experiments with various bar lengths in a 4 bar linkage.

After some experiments it seems that by using a 4 bar linkage it is not possible to produce an exactly straight line.[br][br]Indeed, it can be [i]proven[/i], that 4 bars will never produce a straight line.[br][br]A possible approach is to use more bars. We may consider Peaucellier's cell which has 6 bars and does not produce a straight line in its first form, but is extensible to draw that.[br][br]Here we see the GeoGebra construction of the cell, and by using the command [b]LocusEquation[/b] again, it will be possible find to an extra bar, namely, the 7th one, to produce a straight line.

It is also possible to construct a new figure from scratch without [b]LocusEquation[/b], but finding an appropriate circle and constrain point C on it. In this case we can also use the [i]Relation Tool[/i] to check the perpendicularity of segments ON and NP. We leave the details of this final example to the reader. (You will need the desktop version of GeoGebra to make this experiment, because your browser will not have enough resources for the computations.)