Articulated quadrilaterals

Among the many connecting rod mechanisms that solve problems of a practical interest, the simplest is the articulated quadrilateral, which, because of its very simplicity and versatility, is the basis for many simple instruments that we see every day, some of which can be seen in the panel, from scales to Venetian blinds, to windscreen wipers, cranes, but also in some more sophisticated mechanisms like amputees' prostheses.

Four sides are the minimum to have a mobile mechanism. The triangle is a rigid,non-transformable figure, which because of this stability is used to build stable structures, such as towers, bridges and roofs. On the contrary, a square maintains a certain freedom of movement even when one fixes one if its sides, a freedom which makes it a very effective instrument to draw curves, or if you prefer, to have a piece move along a predetermined path.

Normally one of the sides of the quadrilateral is fixed, e.g. to the table, and remains immobile: thus it is possible to avoid putting it in, and just like in Watt's mechanism, the quadrilateral is reduced to three interconnected rods, of which the first and last are fixed to the table by one extremity, around which they can only rotate. Notwithstanding the extreme simplicity of the mechanism, articulated quadrilaterals are very versatile, and they have numerous applications. In particular, they are very useful to convert oscillatory movements in circular ones and viceversa, as it happens e.g. in a bicycle, where the alternated movement of the cyclist's legs generates the pedals' circular motion, or in the sewing machine, where the pedal's oscillating movement makes the machine's wheel spin.

If then you add two more rods to the quadrilateral, creating a triangle with the middle one, it is possible to draw a great many curves, even rather irregular ones, by properly adjusting the length of the added rods. In the machine shown, the additional rods are substituted with a sheet of Plexiglass, whose holes correspond to the vertices of the added triangle. Depending on the position of the hole, the mechanism describes curves, even very different ones.