According to the Encyclopedia of Pasta, there are hundreds of pasta shapes. At Smithsonian, Elizabeth Chu and D. Lawrence Tarazano of the US Patent Office look at relatively recent machinery to crank out the floury forms. From Smithsonian:
The various shapes can be categorized based on the means by which they are formed: by hand, rolled into sheets, or extruded. For each pasta making method, there have been a number of inventions to ease and mechanize the process.
Pastas formed by hand have been the most difficult to replicate by machine because of the complexity of the actions done by hand. Cavatelli, gnocchi and orecchiette, for example, are made by rolling pasta dough by hand into a long snake shape, cutting it into equal sized dough pieces, and dragging the dough to form a cup like shape. With cavatelli and gnocchi, the dough is dragged against a fork or grooved surface with a thumb to form a curled dough piece in the shape of a hot dog bun; the only real difference between the two is the dough. Gnocchi is made from a dough containing eggs, flour and cooked potatoes, whereas cavatelli are typically made from an eggless semolina wheat dough. Orecchiette, Italian for "little ear," are made by dragging the dough pieces against a flat surface using a small spatula or knife, followed by a little hand shaping to round it out.
Italian inventors Franco Annicchiarico and Adima Pilari, who received U.S. patent no. 4,822,271 on April 18, 1989 for "an improved machine for manufacturing short cut varieties of Italian pasta (orecchiette, etc.)," developed a machine for making these cupped pastas. Comprised of three units, this patented invention allows users to feed the machine with pasta mix that later extrudes into sticks of pasta. Those sticks are then "cut into cylindrical pellets," and finally, three rollers flatten, curl, rotate and form the pasta into a cup shape.
"The Patents Behind Pasta Shapes" (Smithsonian)