http://www.chem.iupui.edu/Research/Robertson/Robertson.html
that includes movies of two buckminsterfullerine gears meshing with
each other. It is easy to recreate these gears with Fungimol.
That paper does not give a machine-readable file describing the structure of the gears, but it does give a recipe:
The paper also gives a formula that relates the number of pentagons, septagons, and octagons that can appear in a closed buckminsterfullerine figure:
pentagons = septagons + 2 * octagons + 12This formula is a consequence of the standard formula for closed polygon meshes
vertices + faces = edges + 2and the fact that buckminsterfullerine figures have three faces coinciding at each vertex and two faces coinciding at each edge.
The formula is also intuitively plausible. A dodecahedron has 12 pentagonal faces, so in the absence of septagons or octagons the constant "12" in the formula is not surprising. A mesh of hexagons is flat, so it is plausible to expect the number of hexagons to be absent from the formula. If pentagons cause a figure to close and hexagons are flat, it is plausible that septagons will have the opposite effect from pentagons and octagons even more so.
We have six teeth, so the recipe with one shaft gives a total of 24 pentagons and 6 octagons on the gear, and 6 septagons and 6 pentagons on the shaft. 24 + 6 = 6 + 2 * 6 + 12, so the recipe is consistent with the formula.
So let's get started by making a tooth. Make an empty scene, and be sure that Fungimol is in a mode to create carbon DesignAtoms and that time is started. Press "6" to get a hexagon. We'll be adding four pentagons around this. We want to space them evenly, two on each side, so select two opposite carbons in the hexagon:
Press "5" to get the four pentagons, then press "6" until the figure has 56 carbons. (You can count the number of atoms in a figure by selecting it, positioning the mouse over the background, and pressing "/".) Viewing it from an angle, it looks like this:![]()
Note the four-atom notch at the bottom of this figure. We will be joining two of these teeth to form an octagon, so it is natural to make the octagon by linking together two of the four-atom notches. To do this, stop time, make two copies of the tooth (saving the original off to the side just in case things go wrong later), and orient them with the four-atom notches next to each other. In this picture I've selected the four atoms that we'll be linking next:
Now form the octagon by linking these four atoms pairwise, and start time:![]()
Stop time and make three copies of this figure. Set the original aside just in case things go wrong later, and arrange the three copies so the teeth form a hexagon:![]()
Add 12 links to link these together with three octagons, and start time so it pulls together:![]()
Now select the whole figure and repeatedly press "6" until it closes. If you linked the teeth together correctly you'll get something like this:![]()
Now we can add the shaft. Select the middle six carbons in the front of the figure:![]()
and press control-x until the hole is the size of the shaft you want. Three times seems about right. Then select an atom in each of the notches at the corner of the hexagonal hole:![]()
Press "7" to put six septagons there. Now you can press "6" as many times as you like to make the shaft as long as you like, except you'll have to turn the figure sideways and periodically drag the new atoms away from the gear to ensure that the shaft grows away from the gear instead of growing inward. In the picture below I had to drag left with right-mouse to prevent ingrowth:![]()
Now we can close the shaft. We have to add six evenly-spaced pentagons around the perimeter. Zoom on the end of the shaft, select an atom so you don't lose track, and count the number of atoms at the end. I get 12; the answer must be a multiple of 6:![]()
Divide the number of atoms of the perimeter by 6, giving 2 in this case. Thus I should select the atom in every second notch at the end:![]()
Now press "5", then select the entire figure and press "6" until it closes. Now we are done:![]()
I have saved this figure in![]()
gear.pdb
.