Nina del Ser - Mathematics
octopus |
19
Extra arms for the Octopus
Now that we have to some extent understood the mechanism for an Octopus with two sets of rotors we can
start to experiment with adding another set of miniature arms at the ends of the secondary rotors. The new
“Dodecapus” ride will look a bit like a fractal version of the Octopus:
1 metre
0.5 metres
S
0.25 metres
figure 52
Note that only one seat out of sixty four is shown so as not to crowd the illustration. The position vector for
seat S can be obtained using the same method as that explained in figure 2 and the accompanying text. Let us
set the angular velocity of the primary rotor to 1 rad/s (we can do this without in any way diminishing the
number of possible arrangements) and call the angular velocities of the secondary and tertiary rotors Ω and Γ
respectively. Although in figure 52 the lengths of the primary, secondary and tertiary rotors are set to 1, 0.5
and 0.25 m, these can be changed for more variety. Again, we will keep the length of the primary rotor fixed
at 1 m and call those of the secondary and tertiary rotors b and c respectively. The set of parametric equations
which describes the position of seat S is therefore:
r x cost b cos 1 Ω t c cos 1 Ω Γ t
r y sin t b sin 1 Ω t c cos 1 Ω Γ t
(11)
Below are some curves generated using these parametric equations (the values of b and c have been kept at 0.5
and 0.25 meters respectively):
123