What makes this design special is its use of two spur wheel differentials
(basics see here). The
carrier plate for the shafts of wheels 3 and 6 rotates freely around the
horizontal main shaft and is fixed to wheel 4. The carrier plate for wheels
9 and 10 is fixed to the chassis.
The basic equations are therefore:
(a:)
n2 * rot2 + n7 * rot7 -
(n2 + n7) * rot4 = 0
(b:)
n8 * rot8 + n11 * rot11
- (n8 + n11) * 0 = 0
(c:)
n4 * rot4 + n5 * rot5 = 0
The other constraints:
(d:)
rot1 = rot2
(e:)
rot7 = rot8
(f:)
rot11 = rot12
Composition (POV is from top respectively from far right):
To make it "south-pointing" requires, that if rot12 is held
0, rot7 has to be exactly one turn when wheel 1 of diameter
d1 covered one full circle (centre at wheel 12's contact to
the ground, radius equal to track width t):
(h:)
d1 * rot1 * PI = 2 * t * PI
(j:)
rot5 = 1
(k:)
rot12 = 0
(g=>)
rot1 = (-1) * ((n2 + n7) / n2)
* (n5 / n4)
(h=>)
d1 = 2 * t / | rot1 |
The same method can be applied to calculate the required size for wheel
12: If rot1 is held 0, rot7 has to be exactly one
turn when wheel 12 of diameter d12 covered one full circle (this
time centre at wheel 1's contact to the ground, radius equal to track width
t):
