The basic design is a little "ugly" as one road wheel
has a very large gear (9) attached to it. Gérard Winkelmuller's next
variant solves this by making wheel 8 like pot, contacting wheel 9 with its rim
but containing the differential inside with wheel 7 fixed to its bottom.
The adapted equation reads
(a:)
n7 * rot7 + n4 *
rot4 - (n7 + n4) * rot6
= 0
The other constraints are straight forward:
(b:)
rot1 = rot2
(c:)
n2 * rot2 + n3 * rot3
= 0
(d:)
rot3 = rot4
(e:)
rot7 = rot8
(f:)
n8 * rot8 + n9 * rot9
= 0
(g:)
rot9 = rot10
Composition (POV is from top respectively from far right):
(j:)
(d=>)
rot4 = rot3
(c=>)
= (-1) * (n2 / n3) * rot2
(b=>)
= (-1) * (n2 / n3) * rot1
(k:)
(e=>)
rot7 = rot8
(f=>)
= (-1) * (n9 / n8) * rot9
(g=>)
= (-1) * (n9 / n8) * rot10
To make it "south-pointing" requires, that if rot10 is held
0, rot6 has to be exactly one turn when wheel 1 of diameter
d1 covered one full circle (centre at wheel 10's contact to
the ground, radius equal to track width t):
(l:)
d1 * rot1 * PI = 2 * t * PI
(m:)
rot6 = 1
(n:)
rot10 = 0
(k=>)
rot7 = 0
(a=>)
n7 * 0 + n4 * rot4 -
(n7 + n4) * 1 = 0
(=>o:)
rot4 = (n7 + n4) /
n4
(j=>)
rot1 = (-1) * (n3 / n2) *
(n7 + n4) / n4
(l=>)
| d1 | = 2 * t * (n2 / n3) *
(n4 / (n7 + n4))
The same method can be applied to calculate the required size for wheel
10: If rot1 is held 0, rot6 has to be exactly one
turn when wheel 10 of diameter d10 covered one full circle
(this
time centre at wheel 1's contact to the ground, radius equal to track
width
t):
