The basic design has one mechanical weakness:
The spider of the differential makes a solid axle impossible, therefore two
halfaxles must be used.
So Gérard Winkelmuller.went back to the
drawing bord and came up with this construction. The differential moves
down to a place between the two horizontal gear wheels, which now can be
made "compounds" (two tooth circles per wheel).
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):
