Type "Chaves"type chaves

This design has its single differential on a horizontal shaft. Although some effort is then needed to get the output to a vertical pointer shaft, the result has an exceptional low profile. Note that idler wheel 3 is needed to facilitate the difference function of the differential. The adapted equations:
(a:) n5 * rot5 + n9 * rot9 - (n5 + n9) * rot11 = 0
(b:) n2 * rot2 - n4 * rot4 = 0
(c:) n7 * rot7 + n8 * rot8 = 0
(d:) n11 * rot11 + n12 * rot12 = 0
(e:) n13 * rot13 - n14 * rot14 = 0
 The remaining constraints:
(f:) rot1 = rot2
(g:) rot4 = rot5
(h:) rot6 = rot7
(i:) rot8 = rot9
(j:) rot12 = rot13
Composition (POV is from top respectively from far right):
(f=>) rot1 = rot2
(b=>)    = (n4 / n2) * rot4
(g=>)    = (n4 / n2) * rot5
(h=>) rot6 = rot7
(c=>)    = (-1) * (n8 / n7) * rot8
(i=>)    = (-1) * (n8 / n7) * rot9
(e=>) rot14 = (n13 / n14) * rot13
(j=>)    = (n13 / n14) * rot12
(d=>)    = (-1) * (n13 / n14) * (n11 / n12) * rot11
(a=>k:) n5 * (n2 / n4) * rot1 - n9 * (n7 / n8)* rot6 + (n5 + n9) * (n14 / n13) * (n12 / n11) * rot14 = 0
To make it "south-pointing" requires, that if rot6 is held 0, rot14 has to be exactly one turn when wheel 1 of diameter d1 covered one full circle (centre at wheel 6's contact to the ground, radius equal to track width t):
(l:) d1 * rot1 * PI = 2 * t * PI
(m:) rot14 = 1
(n:) rot6 = 0
(k=>) n5 * (n2 / n4) * rot1 - n9 * (n7 / n8) * 0 + (n5 + n9) * (n14 / n13) * (n12 / n11) * 1 = 0
rot1 = (-1) * (n4 / n2) * (n14 / n13) * (n12 / n11) * (n5 + n9) / n5
(l=>) d1 = 2 * t / | rot1 |
The same method can be applied to calculate the required size for wheel 6: If rot1 is held 0, rot14 has to be exactly one turn when wheel 6 of diameter d6 covered one full circle (this time centre at wheel 1's contact to the ground, radius equal to track width t):
(o:) d6 * rot6 * PI = 2 * t * PI
(p:) rot1 = 0
(k=>) n5 * (n2 / n4) * 0 - n9 * (n7 / n8) * rot6 + (n5 + n9) * (n14 / n13) * (n12 / n11) * 1 = 0
rot6 = (n8 / n7) * (n14 / n13) * (n12 / n11) * (n5 + n9) / n9
(o=>) d6 = 2 * t / rot6

Given Parameters (Your choice !)

Reference
 Size Description
2
 n2 = [teeth] Spur wheel, fixed to wheel 1
3
 n3 = [teeth] Spur wheel, idler, freerunning on its own shaft
4
 n4 = [teeth] Spur wheel, freerunning on main shaft
5
 n6 = [teeth] Bevel gear, fixed to wheel 4
7
 n7 = [teeth] Spur wheel, fixed to wheel 6
8
 n8 = [teeth] Spur wheel, freerunning on main shaft
9
 n9 = [teeth] Bevel gear, fixed to wheel 8
10
 n10 = [teeth] Bevel gear, freerunning on shaft, which in turn is fixed to horizontal main shaft
11
 n11 = [teeth] Spur wheel, fixed to main shaft
12
 n12 = [teeth] Spur wheel, fixed to auxiliary shaft
13
 n13 = [teeth] Bevel gear, fixed to auxiliary shaft
14
 n14 = [teeth] Bevel gear, fixed to vertical pointer shaft
T
 t = [length units] Track width

Derived Parameters

Reference
 Size Description
1
 d1 = [units of t] Roadwheel, freerunning on axle
6
 d6 = [units of t] Roadwheel, freerunning on axle
© odts 2001