Type "Denny"type denny

This design from the Meccano domain is very similar to the basic "Lanchester" type. What makes it special is the inverse sense of rotation of the differential's runner - caused by the direct path from road wheel 13 to differential gear 10. Consequence is the reversal through wheel 8 to platform 9. As usual the adapted equations:
(a:) n6 * rot6 + n10 * rot10 - (n6 + n10) * rot8 = 0
(b:) n8 * rot8 + n9 * rot9 = 0
(c:) n2 * rot2 + n3 * rot3 = 0
(d:) n4 * rot4 + n5 * rot5 = 0
(e:) n11 * rot11 + n12 * rot12 = 0
 The remaining constraints:
(f:) rot1 = rot2
(g:) rot3 = rot4
(h:) rot5 = rot6
(i:) rot10 = rot11
(j:) rot12 = rot13
Composition (POV is from top respectively from far right):
(f=>) rot1 = rot2
(c=>)    = (-1) * (n3 / n2) * rot3
(g=>)    = (-1) * (n3 / n2) * rot4
(d=>)    = (n3 / n2) * (n5 / n4) * rot5
(h=>)    = (n3 / n2) * (n5 / n4) * rot6
(j=>) rot13 = rot12
(e=>)    = (-1) * (n11 / n12) * rot11
(i=>)    = (-1) * (n11 / n12) * rot10
(b=>) rot8 = (-1) * (n9 / n8) * rot9
(k:) n6 * (n2 / n3) * (n4 / n5) * rot1 - n10 * (n12 / n11) * rot13 + (n6 + n10) * (n9 / n8) * rot9 = 0
To make it "south-pointing" requires, that if rot13 is held 0, rot9 has to be exactly one turn when wheel 1 of diameter d1 covered one full circle (centre at wheel 13's contact to the ground, radius equal to track width t):
(l:) d1 * rot1 * PI = 2 * t * PI
(m:) rot9 = 1
(n:) rot13 = 0
(k=>) n6 * (n2 / n3) * (n4 / n5) * rot1 + (n6 + n10) * (n9 / n8) = 0
rot1 = (-1) * (n6 + n10) * (n9 / n8) * (n3 / n2) * (n5 / n4) / n6
(l=>) d1 = 2 * t / | rot1 |
The same method can be applied to calculate the required size for wheel 13: If rot1 is held 0, rot9 has to be exactly one turn when wheel 13 of diameter d13 covered one full circle (this time centre at wheel 1's contact to the ground, radius equal to track width t):
(p:) d13 * rot13 * PI = 2 * t * PI
(q:) rot1 = 0
(k=>) (-1) * n10 * (n12 / n11) * rot13 + (n6 + n10) * (n9 / n8) = 0
rot13 = (n6 + n10) * (n9 / n8) * (n11 / n12) / n10
(p=>) d13 = 2 * t / rot13

Given Parameters (Your choice !)

Reference
 Size Description
2
 n2 = [teeth] Bevel gear, fixed to wheel 1
3
 n3 = [teeth] Bevel gear, fixed to vertical shaft
4
 n4 = [teeth] Spur gear, fixed to vertical shaft
5
 n5 = [teeth] Spur gear, freerunning on central vertical shaft
6
 n6 = [teeth] Bevel gear, fixed to wheel 5
7
 n7 = [teeth] Bevel gear, freerunning on short shaft, which in turn is fixed to central vertical shaft
8
 n8 = [teeth] Spur gear, fixed to central vertical shaft
9
 n9 = [teeth] Spur gear, fixed to pointerl shaft, 
10
 n10 = [teeth] Bevel gear, freerunning on vertical shaft
11
 n11 = [teeth] Bevel gear, fixed to wheel 10
12
 n12 = [teeth] Bevel gear, fixed to wheel 13
T
 t = [length units] Track width

Derived Parameters

Reference
 Size Description
1
 d1 = [units of t] Roadwheel, freerunning on axle
13
 d13 = [units of t] Roadwheel, freerunning on axle
© odts 2001