Type "Hitachi"

This is essentially type ODTS II - invented independently in Japan, as it seems. Nevertheless I consider it worth an own calculation sheet, as the differential is built with discrete parts, adding some charm to it ;-)

As usual, the dimensioning equations:

(a:) rot₄ + rot₆ - 2 * rot₅ = 0

(b:) n₂ * rot₂ + n₃ * rot₃ = 0

(c:) n₇ * rot₇ + n₈ * rot₈ = 0

(d:) n₈ * rot₈ + n₉ * rot₉ = 0

(e:) n₅ * rot₅ - n₁₁ * rot₁₁ = 0

(f:) n₁₂ * rot₁₂ + n₁₃ * rot₁₃ = 0

The remaining constraints:

(g:) rot₁ = rot₂

(h:) rot₃ = rot₄

(i:) rot₆ = rot₇

(j:) rot₉ = rot₁₀

(k:) rot₁₁ = rot₁₂

Composition

(b,g,h=>) rot₄ = - (n₂ / n₃) * rot₁

(c,d,i,j=>) rot₆ = (n₉ / n₇) * rot₁₀

(e,f,k=>) rot₅ = -(n₁₁ / n₅) * (n₁₃ / n₁₂) * rot₁₃

(a=>l:) 2 * (n₁₁ / n₅) * (n₁₃ / n₁₂) * rot₁₃ = (n₂ / n₃) * rot₁ - (n₉ / n₇) * rot₁₀

To make it "south-pointing" requires, that if rot₁ is held 0, rot₁₃ has to be exactly one turn when wheel 10 of diameter d₁₀ covered one full circle (centre at wheel 1's contact to the ground, radius equal to track width t):

(m:) d₁₀ * rot₁₀ * PI = 2 * t * PI d₁ * rot₁ * PI = 2 * t * PI

(n:) rot₁ = 0 rot₁₀ = 0

(o:) rot₁₃ = -1 rot₁₃ = 1

(l=>) rot₁₀ = (n₇ / n₉) * (n₁₁ / n₅) * (n₁₃ / n₁₂) rot₁ = k * (n₃ / n₂) * (n₁₁ / n₅) * (n₁₃ / n₁₂)

(m=>) d₁₀ = 2 * t / rot₁₀ d₁ = 2 * t / rot₁

The same method can be applied to calculate the required size for wheel 1, see rightmost column of table above.

Reference	Size	Description
2	n₂ = [teeth]	Spur gear, fixed to wheel 1
3	n₃ = [teeth]	Spur gear, fixed to right differential shaft
5	n₅ = [teeth]	Bevel gear, fixed to rotor of differential
7	n₇ = [teeth]	Spur gear, fixed to left differential shaft
8	n₈ = [teeth]	Spur gear, Idler
9	n₉ = [teeth]	Spur gear, fixed to wheel 10
11	n₁₁ = [teeth]	Bevel gear
12	n₁₂ = [teeth]	Spur gear
13	n₁₃ = [teeth]	Spur gear, fixed to platform
T	t = [length units]	Track width

Reference	Size	Description
1	d₁ = [units of t]	Road wheel, free running on axle
10	d₁₀ = [units of t]	Road wheel, free running on axle

Type "Hitachi"

Given Parameters (Your choice !)

Derived Parameters

(a:)	rot₄ + rot₆ - 2 * rot₅ = 0
(b:)	n₂ * rot₂ + n₃ * rot₃ = 0
(c:)	n₇ * rot₇ + n₈ * rot₈ = 0
(d:)	n₈ * rot₈ + n₉ * rot₉ = 0
(e:)	n₅ * rot₅ - n₁₁ * rot₁₁ = 0
(f:)	n₁₂ * rot₁₂ + n₁₃ * rot₁₃ = 0

(g:)	rot₁ = rot₂
(h:)	rot₃ = rot₄
(i:)	rot₆ = rot₇
(j:)	rot₉ = rot₁₀
(k:)	rot₁₁ = rot₁₂

(b,g,h=>)	rot₄ = - (n₂ / n₃) * rot₁
(c,d,i,j=>)	rot₆ = (n₉ / n₇) * rot₁₀
(e,f,k=>)	rot₅ = -(n₁₁ / n₅) * (n₁₃ / n₁₂) * rot₁₃
(a=>l:)	2 * (n₁₁ / n₅) * (n₁₃ / n₁₂) * rot₁₃ = (n₂ / n₃) * rot₁ - (n₉ / n₇) * rot₁₀

(m:)	d₁₀ * rot₁₀ * PI = 2 * t * PI	d₁ * rot₁ * PI = 2 * t * PI
(n:)	rot₁ = 0	rot₁₀ = 0
(o:)	rot₁₃ = -1	rot₁₃ = 1
(l=>)	rot₁₀ = (n₇ / n₉) * (n₁₁ / n₅) * (n₁₃ / n₁₂)	rot₁ = k * (n₃ / n₂) * (n₁₁ / n₅) * (n₁₃ / n₁₂)
(m=>)	d₁₀ = 2 * t / rot₁₀	d₁ = 2 * t / rot₁