If the geometric figure does not appear, click in the center !

Red Lines = 1st Gearsets Pair | Blue Lines = 2nd Gearsets Pair (Simpson)

This interactive nomogram is a real geometric calculator exactly representing the rotational speeds of the transmission's **3x4 = 12** internal shafts for each of its 9 ratios (*+ reverse*), grouped according to their 4 permanent coupling on 4 joint ordinates and 3 independent ordinates.
These ordinates are positioned on the abscissa in strict accordance with the proportions of the sun gears' teeth numbers relative to those of their rings. Consequently, the output ratios on the ordinate **c4** (*carrier of the last planetary gearset*) follows closely those of the actual transmission.
This advantageous geometric construction sets us free from ** Willis'** famous and tedious formula, because all calculations are determined exclusively by lengths ratios, respectively teeth numbers on the abscissa for the 4 epicyclic ratios **Re**, and of rotational speeds on the **c4** ordinate for the 10 gear ratios.

Observe the effect of resizing each of the 4 planetary gears sets on this geometric figure:

- Drag the **C dot** (*C brake*) to change the mechanical dimension of the first planetary gearset **Re1**.

- Drag the **D dot** (*D brake*) to modify the mechanical dimension of the second planetary gearset **Re2**.

- Drag the **third green dot** to change the mechanical dimension of the fourth planetary gearset **Re4**.

- Simultaneously (*shift+click*) drag the dots **C+D+3+5**, or **4+6+A**, to modify the mechanical dimension of the third planetary gearset **Re3**.

*Legend:*

**A** dot: Dog Brake (blocks **s3+s4** sun gears)

**B** dot: Clutch (couples **s1** with input shaft)

**C** dot: Brake (blocks **s1** sun gear)

**D** dot: Brake (blocks **r2** ring gear)

**E** dot: Clutch (couples **c3+r4** with input shaft)

**F** dot: Dog Clutch (couples **r1+s2** with input shaft)

*Warning*:

- The red dots on the abscissa modify simultaneously more than one gearset !

- To restore the factory ratios, please reload this page.

Created with Cinderella by Francois Roulet