The gearbox uses a three-shaft layout — input, counter, and output — with three gear ratios for forward drive and three for reverse. A common gear pair between the counter shaft and output shaft is shared across all forward speeds.

A 20° full-depth involute gear tooth system was selected — it can be cut with standard hobs and the higher pressure angle produces stronger teeth compared to 14½° systems. The minimum number of teeth on any pinion is 18 to avoid interference.

Shaft centre distances are constrained by the gear ratios and the requirement that gear radius $R = mT/2$ must yield a positive whole-number tooth count for a standard module. This creates a combinatorial feasibility problem solved by exhaustive search.

Each gear's radius is determined by the shaft centre distance and the velocity ratio. For example, for the first reverse pinion:

Since $D = m \times T$ (diameter = module × teeth), and both module and teeth count must be discrete (standard module list and integer teeth ≥ 18), the problem becomes a combinatorial search. A brute-force search in Python was used:

1. Choose a module from the standard list and iterate tooth count from 18 upward for the first gear pair, calculating $L_{io}$ for each.
2. For each feasible $L_{io}$, compute radii of the remaining gears. Try every standard module for each pair and keep only combinations yielding integer teeth.
3. Filter: discard any entry with fractional teeth or count below 18. The search produced 233 candidate rows for reverse gears alone.
4. Select the row with the largest module — fewer teeth, easier manufacturing, stronger tooth profile.

Output of the Python search showing all feasible module combinations for the forward gear set. The same iterative method was applied to reverse gears and the common gear pair. Entries with the largest modules were selected to minimise tooth count and maximise strength.

Forward gears create loads in both horizontal and vertical planes. Separate BMDs were computed for each component. The horizontal plane carries the tangential tooth load while the vertical plane carries gear weight.

Combined bending moment diagram for all forward gear engagement cases. The maximum bending moment across all scenarios (reverse + forward) was 9.68 Nm at 3rd reverse engagement. This was used together with the twisting moment (3.2 Nm) to find the equivalent twisting moment and minimum shaft diameter.

The shifting mechanism has 9 positions — three rows (left/middle/right), each with forward, neutral, and reverse. A dog-clutch engagement was used: the shifter moves a collar that slides on a splined shaft to mesh with the target gear.

The shifting lever tip moves approximately the same distance as the dog clutch travel (6.5 mm). The geometry calculations derive the shifting angle $\theta = \tan^{-1}(l_1 / r_1)$ and the inter-fork angle $\alpha = \tan^{-1}(l_2 / r_2)$ to determine lever dimensions.

Dimensions of the lever's engagement part were derived analytically. Height, depth, and width were each constrained by geometric relationships between the fork radius, shifter tip radius, and the angular travel needed for reliable engagement.

The shifting mechanism uses a ball-and-socket joint for smooth multi-axis shifting. The shifter is hollow (2 mm wall thickness) to reduce weight, with a globular tip to minimise contact area and wear against the levers.

Sectional view of the engagement location. The lever engagement parts are aligned in a straight line when all are in neutral position. Levers connect to forks through transition fits that lock relative rotation, while M10 bolts constrain lateral movement.

The socket was designed so that only the allowable shifter movements can be made — the internal geometry acts as a shift gate. Cut dimensions were derived from the shifting geometry calculations. The socket is machined separately and welded to the housing top for tighter tolerances.

Location of the shifter in the overall gearbox housing. Levers are held in place through clearance-fit slots built into the middle housing section, allowing the sliding motion needed during gear shifts. The longest lever has two holding sockets for stability while the shorter ones rely on fork interference fits.