Transmission layouts

A transmission carries rotation between shafts. Choose its ratio and real components before fixing the shaft locations in your plates. As well as tooth count, check that the parts fit each other and can carry the load.

Use Forces and motion to estimate the required torque and speed. Then sketch the transmission around the mechanism's output axis and the space available for its motor.

Choose a ratio

For one ordinary gear, belt, or chain stage:

$$G=\frac{N_{driven}}{N_{driver}}$$

A 20-tooth driver and 60-tooth driven component give 3:1 reduction. The output rotates at one-third the input speed. Ideal torque is three times as large; actual output is lower because of losses.

For multiple stages, multiply the ratios. A 20-to-60 stage followed by an 18-to-36 stage gives 3 × 2 = 6:1. An input at 600 rpm would produce 100 rpm at the final shaft, before considering how the motor's speed changes under load.

In a compound transmission, two components on the intermediate shaft turn together. The 60-tooth gear from the first stage and the 18-tooth gear from the second must both be locked to that shaft. An idler that only sits between two gears is a different arrangement and does not add an independent reduction stage.

Place spur gears

Compatible standard spur gears use the same module and tooth system. Module is a metric measure of tooth size. Their nominal center distance is:

$$C=\frac{m(N_1+N_2)}{2}$$

For module 0.8, a 20/40 pair has 24 mm between shaft centers. Their pitch diameters are 16 and 32 mm. Use those pitch circles to position the shafts. Also draw the actual outside of each gear when checking whether it hits anything nearby.

Create construction circles at the pitch diameters. Dimension the centers, then locate the bearing seats and motor mount from the same references. In the solid model, check face width, hub length, shaft retention, and nearby plates.

External meshing gears reverse direction. Two external gear meshes reverse it twice, so the final shaft turns in the same direction as the input. Confirm the actual arrangement with a slow animation or a hand-turned prototype.

Backlash is the small clearance between mating teeth. It affects play and reversals. Follow the gear supplier's center-distance and mounting guidance; forcing gears tightly together can create friction instead of useful accuracy.

Place timing belts

Timing belts need matching pitch, tooth profile, width, and pulley geometry. The pulley pitch diameter is:

$$D_p=\frac{Np}{\pi}$$

Here $p$ is the belt pitch. A 20-tooth, 2 mm-pitch pulley has a pitch diameter of about 12.73 mm. That is not its flange diameter.

The drive-layout example uses a 20/40-tooth pair, 2 mm pitch, and a 220 mm pitch-length belt. Its geometric center distance is approximately 79.75 mm. Choose an available, compatible belt and use the manufacturer's calculator or installation guidance before detailing the plate.

An ordinary open belt pair turns both shafts in the same direction. Put the pulley working surfaces in the same plane, and keep their axes parallel. If the belt keeps running against a flange, check whether the shafts and pulleys are lined up.

Place chain

Chain and sprockets need matching pitch and width. A chain's rollers sit around a pitch polygon, so its geometry differs from a timing belt's continuous pitch line. For a sprocket with $N$ teeth and chain pitch $p$:

$$D_p=\frac{p}{\sin(\pi/N)}$$

Use radians for the angle in this formula. For a 20-tooth sprocket with 6.35 mm pitch, the pitch diameter is about 40.59 mm. Use the actual tooth and hub geometry for clearance checks.

Choose a chain length that can be assembled with the intended links and connection method. Include an adjustment or take-up arrangement suited to the drive. Check the chain's path near the frame and guard exposed runs where required by your design and safety needs.

Add adjustment

Decide which way the tension adjustment moves, how far it moves, and what holds it in place. A translating motor changes center distance; an idler changes the belt or chain path. These affect contact and bearing loads differently.

For a translating motor, guide the adjustment so the shaft stays parallel to the driven shaft. Keep washers supported at both ends of each slot. Check that the motor body, connectors, and screws remain accessible throughout the range.

For an idler, use a component compatible with the surface it contacts. Check its load, bearing, wrap, and clearance. Wrap is the amount of the pulley or sprocket circumference engaged by the belt or chain. A layout with very little engagement may need a different route.

More tension is not a universal fix for slipping or skipping. Excessive tension adds bearing load and can bend the plates. Check alignment, tooth compatibility, engagement, and the actual installation requirement.

Stack the transmission in three dimensions

A side-view layout can place the axes correctly while the real hubs collide. Add a section along each shaft and assign a plane to each gear, pulley, or sprocket.

For a compound gearbox, place each pair of meshing gears at the right position along its shafts. Include supports, spacers, and collars, and check that you can reach every clamping screw with a tool. Reserve a removal path for the belt or chain and enough room to disengage a gear when replacing it.

Check how each gear, pulley, or sprocket is attached to its shaft. A gear that spins freely on the shaft cannot drive the next stage, even if its teeth mesh correctly. Finish with Shaft supports, then prototype one module before cutting all the robot's transmission plates.