Why do different Technic-style gear pairs fit the same axle holes?

Two external spur-gear pairs can fit the same axle holes when their tooth sums match, even though their turn ratios differ. Our new bench compares a 40-tooth input with an 8-tooth output against a separate 24/24 pair. Each pair has 48 teeth in total and nominal centres 24 mm apart. One input turn predicts five opposite output turns in the first pair and one in the second.

Same holes, different answer

Imagine laying out a gearbox, discovering a new ratio and hoping to keep the same frame. The tempting shortcut is to compare only gear diameters or only ratios. Our Equal Spacing Gear Bench lets you separate those decisions. It uses 37 compatible parts and thirteen assembly steps, with an estimated twenty-minute build time. Two independent inputs sit on opposite long edges of one rigid frame. Neither input drives the other pair.

The credited ssugawara1955 demonstration shows a dense running array of 8-, 20- and 24-tooth gears. Its brief description identifies a Power Functions motor rather than supplying a complete part-by-part assembly guide. A visible reader comment raises the difficulty of arranging the geometry; the creator also explains relative axle speeds. That inspired our question about fitting pairs into a fixed layout. Our four-shaft hand-operated comparison has original geometry and instructions. It does not recreate the creator’s motorized array, its support layout or its gear choices.

Add for spacing, divide for turns

A gear’s pitch circle is an imaginary circle used to describe its rolling relationship with another gear. It runs inside the tooth tips. For standard external spur gears of the same tooth-size module, nominal centre distance is the sum of their pitch radii. These native gear models use a one-millimetre tooth-size module: pitch diameter equals tooth count in millimetres, and pitch radius is half that.

The 40-tooth gear therefore has a 20 mm pitch radius, and the 8-tooth gear a 4 mm radius. Together they require 24 mm. Two 24-tooth gears each have a 12 mm pitch radius, giving the same result. In construction units, 24 mm is three eight-millimetre hole spacings. The term module here has two uses: the tooth-size module is 1 mm; a construction hole pitch is 8 mm. Do not swap those units in a calculation.

To predict turns, use gear ratio. With external gears engaged, every tooth passing the contact point advances the other gear by one tooth interval. Output turns equal input turns times input teeth divided by output teeth, in the opposite direction. Forty divided by eight is five; twenty-four divided by twenty-four is one. An equal sum leaves room for unequal ratios. It does not give extra energy, a load rating or a motor speed prediction.

Predict before choosing a replacement

Keep the lab at 24 mm axle spacing. Start with 40/8, predict that the pitch circles meet and check the explanation. Move the input slider to one turn and read the signed output. Then choose 24/24 without moving the axle centres. Explain why the fit stays the same while the output count changes.

Now change only the input to 24 while leaving the output at eight teeth. Its required spacing becomes 16 mm. At the original 24 mm centres, the nominal pitch circles are too far apart, so the lab deliberately supplies no driven output count. A calculated ratio of three is meaningful only after actual engagement has been established. Return to a supported bench combination before trying the real parts.

The diagram shows pitch circles rather than a tooth collision simulation. Matching circles is a necessary design check, not proof that arbitrary gear families, tooth profiles, axle heights or manufacturing tolerances will work. Only the authored 40/8 and 24/24 arrangements have been reviewed for this bench. Other selections and spacing changes are virtual exercises requiring new support and clearance review before a physical build.

A fair hand-turn experiment

Open the free animated bench instructions. Fit the four retained corner feet, then all four shafts and their spacers before fitting any gear. This order keeps the insertion paths open. Each shaft passes through a round frame hole, with a half bush immediately below and another above. Those stops retain the whole shaft; the full upper spacer and top cap also retain the gear. The frame carries bearing reactions to the feet and table. Fingers hold the stationary frame rather than supplying a missing shaft support.

Use removable dots on each input and output. Turn only the 40-tooth input slowly through one complete revolution, keeping your fingers away from the mesh. Record the opposite output turns. Separately repeat with the 24-tooth input, then repeat both in reverse. Keep the starting marks, viewing side and gentle turning method consistent. Do not compare elapsed time: the independent hand inputs have no common speed control.

We have not physically tested this model. The blank cells invite your own observations. The animation prescribes both independent inputs at the same illustrative speed; it does not demonstrate a mechanical connection between them or report measured performance. If a retainer moves, a shaft wobbles or teeth bind, stop and repair the assembly before interpreting the result.

Find the problem before forcing the gears

• The teeth bind. Check the gear heights and phase. Turn the entire keyed shaft gently so a tooth enters a gap; keep its axle and bushes aligned. Do not force teeth against teeth.
• The gear slides. Seat its spacer and top cap. A valid tooth sum does not replace axial retention.
• Your count differs. Check that you completed a full input turn, distinguish reverse direction from a negative speed claim and repeat slowly. Inspect looseness or rubbing before changing the explanation.
• A replacement does not engage. Check both tooth sum and gear family. Tooth ratio alone cannot tell you whether the parts fit the existing holes.

Try the Dual Output Gear Bench next to see how one input drives two fixed branches. Compare the Speed-Cancelling Gear Bridge for an idler train with equal end speeds. Read about gears, axles and bushes, or browse the free catalogue. The useful design habit is to check layout, support and engagement before using a ratio to predict motion.