A fast middle gear can leave the final speed unchanged because the second mesh cancels the first speed change. In a 40–8–40 train, the eight-tooth idler makes five reverse turns for one input turn, while the second forty-tooth gear makes one forward turn. Equal end tooth counts determine that final ratio; the middle size determines its own speed and the required spacing.
Build the Speed-Cancelling Gear Bridge to inspect this with three supported shafts. This construction-part guide replaces the former fabrication topic at this URL. Our existing original model has been reviewed and its source credited; it is not a newly claimed copy of a long creator machine. Brick Experiment Channel's published description sets an equal-first-and-last-speed goal. Its footage could not be played during this review, so the credit supports that stated idea, not an unseen assembly detail.
Count two meshes instead of one
The first external mesh reverses direction. Forty input teeth passing an eight-tooth gear turn that gear five revolutions for one input revolution. The second external mesh reverses direction again. Eight teeth on the middle shaft driving forty teeth on the output reduce its speed by five. Multiply the two factors: five times one fifth equals one.
More generally, the middle tooth count appears once in the denominator and once in the numerator, so it cancels. This does not make the middle gear physically irrelevant. Its diameter affects shaft spacing, its rotation is faster when it is smaller, and its bearings and teeth still contribute friction. Read idler gears alongside gear ratios to separate direction, speed and losses.
Use the actual assembly order
The free step guide lays a 5×11 frame flat and identifies holes two, five and eight along one long edge. Their centres are three modules apart. Each shaft is retained with a lower bush and an upper bush or half bush. The gear sits above the frame in the common gear plane; the round frame hole supports rotation while the stops limit sliding along the shaft.
Seat the idler teeth in the adjacent gaps before adding the last gear. The published phase is part of the reviewed arrangement. If teeth meet tip to tip, do not bend the shafts or move them toward each other. Keep the specified hole positions, gear heights and axle lengths. Add the third foot on the opposite edge so the bench rests on a flat surface rather than leaning on two points.
The native 3D guide animates these real placements and ordered insertions. Its free illustrated booklet shows the same construction. The operating loop is an ideal gear ratio animation with the actual procedural mesh phase checked; it is not a measured efficiency or speed test.
Try the cancellation challenge
Predict the direction of the output after one input turn, then check the three readouts. Change only the virtual idler tooth count while keeping the ends at forty. Explain why its turn count changes but the last count does not.
Interactive: Speed-cancelling gear bridge. Predict the output direction of a 40–8–40 gear train, then turn the input. One input turn makes five reverse middle turns and one forward output turn: two external meshes reverse the direction twice, and changing only the middle gear leaves the final ratio unchanged.
This calculator is a mathematical comparison. Selecting a different gear does not show that it will mesh at the same physical holes. A sixteen-tooth idler between two forty-tooth gears needs different spacing from the authored eight-tooth idler. Keep the physical bench unchanged unless you design and review its new support and mesh geometry.
Measure a useful physical count
Use a removable witness mark on each top bush. Turn the red input once slowly, watching the small middle gear complete five reverse turns. Check the blue output returns to its witness position after one forward turn. Repeat in reverse, then record three trials. Keep the base flat and every retaining stop installed.
| Trial | Input turns | Middle turns and direction | Output turns and direction | Binding notes |
|---|---|---|---|---|
| 1 | 1 | Record | Record | Record |
| 2 | 1 | Record | Record | Record |
| 3 | 1 | Record | Record | Record |
The table is an observation sheet, not prefilled performance data. A witness mark returning to the start after one turn does not establish low backlash, stiffness under load or negligible friction. Count full revolutions while also checking intermediate motion so a skipped tooth does not hide behind an end-position coincidence.
Diagnose what equal speed does not promise
A climbing gear may have escaped axially or been incorrectly seated. Binding at every mesh can indicate wrong phase or spacing. A shaft that rocks excessively needs support review rather than tighter tooth contact. Removing a bush to make a gear freer can let it leave the common plane; restore retention and check the stack.
Reader comments visible on the credited source raise friction and struggling drive as questions worth teaching, not measurements we can transfer to this bench. A one-to-one ratio does not mean no energy loss. For a shorter starting comparison, try Gear Friends. Continue with friction and the free build catalogue. Explain the count, direction and support separately: that is more informative than calling every equal-speed train efficient.
Interactive: Check yourself. A few quick questions on the ideas in this guide, each with an explanation.
- How many idler turns follow one input turn in 40–8–40?
- What cancels from the overall speed ratio?
- Can you fit any idler at the same shaft positions?
