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The fact-check log

Every claim on this site, written in our own words and checked against the named source on 14 November 2026. Where a catalogue spelling or two ways of writing a ratio need a note, the note is on this page too.

  1. A gear is a machine component consisting of a toothed wheel attached to a rotating shaft. Britannica Scholars: gear

  2. Gears operate in pairs to transmit and modify rotary motion and torque (turning force) without slip. Britannica Scholars: gear

  3. The teeth of one gear engage the teeth on a mating gear. Britannica Scholars: gear

  4. If the teeth on a pair of mating gears are arranged on circles — if the gears are toothed wheels — the ratios of the rotary speeds and torques of the shafts are constant. Britannica Scholars: gear

  5. If the teeth are arranged on noncircular bodies, the speed and torque ratios vary. Britannica Scholars: gear

  6. Most gears are circular. Britannica Scholars: gear

  7. To transmit motion smoothly and with a nonvarying speed ratio at every instant, the contacting surfaces of gear teeth must be carefully shaped to a specific profile. Britannica Scholars: gear

  8. The smaller of a gear pair is called the pinion. Britannica Scholars: gear

  9. If the pinion is on the driving shaft, the pair acts to reduce speed and to amplify torque. Britannica Scholars: gear

  10. If the pinion is on the driven shaft, the pair acts as a speed increaser and a torque reducer. Britannica Scholars: gear

  11. If the driven gear has twice as many teeth as the pinion, the torque of the driven gear is twice the pinion torque, and the pinion speed is twice the speed of the driven gear. Britannica Scholars: gear

  12. The shafts that gears connect must be relatively close, but they may be parallel or nonparallel, and intersecting or nonintersecting. Britannica Scholars: gear

  13. Parallel shafts can be connected by spur gears, with teeth that are straight lengthwise and parallel to the shaft axes. Britannica Scholars: gear

  14. Parallel shafts can also be connected by helical gears, with twisted, screwlike teeth. Britannica Scholars: gear

  15. Intersecting shafts are connected by bevel gears, with tapered teeth arranged on truncated cones. Britannica Scholars: gear

  16. Nonparallel, nonintersecting shafts are usually connected by a worm and gear. Britannica Scholars: gear

  17. The worm resembles a screw, and the gear resembles a quarter section of a long nut that has been bent around a cylinder. Britannica Scholars: gear

  18. The commonest angle between nonparallel shafts, either intersecting or nonintersecting, is a right angle (90°). Britannica Scholars: gear

  19. Because it is basically a screw, a worm gear may have only one thread (tooth). Britannica Scholars: gear

  20. To maintain continuous contact with parallel-shaft gears (spur and helical), the pinion must have at least five teeth. Britannica Scholars: gear

  21. For a large speed ratio in a single gear pair, a worm and gear are well suited. Britannica Scholars: gear

  22. If the shafts must be parallel, it may be necessary to use several gear pairs in series (a train) to obtain a large ratio. Britannica Scholars: gear

  23. Before the Industrial Revolution, power came from three main sources: humans, draft animals, and water. Britannica: gear

  24. In a medieval-style mill, the waterwheel is turned by a stream and is connected to a shaft that leads into the building. Britannica: gear

  25. At the other end of the shaft is a gear. Britannica: gear

  26. A series of gears translates the power from the stream to a shaft that drives a millstone, which grinds flour from grain. Britannica: gear

  27. The wheelwork, or train, of a clock is the series of moving wheels (gears) that transmit motion from a weight or spring, via the escapement, to the minute and hour hands. Britannica Scholars: clock

  28. The wheels and pinions of a clock need to be made accurately, and the tooth form designed so that the power is transferred as steadily as possible. Britannica Scholars: clock

  29. In a clock driven by a weight or a spring, the power is first transmitted by the main, or great, wheel. Britannica Scholars: clock

  30. A pinion is a gear with a small number of teeth designed to mesh with a larger wheel. Britannica Scholars: clock

  31. An arbor is a turning rod to which gears are attached. Britannica Scholars: clock

  32. The gear ratios are such that one arbor, usually the second or third, rotates once an hour and can be used to carry the minute hand. Britannica Scholars: clock

  33. A simple 12-to-1 gearing, known as the motion work, gives the necessary step-down ratio to drive the hour hand. Britannica Scholars: clock

  34. A clock built for Wells Cathedral in England is preserved in the Science Museum in London. Britannica Scholars: clock

  35. Levers, gears, pulleys, wedges, and screws are some examples of machines. OpenStax College Physics 2e

  36. Energy is still conserved for these devices, because a machine cannot do more work than the energy put into it. OpenStax College Physics 2e

  37. Machines can reduce the input force that is needed to perform the job. OpenStax College Physics 2e

  38. The ratio of output to input force magnitudes for any simple machine is called its mechanical advantage (MA). OpenStax College Physics 2e

  39. A crank is a lever that can be rotated 360° about its pivot. OpenStax College Physics 2e

  40. The mechanical advantage for a crank is simply the ratio of the radii ri/r0. OpenStax College Physics 2e

  41. Wheels and gears have this same simple expression for their mechanical advantages. OpenStax College Physics 2e

  42. The mechanical advantage can be greater than 1, as it is for the crank, or less than 1. OpenStax College Physics 2e

  43. The Science Museum Group holds a model of sun and planet gearing made by James Watt, 1782–1784, demonstrating the action designed to produce a rotative motion. Science Museum Group: sun and planet

  44. James Watt was working on the crank and connecting-rod as a way of converting an engine beam’s reciprocating motion into circular motion when he was forestalled by a patent taken out in 1780 by James Pickard. Science Museum Group: sun and planet

  45. Watt, instead of contesting the patent, decided to adopt other mechanism, and patented several such mechanisms in 1781. Science Museum Group: sun and planet

  46. Of those mechanisms, only the sun and planet gear came into use. Science Museum Group: sun and planet

  47. It is an epicyclic gear, with a sun wheel keyed on the end of the fly-wheel shaft and a planet wheel bolted to the connecting-rod end. Science Museum Group: sun and planet

  48. The planet wheel is held in gear with the sun wheel by a link loose on their centres, or by a pin in the centre of the planet wheel moving in an annular slot. Science Museum Group: sun and planet

  49. When both wheels are of the same diameter, the fly-wheel makes twice the number of revolutions that it would if actuated by a crank and connecting-rod. Science Museum Group: sun and planet

  50. The extra revolution is due to the fact that the planet wheel, although going round in a circle, does not revolve on its own axis. Science Museum Group: sun and planet

  51. In some of Watt’s engines the diameter of the planet wheel was less than that of the sun wheel, and shaft speeds were then only about 50 per cent greater than they would have been with a simple crank. Science Museum Group: sun and planet

  52. The Science Museum Group holds a teaching model of two heart wheels in gear, transmitting a variable velocity ratio, made by J. Schröder in 1868. Science Museum Group: heart wheels

  53. The model illustrates the point that gears do not have to be circular, provided that their shapes are correctly matched. Science Museum Group: heart wheels

  54. Gears of this type can provide a transmission of varying speed, a useful feature in, for example, some textile machinery. Science Museum Group: heart wheels

  55. The model was purchased from Herr J. Schröder, an educational model maker from the Polytechnic Institute in Darmstadt, Germany. Science Museum Group: heart wheels

  56. The Science Museum Group holds a Sturmey-Archer three-speed epicyclic hub gear for cycles, dated 1906. Science Museum Group: Sturmey-Archer

  57. It is an example of the variable-speed hub for bicycles patented by J. J. H. Sturney and J. Archer between 1901 and 1904. Science Museum Group: Sturmey-Archer

  58. The hub gives three speeds: a normal one equal to that of the chain sprocket, one 31.25 per cent above, and a third 23.8 per cent below the normal. Science Museum Group: Sturmey-Archer

Notes

The catalogue spelling “Sturney”

The Science Museum Group catalogue names the patentee as J. J. H. Sturney. The hub itself is widely known as Sturmey-Archer. We keep the catalogue spelling when quoting the patent, and the familiar name for the hub.

Teeth and radii

Britannica counts teeth to explain how a pair trades speed for turning force. OpenStax gives the mechanical advantage of wheels and gears as the ratio of the radii, written ri/r0. For ordinary circular gears the two pictures agree, because the number of teeth is proportional to the radius; they are two ways of writing the same trade-off.

Clockwork already tells the clock’s story

Clock trains, escapements, pendulums and John Harrison’s sea clocks are covered in depth on clockwork.mechanics.im. This site explains the ratio idea — the great wheel, the motion work, and the 12-to-1 step-down to the hour hand — and then points you there.

Five teeth, or one thread

A worm may have only one thread (tooth). The “at least five teeth” rule is for the pinion of a spur or helical pair, so that it keeps continuous contact. The two figures answer different questions.