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[![enter image description here][1]][1]Is it possible for a hypoid bevel gear like the one pictured below to have a 1:1 ratio? If 1:1 isn’t possible, any idea what the smallest ratio could be in order to output the least amount of gear reduction?

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As far as I know, there isn't any mathematical limitation that would rule out using Hypoid gears for a 1:1 transmission (known as Mitre /Miter gears). You won't find any commercially, however, since they are less mechanically efficient than spiral gears (due to sliding along the teeth). Hypoid gears are favoured in some situations for their ability to achieve a high reduction in a small space through behaving much like a worm-gear (see the high-ratio hypoid set below). For a 1:1 ratio, there is no benefit in selecting a Hypoid form, and so Spiral or Straight is the industry preference.

Spiral Miter Gears

Spiral Miter Gears

High Reduction Hypoid Gears

High Reduction Hypoid Gears

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  • $\begingroup$ I do in fact need the offset which is why I couldn’t use spiral or straight bevel gears. $\endgroup$
    – Nev
    Jan 5, 2018 at 21:06
  • $\begingroup$ Ah bummer. If you don't mind me asking, why is the offset a requirement? Perhaps there is some other way to solve the base problem? $\endgroup$ Jan 5, 2018 at 21:55

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