Gears 7, 8 and 9 slide along square guide a of driving shaft 1 and can be shifted into engagement with gears 12, 13 and 14 which are keyed, together with gear 15, to sleeve 22. Sleeve 22 rotates freely on intermediate shaft 5. Gear 15 is in constant engagement with gear 10. Gears 10 and 11 are keyed to sleeve 23 which rotates freely on shaft 1. Gear 16 slides along square guide b of shaft 5 so that it can be shifted out of engagement with gear 11 and into engagement, by means of clutch members, with gear 15. Gear 20 is keyed to shaft 5 and is in constant engagement with gear 19 which, together with gear 18, is keyed to shaft 4, one of the driven shafts. Gear 17 slides along square guide c of shaft 2, the second driven shaft, so that it can either mesh with gear 18 or be shifted into engagement, by means of clutch members, with gear 20. Gear 21 is keyed to shaft 2 and is in constant engagement with gear 6 which is keyed to shaft 3, the third driven shaft. Thus, when driving shaft 1 rotates, driven shafts 2, 3 and 4 rotate at different speeds. If, for example, gear 8 is in engagement with gear 13, gear 10 with gear 15 and gear 18 with gear 17, the three transmission ratios from the driving to the three driven shafts are •i₁₂=-(z₁₃/z₈)(z₁₀/z₁₅)(z₁₆/z₁₁)(z₁₉/z₂₀)(z₁₇/z₁₈), i₁₃=(z₁₃/z₈)(z₁₀/z₁₅)(z₁₆/z₁₁)(z₁₉/z₂₀)(z₁₇/z₁₈)(z₆/z₂₁) and i₁₄=(z₁₃/z₈)(z₁₀/z₁₅)(z₁₆/z₁₁)(z₁₉/z₂₀). Now, if gear 17 is shifted out of engagement with gear 18 and into engagement with the clutch member of gear 20, the three transmission ratios are •i₁₂=-(z₁₃/z₈)(z₁₀/z₁₅)(z₁₆/z₁₁), i₁₃=(z₁₃/z₈)(z₁₀/z₁₅)(z₁₆/z₁₁)(z₆/z₂₁) and i₁₄=(z₁₃/z₈)(z₁₀/z₁₅)(z₁₆/z₁₁)(z₁₉/z₂₀) i.e. transmission ratio i₁₄ is unchanged. Two other series of transmission ratios are obtained when gears 7 and 12 or 9 and 14 are in engagement instead of gears 8 and 13. If gears 7 and 8 are not in engagement, gear 17 is shifted into engagement with gear 20 and gear 9 with gear 10, the three transmission ratios are •i₁₂=-(z₁₆/z₁₁), i₁₃=(z₁₆/z₁₁)(z₆/z₂₁) and i₁₄=(z₁₆/z₁₁)(z₁₉/z₂₀). The remaining eight transmission ratios are obtained by engaging gear 16 to gear 15, shifting gear 7 or 8 or 9 into engagement with gear 12 or 13 or 14, and gear 17 with gear 18. In all of the equations, z₇, z₈, . . . , z₂₁ are the numbers of teeth of gears 7, 8, ..., 21. Thus, when driving shaft 1 rotates, driven shafts 2, 3 and 4 can have any three of sixteen different speeds.
$2867$CxG,SR$