Gears 7, 8, 9 and 10 rotate freely on shaft 1 and are in constant engagement with gears 15, 16, 18 and 20 which are keyed to intermediate shaft 21. Gears 11, 12, 13 and 14 rotate freely on shaft 2 and are in constant engagement with gears 15, 17, 19 and 20 which are keyed to shaft 21. Four symmetrically located clutches, 3, 4, 5 and 6, slide along square guides a, b, c and d of shafts 1 and 2. Only one of the clutches on each shaft can be engaged at the same time. If clutch 3 is engaged to gear 7 (clutch 4 being disengaged) and clutch 5 is engaged consecutively to gears 11 and 12, and then clutch 6 is engaged consecutively to gears 13 and 14, four different transmission ratios can be obtained. Thus
i₁₂=z₁₁/z₇, i₁₂=(z₁₅/z₇)(z₁₂/z₁₇), i₁₂=(z₁₅/z₇)(z₁₃/z₁₉) and i₁₂=(z₁₅/z₇)(z₁₄/z₂₀). If clutch 3 is engaged to gear 8 (clutch 4 being disengaged again), and clutches 5 and 6 are engaged consecutively to gears 11, 12, 13 and 14, the next four transmission ratios can be obtained. Four more can be obtained by disengaging clutch 3 and engaging clutch 4 to gear 9, and the final four by engaging clutch 4 to gear 10, clutches 5 and 6 being consecutively engaged, in each case to gears 11, 12, 13 and 14. Thus i₁₂=(z₁₆/z₈)(z₁₁/z₁₅), i₁₂=(z₁₆/z₈)(z₁₂/z₁₇), i₁₂=(z₁₆/z₈)(z₁₃/z₁₉) and i₁₂=(z₁₆/z₈)(z₁₄/z₂₀); i₁₂=(z₁₈/z₉)(z₁₁/z₁₅), i₁₂=(z₁₈/z₉)(z₁₂/z₁₇), i₁₂=(z₁₈/z₉)(z₁₃/z₁₉) and i₁₂=(z₁₈/z₉)(z₁₄/z₂₀); i₁₂=(z₂₀/z₁₀)(z₁₁/z₁₅) , i₁₂=(z₂₀/z₁₀)(z₁₂/z₁₇), i₁₂=(z₂₀/z₁₀)(z₁₃/z₁₉) and i₁₂=z₁₄/z₁₀, where z₇, z₈, ..., z₂₀ are the numbers of teeth of gears 7,8, ......, 20. Thus, when driving shaft 1 rotates, driven shaft 2 can have any one of sixteen different speeds.
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