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LEVER-GEAR INTERNAL PLANETARY SLIDER-CRANK MECHANISM

Internal gear 1 rotates about fixed axis A and meshes with gear 3 which is rigidly attached to (or integral with) connecting rod 4. Crank 2 rotates about axis A and is connected by turning pair B to connecting rod 4 which, in turn, is connected by turning pair C to slider 5. Slider 5 moves along fixed guides a-a. When driving gear 1 rotates, slider 5 reciprocates. The transmission ratio i₁₂=ω₁/ω₂, where ω₁ and ω₂ are the angular velocities of gear 1 and crank 2, is equal to i₁₂= i₄₂i₁₄+(1-i₁₄) where i₄₂=ω₄/ω₂, i₁₄=ω₁/ω₄=z₃/z₁, ω₄ is the angular velocity of connecting rod 4 and gear 3, and z₁ and z₃ are the numbers of teeth of gears 1 and 3. Transmission ratio i₄₂ is determined from the lengths of the links of slider-crank linkage ABC. In one full cycle, the speeds n₂ and n₁ of crank 2 and gear 1 (in rpm) are related by the equation n₁=n₂(z₁-z₃)/z₁. If the number of teeth comply with the condition: z₁=2z₃, then n₁=n₂/2 i.e. slider 5 makes two full strokes (back and forth) to each revolution of gear 1.
$2417$LrG,5L$