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LEVER-GEAR RACK-AND-PINION MECHANISM

Crank 1 rotates about fixed axis A and drives connecting rod 2 which slides in guiding link 3. Link 3 turns about fixed axis C. Connecting rod 2 has straight gear rack a which meshes with circular pinion 4. When crank 1 rotates, pinion 4 has an oscillating motion about axis C. The total angle of rotation of pinion 4 in one direction is equal to ϕ=sqrt(((l+k)/(r±e))²-1)-sqrt(((l-k)/(r±e))²-1) where k is the length of link 1 (A͞B), l is the distance A͞C, r is the pitch radius of pinion 4, and e is the distance from point B to the pitch line of rack a in the direction perpendicular to the pitch line.
$2412$LrG,5L$