Scotch Yoke vs Slider-Crank (2D)

A crank pin in a slotted yoke gives pure sine motion; compare with a conrod slider. Same 42 mm stroke drive as the 3D page.

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The science

With the crank at angle theta the yoke position is x = r sin(theta), velocity r w cos(theta) and acceleration -r w^2 sin(theta): exactly simple harmonic motion. A slider-crank with rod length l has x ~ r cos(theta) - r^2 / (4 l) (1 - cos(2 theta)), i.e. an extra second harmonic of amplitude r^2 / (4 l).

The inertia force is m r w^2; the crank torque -m r^2 w^2 sin(theta) cos(theta) averages to zero over a turn (no friction, energy conserved).
Simplifications: rigid parts, frictionless slot, no pin-slot clearance, constant crank speed.

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