Scotch-Yoke Simple Harmonic Motion

A scotch yoke - a crank pin in a slotted yoke - gives EXACT simple harmonic motion with no connecting rod: x = r(1 - cos theta), v = r omega sin theta, a = r omega^2 cos theta, with omega = 2 pi N/60. No rod obliquity, so the motion is symmetric and the slider is exactly at mid-stroke at 90 degrees. Stroke is 2r; speed peaks at r omega at mid-stroke and is zero at the ends, while acceleration peaks at r omega^2 at each END (zero at mid-stroke) - and that end acceleration times the reciprocating mass is the inertia force, which grows with the SQUARE of rpm. A 2 in crank at 300 rpm gives a 4 in stroke, 5.24 ft/s peak speed, and 5.11 g peak acceleration. Used for reciprocating pumps and compressors, valve and gate actuators, and sine-motion shaker or vibration-test rigs. Ideal rigid mechanism; friction, yoke side thrust, and the driven load are separate. A design aid; Machinery's Handbook and the machine builder govern.

omega = 2 pi N/60; x = r(1 - cos theta); v = r omega sin theta; a = r omega^2 cos theta; stroke = 2r; peak speed = r omega (mid-stroke); peak accel = r omega^2 (ends).

The scotch-yoke simple harmonic motion x = r(1 - cos theta), v = r omega sin theta, a = r omega^2 cos theta (Machinery's Handbook; standard mechanism kinematics), by name.

Simple harmonic motion is a standard published kinematics result; the crank radius, speed, and angle are the user's inputs.

Estimate. AHJ and licensed professional govern.

Field names used by the API: crank_radius_in, crank_rpm, crank_angle_deg, stroke_in, peak_velocity_fps, peak_accel_g

• Motion x = r(1 - cos theta), v = r omega sin theta, a = r omega^2 cos theta - exact simple harmonic motionMachinery's Handbook
• Peaks peak speed r omega at mid-stroke; peak acceleration r omega^2 at the ends (sets the inertia load)kinematics
• Scope ideal rigid mechanism; friction, yoke side thrust, clearance, and driven load are separatescope of this tile