Before revision: Position Position with respect to crank angle (from the triangle relation, completing the square, utilizing the Pythagorean identity, and rearranging): Velocity Velocity with respect to crank angle (take first derivative, using the chain rule): Acceleration Acceleration with respect to crank angle (take second derivative, using the chain rule and the quotient rule): Non Simple Harmonic Motion The angle domain equations above show that the motion of the piston (connected to rod and crank) is not simple harmonic motion, but is modified by the motion of the rod as it swings with the rotation of the crank.
After revision: (geometry)Position Position with respect to crank angle (from the triangle relation, completing the square, utilizing the Pythagorean identity, and rearranging): Velocity Velocity with respect to crank angle (take first derivative, using the chain rule): Acceleration Acceleration with respect to crank angle (take second derivative, using the chain rule and the quotient rule): Non Simple Harmonic Motion The angle domain equations above show that the motion of the piston (connected to rod and crank) is not simple harmonic motion, but is modified by the motion of the rod as it swings with the rotation of the crank.