Steadily rotating crank ( displacement of the end of the connecting rod )

Description

A crank is an arm attached at right angles to a rotating shaft by which reciprocating motion is imparted to or received from the shaft. It is used to convert circular motion into reciprocating motion, or vice-versa. The arm may be a bent portion of the shaft, or a separate arm or disk attached to it. Attached to the end of the crank by a pivot is a rod, usually called a connecting rod. The end of the rod attached to the crank moves in a circular motion, while the other end is usually constrained to move in a linear sliding motion. The displacement of the end of the connecting rod is approximately proportional to the cosine of the angle of rotation of the crank, when it is measured from top dead center (TDC). So the reciprocating motion created by a steadily rotating crank and connecting rod is approximately simple harmonic motion.

Related formulas

Variables

xThe displacement of the end of the connecting rod (m)
rThe length of the crank (distance between crank pin and crank center) (m)
aThe angle of the crank measured from top dead center (TDC) (radians)
lThe length of the connecting rod (distance between piston pin and crank pin) (m)