Four-Bar Linkage
The four-bar linkage is the most fundamental planar mechanism: four rigid bars connected by revolute joints, producing rich families of motion from simple geometry. Adjust link lengths to explore crank-rockers, double-cranks, and double-rockers, and watch the coupler curve trace intricate paths.
About this lab
The four-bar linkage is one of the oldest and most studied mechanisms in engineering. It consists of four rigid links connected end-to-end by revolute (pin) joints forming a closed loop. One link is fixed (the ground or frame), and the motion of the remaining three links is fully determined by a single input angle. Despite its simplicity, the four-bar linkage can generate a remarkable variety of output motions and coupler curves.
The Grashof condition determines the type of motion: if the sum of the shortest and longest links is less than the sum of the other two, at least one link can fully rotate. Depending on which link is the ground, the mechanism may be a crank-rocker (one full-rotation link, one oscillating), a double-crank (both rotate fully), or a double-rocker (neither rotates fully, but the coupler does). The coupler curve --- the path traced by a point on the floating coupler link --- can produce an astonishing variety of shapes including circles, ellipses, figure-eights, and intricate looping curves.
Four-bar linkages are used throughout mechanical engineering: in windshield wipers, sewing machines, steam locomotives, aircraft landing gear, and robotic arms. The mathematical study of coupler curves belongs to the field of algebraic geometry --- a general coupler curve is a tricircular sextic, a degree-six algebraic curve with three circular points at infinity. This lab lets you explore these curves interactively by adjusting link lengths and the position of the coupler point.