/COURSES/MACHINE_DESIGN/SIM_FOUR_BAR

Four-Bar Linkage: Interactive

One input, one motion. Four links and four pins give one degree of freedom. Turn the crank, and the position of the full linkage is set. Drag to turn the crank by hand. The point on the coupler draws its curve.

FOUR-BAR // GRASHOF
θ2 crank+000° θ4 rocker+000° μ transmit90° DOF1
Drag to turn the crank
crank 0.6 · coupler 1.6 · rocker 1.2 · ground 2.0

Why it has one degree of freedom

Four links, four pin joints. The planar mobility count from the notes gives:

$$ M = 3(L-1) - 2J_1 - J_2 = 3(4-1) - 2(4) - 0 = 1 $$

so one input, the crank angle $\theta_2$, sets the full linkage. The Grashof condition tells you if the crank can turn fully. With the shortest link $s$, the longest link $l$, and the other two links $p, q$:

$$ s + l \le p + q $$

This linkage is a crank-rocker ($s+l = 2.6 \le p+q = 2.8$, with the shortest link adjacent to the ground). The crank turns fully. The rocker oscillates. The transmission angle $\mu$ is the angle between the coupler and the rocker. The linkage pushes well when $\mu$ is near $90^\circ$. It binds near $0^\circ$ or $180^\circ$ (shown in red). The course notes give the background.