4 Bar Link - Calculator

Solving for (\theta_3) and (\theta_4) (the coupler and follower angles) requires solving a , often handled via the Freudenstein equation:

[ \mathbf{r}_1 + \mathbf{r}_2 = \mathbf{r}_3 + \mathbf{r}_4 ]

Given link lengths and crank angle, output the angles of the coupler and follower, plus the coupler point position.

The angle between the coupler and follower—critical for force transmission. Values near (90^\circ) are ideal; below (40^\circ) or above (140^\circ) cause poor mechanical advantage.

[ K_1 \cos\theta_4 + K_2 \cos\theta_2 + K_3 = \cos(\theta_2 - \theta_4) ]

where (K_1, K_2, K_3) are constants derived from link lengths. A 4-bar link calculator automates this solution, handling the two possible assembly configurations (open vs. crossed). A comprehensive 4-bar link calculator typically offers:

Breaking into (x) and (y) components for a given crank angle (\theta_2):