Second derivatives provide angular accelerations, essential for force and inertia calculations.
Solving for (\theta_3) and (\theta_4) (the coupler and follower angles) requires solving a , often handled via the Freudenstein equation:
Breaking into (x) and (y) components for a given crank angle (\theta_2): 4 bar link calculator
[ \mathbf{r}_1 + \mathbf{r}_2 = \mathbf{r}_3 + \mathbf{r}_4 ]
[ r_2 \cos\theta_2 + r_3 \cos\theta_3 = r_1 + r_4 \cos\theta_4 ] [ r_2 \sin\theta_2 + r_3 \sin\theta_3 = r_4 \sin\theta_4 ] crossed)
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:
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. Given link lengths and crank angle, output the
Given link lengths and crank angle, output the angles of the coupler and follower, plus the coupler point position.
Differentiating the loop equations yields angular velocities using the known input angular velocity.
[ K_1 \cos\theta_4 + K_2 \cos\theta_2 + K_3 = \cos(\theta_2 - \theta_4) ]