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