4-Bar Linkage

input (φ) =

0°90°180°270°360°

output (θ) = 39.1°

Load Example Mechanism

AD — ground

AB — crank

BC — coupler

CD — rocker

Ground orientation (°)

Coupler Point Study

Place a study point anywhere on or near the coupler. You can also drag the orange dot directly on the canvas.

Along coupler (0 = B, 1 = C)

Normal offset

Mechanism type & motion

Crank-Rocker

Geometric Solution

Click each step to see the construction on the canvas. Algebra and transpositions shown at every step.

Known Values

Start with the given measurements

Use these current link lengths and input angle before working through the geometry steps below.

Step 1

Crank Projections

Project the input crank onto x and y to locate point B (also called B′ in construction).

Step 2

Diagonal from D to B′

Use the right triangle from D to point B′ to find the diagonal length h₁ and angle θ₁.

Step 3

Oblique Triangle (Law of Cosines)

Solve ▵D–B′–C using the Law of Cosines to find θ₂.

Step 4

Final Output Angle

Combine the two sub-angles to get the rocker angle θ.

Three-Position Synthesis

Design your own four-bar linkage: Pick three positions where you want the moving bar (the coupler) to go. The program finds the ground pivots A and D that hit all three — when the geometry works out. Sometimes you'll need to nudge a position slightly to get a clean result.

Step 1

Define coupler

Define the moving bar (coupler). Points P and Q set its length and shape. This distance stays the same in every position — drag or type the numbers to set it.

Point P

x y

Point Q

x y

Step 2

Position 1

Position 1 (starting pose): Drag the red bar to move it, or drag point Q to spin it around P. This is the home position — the fixed pivots will connect here.

Step 3

Position 2

Position 2: Move and rotate the orange bar to your second position. Watch the blue dashed lines update — they show where the fixed pivot A could be.

Step 4

Position 3

Position 3 (final pose): Move the green bar to your last position. The dashed circles and fixed pivots A and D will appear — drag to adjust until everything looks good.

Step 5

Bisectors for positions 1 → 2

Pivot A has to sit the same distance from P in every position — that's how a fixed-length crank works. The blue dashed lines are perpendicular bisectors: every point on a bisector is the same distance from the two P's it sits between. Where both bisectors cross is the one spot equidistant from P₁, P₂, and P₃ — your pivot A. Same idea gives D from Q₁, Q₂, Q₃.

Step 6

Bisectors for positions 2 → 3

Your four-bar is built. When the geometry checks out, the moving bar will hit all three positions you set. Check the lengths below, then send it to Explore mode to see how it moves between those positions.

Step 7

Connect the bars

Everything is connected. Pivots A and D stay fixed while the coupler (P–Q) passes through your three positions. Check the lengths, then click Send to Explore to watch it move in real time.

The grid snaps every 0.1 inch. Tip: Once the pivots show up, drag Position 2 or 3 and watch the whole linkage update live — you can design the motion just by eye!