Four-Bar Linkage Simulator

Modified: Mar. 19, 2026

Published: Mar. 19, 2026

The four-bar linkage is the simplest closed-loop mechanism and the building block for most complex machine motion: windshield wipers, excavator booms, aircraft landing gear, and robotic arms all reduce to four-bar chains. This simulator provides complete kinematic analysis with Grashof condition checking, coupler curve tracing, and angular velocity profiles. #FourBarLinkage #MechanismSimulator #KinematicAnalysis

Open Simulator

What You Can Analyze

Angular Positions

Coupler and follower angle profiles across 360 degrees of input crank rotation. See how link proportions control the output motion pattern.

Angular Velocities

Coupler and follower angular velocity profiles. Understand velocity ratios and how they vary through the cycle, critical for timing and speed control.

Transmission Angle

Monitor the angle that determines force transmission quality. When it drops below 40 degrees, the mechanism jams under load. The simulator shows exactly where this happens.

Grashof Condition

Automatic classification: crank-rocker, double-crank, double-rocker, or change-point. Instantly see whether the input link can make a full rotation.

Key Features

Real-Time Animation with Coupler Curve Watch the mechanism move with angle arcs (theta and mu) visible on the diagram. The coupler midpoint traces its characteristic curve. Toggle paths, adjust rotation direction, and export as PNG or animation video.
Eight Analysis Plots Coupler angle, follower angle, coupler angular velocity, follower angular velocity, transmission angle, mechanical advantage, joint B velocity, and coupler curve (X-Y path). All with A/B comparison overlay.
Five Engineering Presets Crank-rocker, double-crank, double-rocker, triple-rocker (non-Grashof), and parallelogram. Each demonstrates a different Grashof classification with pre-verified parameters.
Ground Offset Shift the output pivot vertically from -50 to +50mm. This changes the effective ground length and can flip the Grashof classification, a feature not available in other online simulators.
Open and Crossed Circuits Switch between the two possible assembly configurations to see how the same link lengths produce completely different motion.
Professional Downloads Export CSV data (361 points, 14 variables), PNG charts, animation video (.webm), design specifications with Freudenstein constants and kinematic analysis, lab reports, and FreeCAD Python scripts. Two separate CSVs when A/B comparison experiments are run.

Preset Configurations

Preset	Crank (a)	Coupler (b)	Follower (c)	Ground (d)	Speed	Grashof
Crank-Rocker	40 mm	120 mm	80 mm	100 mm	60 RPM	Yes (a shortest)
Double-Crank	60 mm	80 mm	70 mm	40 mm	30 RPM	Yes (d shortest)
Double-Rocker	80 mm	35 mm	60 mm	100 mm	30 RPM	Yes (b shortest)
Triple-Rocker	70 mm	90 mm	60 mm	110 mm	45 RPM	No
Parallelogram	60 mm	100 mm	60 mm	100 mm	60 RPM	Yes (a=c, b=d)

Equations

Position analysis uses the Freudenstein equation and half-angle substitution:

K1*cos(theta4) - K2*cos(theta2) + K3 = cos(theta2 - theta4)

K1 = d/a,  K2 = d/c,  K3 = (a^2 - b^2 + c^2 + d^2) / (2*a*c)

Velocity analysis from the velocity loop:

omega3 = a*omega2*sin(theta4 - theta2) / (b*sin(theta3 - theta4))
omega4 = a*omega2*sin(theta2 - theta3) / (c*sin(theta4 - theta3))

Where a = input crank, b = coupler, c = follower, d = ground, and omega2 = input angular velocity.

Guided Experiments

Nine structured experiments are available in the Mechanism Design and Simulation course, each with Python analysis scripts and design questions:

Grashof Condition: verify the fundamental classification that determines whether a link can fully rotate
Transmission Angle: map the angle that controls force transmission quality
Comparing Presets: crank-rocker vs double-crank vs double-rocker vs parallelogram
Open vs Crossed: two assembly configurations, same link lengths, different motion
Coupler Curves: trace the paths that generate complex output motion
Parametric Sensitivity: which link length matters most for manufacturing tolerances
Angular Acceleration: inertia forces and speed scaling
Breaking the Mechanism: geometric constraints and failure modes
Ground Offset: how vertical pivot displacement changes Grashof classification and mechanism performance

Try it now: Open the Four-Bar Linkage Simulator
Crank-slider comparison: Crank-Slider Mechanism Simulator
Theory background: Planar Mechanics course

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