Why does the rocker only swing back and forth instead of rotating in a full circle?

This is defined by the Grashof condition and the specific arrangement of link lengths. In a crank-rocker, the shortest link is designated as the crank and can rotate fully. The rocker is adjacent to the fixed ground link and is longer than the crank; its length and the geometry of the other links constrain its motion to an oscillating swing. If all links could rotate fully, it would be a double-crank mechanism.

What is the practical use of the complex path traced by the coupler point?

The coupler curve can generate precise non-circular motions without cams or gears. This is exploited in machinery for tasks requiring specific tracing paths. For example, certain coupler curves approximate straight lines, used in early automotive suspension designs and drafting machines. Others create dwell periods or specific lifting profiles in agricultural and packaging equipment.

Does the simulator account for the forces needed to move the linkage?

No, this is a purely kinematic model. It calculates positions, velocities, and accelerations based on geometry and input motion, assuming ideal, massless links. To analyze forces, torques, or power requirements, a dynamic analysis using Newton's laws or Lagrangian mechanics would be required, considering mass, inertia, and external loads.

How does changing the crank speed affect the motion of the other links?

Changing the crank's angular speed scales all angular velocities and accelerations linearly and quadratically, respectively, but does not alter the fundamental path or range of motion. The kinematic geometry (link lengths) determines the path and oscillation angles. Speed changes affect how quickly the linkage moves through its cycle, impacting velocities and inertial forces in a real system.

Four-Bar Linkage

Crank–rocker geometry with coupler-curve trace; link lengths and crank speed.

About this model

A four-bar linkage is a fundamental mechanism in mechanical engineering, consisting of four rigid links connected by four pin joints to form a closed kinematic chain. This simulator specifically models a crank-rocker configuration, where the shortest link (the crank) rotates fully, driving the rocker link that oscillates through a limited arc. The remaining two links are the fixed ground link and the floating coupler link. The core physics involves planar rigid-body kinematics, governed by the Grashof condition for mobility: the sum of the shortest and longest link lengths must be less than the sum of the other two lengths for at least one link to rotate fully. The motion is solved using loop-closure equations, typically expressed in complex number or vector form: a*e^(iθ_a) + b*e^(iθ_b) = d + c*e^(iθ_c), where a, b, c, d are link lengths and θ are their angles. By varying the crank's angular velocity, users observe the resulting angular velocities and accelerations of the other links, derived through differentiation of the position equations. A key feature is the tracing of the coupler curve—the complex path traced by a point on the coupler link. This path can approximate straight lines, arcs, or more complex shapes, demonstrating why four-bar linkages are ubiquitous in applications like windshield wipers, folding chair mechanisms, and automotive suspensions. The simulator simplifies reality by assuming ideal, massless, rigid links with perfect joints (no friction or backlash) operating in a plane. Interacting with it, students learn to visualize kinematic chains, apply the Grashof criterion, understand the relationship between geometric parameters and motion output, and see how complex motions are generated from simple rotary inputs.

Who it's for: Undergraduate engineering students in courses on dynamics, mechanism design, or robotics, as well as advanced high-school students in project-based STEM programs.

Key terms

Four-Bar Linkage
Kinematics
Grashof Condition
Crank-Rocker Mechanism
Coupler Curve
Loop-Closure Equation
Planar Mechanism
Degrees of Freedom

How it works

Grashof-class mechanisms can produce a full crank rotation; the traced path is a coupler curve used in machine design for guided motion.

Frequently asked questions

Why does the rocker only swing back and forth instead of rotating in a full circle?: This is defined by the Grashof condition and the specific arrangement of link lengths. In a crank-rocker, the shortest link is designated as the crank and can rotate fully. The rocker is adjacent to the fixed ground link and is longer than the crank; its length and the geometry of the other links constrain its motion to an oscillating swing. If all links could rotate fully, it would be a double-crank mechanism.
What is the practical use of the complex path traced by the coupler point?: The coupler curve can generate precise non-circular motions without cams or gears. This is exploited in machinery for tasks requiring specific tracing paths. For example, certain coupler curves approximate straight lines, used in early automotive suspension designs and drafting machines. Others create dwell periods or specific lifting profiles in agricultural and packaging equipment.
Does the simulator account for the forces needed to move the linkage?: No, this is a purely kinematic model. It calculates positions, velocities, and accelerations based on geometry and input motion, assuming ideal, massless links. To analyze forces, torques, or power requirements, a dynamic analysis using Newton's laws or Lagrangian mechanics would be required, considering mass, inertia, and external loads.
How does changing the crank speed affect the motion of the other links?: Changing the crank's angular speed scales all angular velocities and accelerations linearly and quadratically, respectively, but does not alter the fundamental path or range of motion. The kinematic geometry (link lengths) determines the path and oscillation angles. Speed changes affect how quickly the linkage moves through its cycle, impacting velocities and inertial forces in a real system.

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About this model

How it works

Frequently asked questions

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Frequently asked questions