For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...
🚀 New Design Guide Available
Don't just read about it—build it. Check out our new tutorial:
How to Design a Hoeken’s Linkage in Excel (with Free VBA Simulator) »
Don't just read about it—build it. Check out our new tutorial:
How to Design a Hoeken’s Linkage in Excel (with Free VBA Simulator) »
Introduction to the Hoekens Linkage
The Hoekens linkage is a specialized four-bar mechanism designed to convert rotational motion into an approximate straight-line motion. While it serves a similar purpose to other straight-line generators, its unique coupler curve—a "tear-drop" shape—makes it exceptionally useful for intermittent motion and walking machines.
One of the most fascinating aspects of kinematic theory is the concept of "Cognates." The Hoekens linkage is actually a cognate linkage of the Chebyshev Straight-line Mechanism. This means that while the physical structure and link lengths differ, they can generate the exact same coupler curve geometry.
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Kinematics and Optimization
Unlike the Watt linkage, which has a central pivot, the Hoekens linkage relies on a rotating crank to drive a floating coupler arm. The "straight" portion of the curve occurs when the mechanism is roughly at the bottom of its cycle.
In his classic text Design of Machinery, Robert L. Norton highlights the specific link ratios required to achieve the smallest structural error. This optimization is critical; slight deviations in link length can turn the straight line into a curve, causing vibration or inaccuracy in the machine.
Why is the "Tear Drop" Shape Important?
The coupler curve has two distinct phases:
- The Straight Phase: Roughly 180 degrees of the crank rotation results in near-linear motion with relatively constant velocity.
- The Return Phase: The mechanism quickly retracts and loops back to the start.
Application: Walking Robots
This velocity profile makes the Hoekens linkage a favorite for walking robots. The straight line acts as the "foot" dragging along the ground (propelling the robot forward at a constant speed), while the loop phase lifts the leg and returns it to the front.
It is often compared to the Klann Linkage or the Jansen Linkage, but the Hoekens is significantly simpler to build as it requires fewer moving parts.
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Video Examples
Below are excellent examples of the mechanism in action, ranging from robotics to kinetic art.
1. Walking Robot Leg Test
Notice how the "foot" stays flat against the ground for half the cycle.
2. Marble Machine Application
Here, the linkage is used to lift marbles in a straight vertical line.
3. Multi-Legged Simulation
A simulation showing how multiple legs coordinate.
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