Animations of linkage movement.

Trifolium Linkage using contra parallelograms

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Yang Liu designed this linkage using contra parallelograms to trace the trifolium curve.

Fourier Curve Tracing

Fourier Curve Tracing

Fourier Curve Tracing

This is the latest from Yang Liu. It is a mechanical synthesis of the Fourier expansion of the batman logo found on Wolfram.com. The video below shows the operation of this harmonic synthesis.

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SIAM News: Biologically inspired linkage design

SIAM News

SIAM News

This article by Jon Hauenstein with me for SIAM News (Society for Industrial and Applied Mathematics) describes research by Mark Plecnik in the computer-aided design of linkages to provide mechanical movement of a bird’s wing. Here is Mark’s video of the his wing flapping mechanism.

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Heart Trajectory

Heart Linkage

Heart Linkage


This mechanical system was designed by Yang Liu to trace the shape of a heart. The work is inspired by the mechanical 32-element harmonic synthesizer described by Dayton Miller in the 1916 article in the Journal of the Franklin Institute.

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Full Size Folding Bicycle

Folding Bicycle

Folding Bicycle

Michael Sutherland and his team at Zennen Engineering designed this full-size folding bicycle that has a dramatically different folding action from current designs.

Montague Bikes provides a popular line folding full sized bicycles, which fold sideways around the seat tube.
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Zennen Engineering has a new concept that they are kind enough to say was inspired by our UCI Folding Structure. This new design rotates the rear wheel support around the bottom bracket, and folds the front forks against the down tube and seat tube to form a compact package. It is a unique movement.

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Jon Stokes, in our Robotics and Automation Lab, helped by adding the four-bar function generator to combine the two folding actions. It is a great concept, and it will be interesting to see if it achieves commercial success.

Origami Art at BYU

Origami Art BYU

Origami Art BYU


Mechanical engineering students in Prof. Larry Howell’s Compliant Mechanisms Research Group designed and constructed this kinetic structure for the BYU Museum of Art. It illustrates paper folding known as origami.
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A four-bar linkage provides a shape changing extrusion die

Fourbar Extrusion

Fourbar Extrusion

Prof. Andrew Murray and his team at the Design of Innovative Machines Laboratory have developed a dynamic extrusion die that changes shape while in operation. This provides a new capability for rapid manufacture of innovative geometry for metal and plastic bars, channels, hoses, and more. For more information see his laboratory website, University of Dayton DIMLab.

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This video provides an extreme introduction to the DIM Lab at the University of Dayton.

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Mark Plecnik, PhD and Kaustubh Sonawale, PhD

Kaustubh and Mark

Kaustubh and Mark


Mark Plecnik and Kaustubh Sonawale both successfully presented their dissertation defense this week. Their kinematics research has resulted new computational procedures that have made possible many new designs.

See Mark’s web page and Kaustubh’s web page for examples of interesting devices that are the result of their research.

Walking Machines

Leg Mechanisms

Leg Mechanisms

An outcome of Mark Plecnik’s research on the kinematic synthesis of six-bar linkages is a variety of designs for the leg mechanisms of small walking machines.

We hope to build this walker over the summer. It has one drive motor on each side:
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This is my favorite because it couples the legs on one side with a pantograph linkage. The leg joints are living hinges. and it seems this the entire leg system can be cut from a single sheet of plastic:
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This is a design study for a walker with eight legs on one side, 16 total:
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Another version of the six-bar folding linkage

Another version of a six-bar folding linkage

Another version of a six-bar folding linkage


This is a little more compact version of the six-bar folding linkage that Kaustubh Sonawale found using MechGen 3.0.
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