Animations of linkage movement.

Trifolium Contra-parallelograms

Trifolium using contra-parallelograms

Trifolium Contra-parallelograms

Trifolium Contra-parallelograms

Yang Liu shows that a simple linkage can draw the trifolium curve.

For comparison here is the Kempe linkage that draws a trifolium curve obtained by Alexander Kobel.

Fourier Curve Tracing

Fourier Curve Tracing

Fourier Curve Tracing

Fourier Curve Tracing


This animation by Yang Liu is inspired by the mechanical Fourier synthesizer described by Dayton Miller, see A 32-element harmonic synthesizer.

This mechanical system combines the terms of a Fourier approximation of the batman curve found on Wolfram.com. The video below shows this device draws the batman curve.

SIAM News

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.

Heart Linkage

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.

Folding Bicycle

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.

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.

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.

Montague Bikes provides a popular line folding full sized bicycles, which fold sideways around the seat tube.

Target Profiles for Morphing Linkage

Actuating Morphing Linkages

Target Profiles for Morphing Linkage

Target Profiles for Morphing Linkage

Lawrence Funke and Prof. James Schmiedeler of the University of Notre Dame Locomotion and Biomechanics Lab show that the movement of a morphing linkage through its target profiles can be improved by coordinating actuation of the sub-chains. This was presented at the Mechanisms and Robotics Conference which was part of the 2015 ASME Design Engineering Technical Conferences, August 2-5, in Boston, MA. The video below shows the improvement obtained by moving from 1 to 3 coordinated actuators.

Fourbar Extrusion

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.

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

Leg Mechanisms

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:

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:

This is a design study for a walker with eight legs on one side, 16 total:

Another version of a six-bar folding linkage

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.

A six-bar linkage designed to fold a structure

Six-bar linkage folds a structure

A six-bar linkage designed to fold a structure

A six-bar linkage designed to fold a structure

This six-bar linkage was designed to deploy and stow a structure. It was developed by Kaustubh Sonawale to demonstrate the capabilities of MechGen 3.0.