Fourbar Extrusion

A four-bar linkage provides a shape changing extrusion die

Prof. Andrew Murray and his team at the Design of Innovative…
MK1 Schematic

MK.1 Mechanical Computer

Nicholas Bodley sent me to for information about…
Bernie Roth

Bernard Roth: The Achievement Habit

I found this book to be remarkable. First, because the initial…
RaceLabTV wants to follow FSAE Teams

Ian Campbell and Jerry Magana are a director/producer team…
Truman Studio

Wheelchair Seating and Racecar Engineering

Truman Pollard's wheelchair seat design which repurposes…
Leg Mechanisms

Walking Machines

An outcome of Mark Plecnik's research on the kinematic synthesis…

MechGen Suspension

MechGen Suspension is our latest iPad app. It is an ambitious…
MechGen on iPhone

MechGen FG is on the iPhone

MechGen FG is now on the iPhone, thanks to the excellent…
Port Closure

Eight-bar Port Closure Tool

This port closure tool curls back on itself to provide internal…
Long travel suspensions

Long-travel six-bar vehicle suspension

Mark Plecnik has applied his research on the design of six-bar…

JPL's ATHLETE Rover Walks, Rolls, and Slides

The ATHLETE Rover is a mixture of a wheeled rover and a walking…
Mechanical Flapping Wing

Linkage Design for Wing Flapping

Mark Plecnik shows that six-bar function generators can be used…
Disney Prototyping System

Linkage Synthesis at Disney Research Zurich

Researchers at Disney Research Zurich provide yet an other design…

Lamina Emergent Mechanisms

BYU Professor Larry Howell studies lamina emergent mechanisms,…
DNA origami mechanisms, Advances in Reconfigurable Mechanisms and Robots, Springer 2012

DNA Origami Mechanisms and Machines

Professors Carlos Castro and Haijun Su have developed what…

MechGen FG App Makes Design Calculations Easy

The MechGen iPad App helps you design a link that connects an…
Shape Changing Linkage

Shape Changing Mechanisms Solve Design Problems

A design problem that engineers frequently encounter is a curve…
Demining Training Aids

3D Printed Demining Training Aids

Training people to diffuse landmines and other live ordnance…

Wearable Robotics Put Spring in Your Step

Wearable electronics or “wearables” are seen as the next…
Waldron Celebration

Waldron Fest: May 16-17, 2013

This poster was prepared as a gift to Ken Waldron on his…
21st Century Kinematics

21st Century Kinematics

The NSF Workshop on 21st Century Kinematics at the 2012 ASME IDETC Conference in Chicago, IL on August 11-12, 2012 consisted of a series of presentations and a book of supporting material prepared by the workshop contributors.

The book is now available at 21st Century Kinematics–The 2012 NSF Workshop.

And here are the seven primary presentations given at the workshop.

  1. Computer-Aided Invention of Mechanisms and Robots. J. Michael McCarthy, Professor, University of California, Irvine.
  2. Mechanism Synthesis for Modeling Human Movement. Vincenzo Parenti-Castelli, Professor, University of Bologna.
  3. Algebraic Geometry and Kinematic Synthesis. Manfred Husty, Professor, University of Innsbruck.
  4. Kinematic Synthesis of Compliant Mechanisms. Larry Howell, Professor, Brigham Young University.
  5. Kinematics and Numerical Algebraic Geometry. Charles Wampler, Technical Fellow, General Motors Research and Development.
  6. Kinematic Analysis of Cable Robotic Systems. Vijay Kumar, Professor, University of Pennsylvania.
  7. Protein Kinematics. Kazem Kazerounian, Professor, University of Connecticut.

Colleagues joined in with two additional presentations:

Many thanks to the contributors and the attendees for an outstanding workshop.

Update: The presentation links have been fixed.

T2 Two and Three Position Synthesis

Four-bar Linkage Synthesis, Two and Three Task Positions

These notes for the Stanford University course ME 322 Kinematic Synthesis of Mechanisms introduce the synthesis of a four-bar linkages that guide the coupler link through two and three specified task positions.

Update.  December 12, 2017.  These notes have been revised to introduce Sandor and Erdman’s formulas for linkage synthesis which solve for the input and output cranks.  This provides a nice pairing with the related equations that are solved for the fixed and moving pivots, directly.

T2 Two and Three Position Synthesis revised v2



T1 Four-bar Linkage Analysis

Four-bar Linkage Analysis Notes

These notes have been prepared for the Stanford University graduate course ME 322 Kinematic Synthesis of Mechanisms.  This first set details the position and velocity analysis of a four-bar linkage. 

Update:  December 12, 2017.  These notes have been revised to represent rotation matrices using boldfaced letters.  Remarkably, because 2×2 matrices commute this allows these matrices to be replaced by complex exponentials and the coordinate vectors to be replaced by complex numbers and the derivations and calculations do not change.

T1 Four-bar Linkage Analysis revised

Superluminal Chapter 4

David finds that surpassing Siggy and Kwan to get to Satellite 9 may have benefits he did not expect. 



Superluminal Chapter 4