Kinematic Synthesis of Mechanisms

Walker Group 6

Walker Solid Model Animations

Here are the solid models of some of the walkers designed by…
Leg Mechanism AnimationJMM

Animation of the Leg Mechanism

This is an animation of the leg mechanism designed using function…
Three Position Synthesis 2

Construction for Three-Position Synthesis of a Four-Bar Linkage

The graphical construction of a four-bar function generator…
MechGen on iPhone

Five Position Synthesis of Four-bar Function Generators

Our MechGen FG iOS application provides five position synthesis…
Two position synthesisJMM

Construction for Two-Position Synthesis of a Four-Bar Linkage

The graphical construction of a four-bar linkage that coordinates…
Skew Pantograph Leg MechanismJMM

Construction of a Skew Pantograph Leg Mechanism

This video adds a skew pantograph to a four-bar linkage in order…
Klann-style Leg MechanismJMM

Construction of Klann-style Leg Mechanism

In this video, we start with a four-bar linkage and coupler…
Construct a Translating LinkJMM

Construction of a Translating Link for a Leg Mechanism

This video starts with a four-bar linkage with a coupler curve…
Cubic of Stationary CurvatureJMM

Construction of the Cubic of Stationary Curvature for a Four-bar Linkage

This video shows the construction of the cubic of stationary…
Inflection CircleJMM

Construction of the Inflection Circle for a Four-Bar Linkage

This tutorial constructs the inflection circle for a particular…
Tutorial: Canonical FrameJMM

Construction of the Canonical Coordinate System for a Four-Bar Linkage

This tutorial shows how to use Geogebra to construct the canonical…
Walking Robot Student Project

Walking Machine Class Projects: Ohio State ME 5751

Prof Haijun Su at Ohio State University had his students design…

Sphinx and Sphere VR and the History of Kinematic Synthesis

Our Sphinx software was the first computer-aided design system…

LINCAGES and the History of Kinematic Synthesis

The linkage design software developed by Art Erdman and his…

KinSyn and the History of Kinematic Synthesis

My first experience with computer based kinematic synthesis…

Machine Design

DMG-LIB Library mechanism library

The Digital Mechanism and Gear Library has a terrific collection…
ipad screenshot

MechGen Suspension

MechGen Suspension is an iPad application that calculates…
Veyron W16

W16 Veyron engine

This animation shows the W16 Bugatti Veyron engine with four…
V8 Valves

Cam actuation in a V8 engine

This animation shows the operation of the cam shaft, lifters…
Diesel Engine

Diesel engine animation

This animation shows the part by part assembly of a four cylinder…

Engine animations

The web-site provides animations of a variety…

Spherical Four-bar Linkage Design: Mech Gen 4

This version of Mechanism Generator uses five orientations of…
Design Exchange

Design Exchange and HCD Connect

Interesting examples of web-sites designed to share information…
MechGen 3

Mechanism Generator 3.0

Our Mechanism Generator 3.0 software reads a SolidWorks sketch…
MechGen 2

Mechanism Generator 2.0 (MechGen 2)

We have a trial version of our Mechanism Generator 2.0 software…

Lecture Notes

Introduction to Linkage Synthesis

This introduction to the graduate course ME 322 Kinematic…
Curvature Theory

Curvature Theory for Planar Point Trajectories

These notes for the Stanford University graduate course ME 322…
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…
T1 Four-bar Linkage Analysis

Four-bar Linkage Analysis Notes

These notes have been prepared for the Stanford University graduate…
Type synthesis

Type Synthesis, Assur Groups, and Rigidity

These lecture notes introduce students to research on classifying…
MK1 Schematic

MK.1 Mechanical Computer

Nicholas Bodley sent me to for information about…
Four-bar function generator

Four-bar function generator: Open a door

Select this link, Four-bar linkages, for a Geogebra book…
Kinematics Summer School

Kinematics Summer School

Profs. Carl Nelson and Anurag Purwar organized a Summer School…
Introduction to Linkages

Introduction to Linkages

Please select this link to open the Geogebra Book containing…
Mechanical Advantage

Mechanical Advantage

This video from the University of Dayton narrated by Prof.…
Svoboda Computing Mechanisms

A. Svoboda: Computing Mechanisms and Linkages

Select this link to download a .pdf version of A. Svoboda,…
Kempe Straight Line

A. B. Kempe: How To Draw A Straight Line

Select this link to download a .pdf version of A. B. Kempe,…
Workshop Schedule: 21st Century Kinematics

Workshop Presentations: 21st Century Kinematics

The NSF Workshop on 21st Century Kinematics at the 2012 ASME…
Wikipedia Logo

Machines on Wikipedia

I have spent quite a bit of time revising articles on machines…
Spherical Fourbar

Spherical Four-Bar Linkages

Here is something new. Our Mathematica notebook can find…

Have a linkage design challenge? We can help.

MechGen 3 Contact us on this feedback form. We look forward to providing our MechGen synthesis software to simplify your linkage design process in SolidWorks.

Linkage Synthesis Theory

The mathematical synthesis of linkage movement provides a powerful tool for invention. However, the specified task may not have useful solutions, and the search for successful tasks can be discouraging.

To address this, we automate the search and evaluation process within tolerance zones specified by the designer.  These Mathematica notebooks implement our approach to finding defect-free four-bar linkage designs.

RR Constraint Synthesis for Function Generation

Synthesis of an RR Constraint

Synthesis of an RR Constraint

An important technique in kinematic synthesis is the design of an RR constraint that controls the movement of two joints of an existing serial chain. For a given RR serial chain, like OA shown above, we can specify its movement through five required task positions. This provides the information needed to design an RR constraint, GW above, that ensures the system moves through the required task positions.

This technique is called function generation in the kinematics synthesis literature, because the synthesized RR constraint maintains a specified relationship between the joint angles alpha and beta at joints O and A.


Select this link to download our Mathematica notebook: RR-Constraint Synthesis. It uses a given RR chain and the associated task to determine tolerance zones, where it searches for defect-free designs.  As above, this file may download as text file so remove the .txt extension, then it should be readable by Mathematica. If you have any questions, please contact me.

Five-Position Synthesis of a Four-bar Linkage

Here we show a four-bar linkage designed to guide the coupler through five required task positions.

Please download and try our updated Mathematica notebook: Five-Position Synthesis. It searches in the vicinity of the required task for sets of positions that yield defect-free four-bar linkages.  It may download as textfile so remove the .txt extension, then it should be readable by Mathematica.

The video below shows the operation of this notebook.

If you have any problems or advice, please contact me.