Kinematic Synthesis of Mechanisms

More Halloween ProjectsMDA

More Halloween Linkage Designs

The Halloween decorations designed by project teams 4, 5 and…
Halloween design componentsMDA

Halloween Design Project

Students in my MAE 245 Advanced Kinematic Synthesis class have…
Walker Group 6

Mechanical Walker Project Animations: Spring 2019

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

Leg Mechanism for a Mechanical Walker

This is an animation of the leg mechanism for a mechanical walker…
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…

Machine Design

Oberlin Sphere

Instruments for Natural Philosophy

This site has photographs of a large number of devices used to…
Four-bar Synthesis

Linkage Synthesis Demonstration

This shows the operation of our Mathematica notebook for five-position…

Technical information for mechanical components

Stock Drive Products has an array of downloadable catalogs…

Automotive components

Chris Longhurst has assembled a number of descriptive articles…

Parallel Mechanisms information center

Ilian Bonev maintains bibliography and patent databases on parallel…

Mechanical Properties of Steel

The MatWeb site provides detailed information about materials…
Total Materia

Unified Numbering System for Materials

There are a variety of numbering systems for materials such as…

Material Properties Charts

Cambridge University provides a useful overview of materials…
Periodic Table

NIST Periodic Table

The National Institute of Standards and Technology provides…

Materials Selection in Mechanical Design

Michael Ashby presents materials information in a practical format…

Lecture Notes

21st Century Kinematics

21st Century Kinematics

This is a draft of my editorial on 21st Century Kinematics for…
Kinematics and Computers

Kinematics, Polynomials and Computers–A Brief History

Select this link to the .pdf of Kinematics, Polynomials,…
Mathematica Notebook for Linkage Synthesis

Mathematica Notebook for Four-Bar Linkage Synthesis

Select this link to download our Mathematica notebook for…
Cam Driven Artist

Cam-driven artist mechanical toy

This video shows the operation of a cam-driven toy artist. I…
Delft Models

Linkage models at TU-Delft

Prof. A. J. Klein Breteler maintains an array of mechanism models…
Elementary Robotics

Elementary Robotics

The basic properties of robots can developed by studying planar…
Intro to Mechanisms

CMU’s Introduction to Mechanisms

Yi Zhang, Susan Finger and Stephannie Behrens have prepared an…

Four-bar linkage analysis: Slider-crank

The slider-crank is an important mechanism with a wide range…
Four-bar linkage analysis

Four-bar linkage analysis: 4R quadrilateral

The four-bar linkage is a basic machine component. It comes in…

DC motor torque and power

A copy of my notes on DC motor torque and power can be downloaded…

DC motor basics

The basic principles of DC motors are presented by Joe Wolfe…

Geometric Dimensioning and Tolerancing

This is a link to notes on Geometric Design and Tolerancing by…
Chris Sangwin

C. J. Sangwin’s linkage movies

Chris Sangwin has a nice collection of linkage movies at How…

Brock Engineering’s mechanism home page

Fred Klingener has generated a number of interesting mechanism…

Kinematic models for design

The KMODDL team at Cornell University maintains an excellent…

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.