Machine Design

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Diesel Engine

Diesel engine animation

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

Engine animations

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MechGen 4

Spherical Four-bar Linkage Design: Mech Gen 4

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

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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

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Type Synthesis

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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

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

Workshop Presentations: 21st Century Kinematics

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Smitty Training

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Spherical Fourbar

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21st Century Kinematics

21st Century Kinematics

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

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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…

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.