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

This tutorial shows how to use Geogebra to construct the canonical coordinate system for a particular configuration of a four-bar linkage.

It starts with a quadrilateral which is to be the configuration of the linkage at a particular instant. Then constructs the velocity pole and the instant center of the positions of the input and output cranks. Connecting these lines defines the collineation axis.

Bobillier’s theorem completes the construction by defining the tangent to the moving centrode.

Walking Robot Student Project

Walking Machine Class Projects: Ohio State ME 5751

Prof Haijun Su at Ohio State University had his students design walking machines for their final project in ME 5751. Here are videos of four project teams from that event.

Team A:

Team B:

Team C:

Team D:

Sphinx and Sphere VR and the History of Kinematic Synthesis

Our Sphinx software was the first computer-aided design system for spherical linkages. It used IRIS system by Silicon Graphics. Collaboration with Judy Vance lead to a Virtual Reality version of this design system.

This is a link to the description of this research at Iowa State University.

This video shows the operation of these two design systems;


LINCAGES and the History of Kinematic Synthesis

The linkage design software developed by Art Erdman and his students at the University of Minnesota, called LINCAGES: Linkage INteractive Computer Analysis and Graphically Enhanced Synthesis Package, was developed in 1977 through 2000. This is a link to his information site. His guide map that evaluates all of the linkages formed from points on the circle-point and counter-point curves was a nice innovation.

This link connects to a YouTube video shows the linkage design process using LINCAGES:


KinSyn and the History of Kinematic Synthesis

My first experience with computer based kinematic synthesis was a 1982 presentation by Roger Kaufman of his KinSyn linkage design software on an Apple II microcomputer. This is a link to his description of his experience in those early days of computer-aided design of linkages.

His paper that describes this software can be found here. The photos are a terrific look into the computer technology in the 1970’s.

Here is a video that describes the operation of KinSyn, which I find to be an impressive integration of kinematics calculations in the background with a useful graphical presentation of information to the designer. I have to say that the graphical display was impressive in its day.


Strider and TrotBot at

Just after I published my book Kinematic Synthesis of Mechanisms with its emphasis on leg mechanisms, I found two more interesting eight-bar legs from the designers at

This is a Geogebra animation of the leg mechanism for the Strider walker. It is a symmetrical design that allows the formation of a second foot assembly by simply adding two more bars.

Strider leg mechanism.

This is an animation of the leg mechanism in the TrotBot walker.

TrotBot leg mechanism.

About Geogebra-Kinematic Synthesis of Mechanisms

The animated four-bar linkage FHJD is constructed using dimensions as the quadrilateral ABCD. The dynamic geometry software Geogebra maintains the dimensions of FHJD as the points of ABCD are moved. The result is that the animated linkage changes to match the new dimensions. This can be seen in following Movie.  For more information see Kinematic Synthesis of Mechanisms.

Chapter 6 Animations-Kinematic Synthesis of Mechanisms

Here are the eight Movies in Chapter 6 of Kinematic Synthesis of Mechanisms.

Movie 6.1

Movie 6.2

Movie 6.3

Movie 6.4

Movie 6.5

Movie 6.6

Movie 6.7

Movie 6.8

Chapter 5 Animations-Kinematic Synthesis of Mechanisms

Here are the four Movies in Chapter 5 of Kinematic Synthesis of Mechanisms.

Movie 5.1

Movie 5.2

Movie 5.3

Movie 5.4

Chapter 4 Animations-Kinematic Synthesis of Mechanisms

Here are the four Movies in Chapter 4 of Kinematic Synthesis of Mechanisms.

Movie 4.1

Movie 4.2

Movie 4.3

Movie 4.4