Construction of a Skew Pantograph Leg Mechanism

This video adds a skew pantograph to a four-bar linkage in order to reorient and change the size of the coupler curve. The result is a six-bar leg mechanism with a foot trajectory that is a scaled version of the original coupler curve.

Construction of Klann-style Leg Mechanism

In this video, we start with a four-bar linkage and coupler curve and construct an additional crank with a floating link connected to the coupler point. This floating link becomes the leg of the Klann-style leg mechanism. Adjustment of the dimensions of the added links shapes the foot trajectory.

Construction of a Translating Link for a Leg Mechanism

This video starts with a four-bar linkage with a coupler curve that is to be used as the foot trajectory for a leg mechanism. It presents a Geogebra construction of two additional bars, one of which is connected to the coupler point and moves without rotating. This means the bar can be expanded into a leg that places the desired coupler curve where the designer specifies. This is described in Chapter 4 of Kinematic Synthesis of Mechanism.

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

This video shows the construction of the cubic of stationary curvature. The intersection of the cubic of stationary curvature with the inflection circle, iw Ball’s point which is a coupler point that traces a locally straight line trajectory.

This video also shows how to vary the coupler point and the dimensions of the reference polygon for the four-bar linkage to vary the shape of the coupler curve.

Construction of the Inflection Circle for a Four-Bar Linkage

This tutorial constructs the inflection circle for a particular configuration of a four-bar linkage. This construction was recommended by my colleague Gordon Pennock because it is simpler than the one I provide in my book Kinematic Synthesis of Mechanisms.

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.