Kinematic Synthesis of Mechanisms: A project based approach

This book is an introduction to the geometric theory used to design linkage systems that are critical components of machines ranging from vehicle suspensions to robot arms. The focus throughout is on graphical synthesis of linkages to control the movement of the legs for a walking machine.

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Increasingly complicated walking machines obtained from patent drawings, art and technology are used to motivate the theory. Starting with legs formed by rotating cranks, we move to legs constructed from four bar linkages with specially shaped coupler curves. This leads to a search for coupler points that have near straight line trajectories, and motivates constructions for the inflection circle and cubic of stationary curvature. We also consider cognate linkages and those with symmetric coupler curves.

The use of an RR chain controlled by the coupler of a four-bar linkage is our introduction to six-bar linkages. Then skew pantographs that provide scaling and reorientation of a coupler curve for better walking movement yields eight-bar linkages. The legs designed by Theo Jensen and Amanda Gassaei are shown to implement four bar function generators that control the joint movement of an RR chain. This leads to graphical two and three position synthesis of four-bar function generators, which are applied to the design of legs with two and three specified configurations.

We end with a description of the duty factor and support pattern needed for two, four and six legged walking machines. The challenge of steering and suspension is left for the future.

Chop Wood Carry Water by R. A. White

R. A. White is the author of Chop Wood Carry Water and Superluminal.  He often writes under the pseudonym R. W. Frost.  Here is his IMDB page.  He is a lecturer in the theater arts program at UCLA, and the director of the Toni Martini Variety Hour.

2013 Energy Invitational

Smitty’s Video Lectures on Racecar Engineering

Here are Smitty’s video lectures on Introduction to Racecar Engineering assembled into one post. I am sure you will find these 20 videos to be of great value.

01 Getting Started

02 Weight and Balance

03 Strength and Stiffness

04 Chassis Design

05 Suspension Design

06 Shock Absorbers

07 More on Suspensions

08 Springs

09 Steering

10 Caster

11 King Pin Inclination

12 Toe and Camber

13 Tires

14 Transmission

15 Electronic Fuel Injection

16 Performance Ideals

17 Team Don’ts

18 Team Do’s

19 Smitty’s Library

20 Thank you

Chop Wood Carry Water on Amazon

Chop Wood Carry Water on

Chop Wood Carry Water is now available on Please select the link Chop Wood Carry Water.


Introduction to Theoretical Kinematics, paperback on

I am pleased to report that a paperback version my book Introduction to Theoretical Kinematics: the mathematics of movement is on-line with I have updated it to reflect current terminology in Robotics and to correct all of the errors that I could identify. Please select the link Introduction to Theoretical Kinematics.

Design of Linkages to Draw Curves, GRASPLab Seminar

On May 8, 2018, I was pleased to give a seminar at the University of Pennsylvania GRASPLab:  McCarthy Seminar.

They also videotaped my lecture.  Here it is:

2018 UCI Phantom FSAE Autocross

This video captures the first autocross run by Matt Clark at the 2018 FSAE Lincoln competition. If I remember correctly is was 62.7sec, just behind their earlier 61.9sec run. Matt’s second run, the final of four runs, was anticipated to be even better but there was a problem with the car.

This view of the course, driver, and front wheels is excellent for understanding the challenges of this competition.

Chop Wood Carry Water on iTunes

R. W. Frost’s story Chop Wood Carry Water is now available on iTunes. Select the image to link to the iTunes Preview website.

Itunes Chop Wood Carry Water

Itunes Chop Wood Carry Water

Chop Wood Carry Water, Full Length

This is a combination of the 10 episodes of R. W. Frost’s Chop Wood Carry Water into one publication. Scroll in the window or use the page up and page down buttons at the bottom.

Chop Wood Full Length 2
Fab 03 Hand tools

Smitty’s Fabrication Training Videos

This series of training videos were prepared by Robert “Smitty” Smith to help our engineering students understand the principles of fabrication necessary for project based learning.

Hand Tools



Measurements and Layouts

Metal Forming, Part 1

Metal Forming, Part 2

Cutting, Grinding and Fitting

Advanced MIG Welding