View Full Version : Re: Homogeneous transformations and the history of matrix algebra

07-08-2005, 09:15 AM
Hello Paolo:

I suspect you are hinting at calling these affine transformations rather
than homogeneous, though I am not sure. I don't have the information at my
fingertips to trace it back further than below, but these would be great
starting points:

Denavit, J. and Hartenberg, R. S., "Kinematic Notation for Lower-Pair
Mechanisms Based on Matricies," ASME J. of Applied Mechanics, June
1955: 215-221.
Hartenberg, R. S. and Denavit, J., "Kinematic Synthesis of Linkages,"
McGraw-Hill, New York, 1964, Chapter 12.

In robotics, these two are credited with quite a number of applications,
however they are probably not the first to use it. These are the earliest
references I have found for this transformation and I suspect that one of
those articles will have other references or authors who did it [probably
much] earlier.

Good luck tracing back the history, I'm interested in what you uncover.

Best regards,


Daniel R. Baker, Ph.D., President
Kinetic Research & Design, Inc. -- "Biomedical Systems and Solutions"
13203 39th Ave. NE, Suite 101
Seattle, WA 98125-4615 USA
206.361.8324 (phone) -- 206.417.7873 (fax)
Aff. Assist. Professor -- Dept. of Bioengineering, University of Washington


**NOTE** (legalese) This email belongs to
Kinetic Research & Design, Inc. and its intended recipients.
Any other use is strictly prohibited. If you received this in error,
destroy all copies and notify the sender. This is confidential
and does not belong to you.