People have periodically asked me for "mathematical proof" to back up the written explanations of how dw-link creates its position sensitive anti squat response. I usually point people to the dw-link patents. In the patents I've taken care to describe in detail how to analyze and kinematically characterize a chain or shaft driven suspension system.
The written description of how to characterize performance of a linkage suspension system in dw-link's 7,128,329 patent is and remains to be the worlds first and only complete and accurate written text on the subject. The method of plotting a curve of anti-squat versus travel (to use a s a verifying metric during the design and testing process) was also first published in the 329 patent. I later discussed this idea with author Tony Foale in late 2005, and he was receptive enough to include anti-squat graphs in his latest revision of his book, Motorcycle Handling and Chassis Design. If you are interested in this type of thing, you should buy this book.
I realize that not everyone knows that patents are available for anyone to read online at any time, so here is a link to one of the dw-link patents, the '329 version.
I also realize that not every person who reads this is going to be able to readily understand how to analyze suspensions, but those who are skilled in the art will have no problems at all. I tried to break this subject down to its simplest and most concise terms in a step by step fashion. Take your time and have fun!
dw-link 7128329 patent, September 2004.
Keep in mind that all figures and curves in the '329 patent are purely hypothetical, and intentionally not an exact replica or necessarily accurate to what you would find on a dw-link bike. The curves and figures are presented to prove the kinematic analysis and nothing further.. :)