Theory, text, illustrations, and editing by Ken Sasaki
4-bar path analysis by Peter Ejvinsson
Spanish Version translated by Antonio Osuna
Additional translation and edition for the web y José Rubio
“Linkage” suspension simulation by Gergely Kovacs
© Kenneth M. Sasaki 2001, all rights reserved
{The authors welcome the reposting or reprinting of this page or any part of it, so long as full credit is given to the authors}
Path Analysis (PA) is a qualitative method for analyzing the pedaling, braking, and shock absorption characteristics of full suspension frames. The objective is to allow anyone to determine the true merits of any suspension design claims with regard to these characteristics. While the principles here apply in general, we have focused on the non-URT (this usually means bottom bracket on the front triangle and we will use the term to mean so in this work unless otherwise stated), since these designs constitute the lion’s share of bikes produced these days.
Most theories on bicycle suspensions one sees attempt to find “the proper pivot point or points” which will make the frame shock non-reactive to pedaling at equilibrium or “sag” (in fact, it is impossible for any frame geometry to do this either exactly or universally, and getting close in any particular case will introduce other problems). A precise quantitative treatment of suspension geometries is a very involved process that requires significant assumptions, even in the most simple of cases. A number of simple theories purport to find correct geometries that eliminate rear shock activation at sag, but to this author’s knowledge, none are sound (this excludes the Giant NRS which is meant to be run with no sag). We look at a few of these at the end of the work to demonstrate how PA can be used.
The consumer should be most concerned about getting past industry hype. So rather then spending a lot of time trying to identify proper pivot locations and so forth (beyond an intuitive understanding), we will focus on the issue of what performance characteristics are achievable with viable suspension designs and how one might achieve them in principle. This analysis method is intended as a consumer tool that will allow one to accurately judge marketing claims, as well as the relative merits of suspension designs and theories.
We want this work to be useful to those with absolutely no technical background, so we present the “Main Conclusions” up front in this first chapter. Those with no technical background should also find the “Bogus Marketing” section completely accessible.
In chapters II, III, IV, and V we have included recommendations for reading and difficulty for each numbered section, stating:
Read this section if:
You wish to accomplish “this or that” objectives. This section is of “such and such” importance.
Skip this section if:
You are not interested in “this or that” objectives.
This section is “stated difficulty rating”.
Here, “stated difficulty rating” varies among: Not difficult, less difficult, moderately difficult, more difficult, and most difficult. The level of difficulty is referenced to a typical person with about a year of good solid college physics.
We hope that this will help those with a less technical background navigate around the more difficult and less necessary sections. Those with a less technical background should still find the not difficult and less difficult sections, as well as the conclusions from all sections, understandable.
About the second chapter, “Some Useful Suspension-Related Mechanics”:
We have chosen methods of analysis with an eye toward keeping math to a minimum, but some basic physics knowledge is unavoidable.
Much of this chapter is not necessary if one merely wishes to use Path Analysis to evaluate different suspension designs (which is the main intent of this paper). For this application, we strongly recommend only the “Reference Frames” section.
We have included this chapter mainly as a physics primer for those who wish to rigorously verify Path Analysis and delve more deeply into bicycle suspension physics. If one wishes to independently verify the validity of PA, the “Some Important Concepts” section is most critical to understand. The concluding statements in “An Intuitive Look at Forces and Torques” are also of value. We reemphasize; much of the rest of this chapter is related to Path Analysis only in establishing finer points and is not truly necessary (although, the knowledge will be useful to anyone contemplating bicycle design and some of it will make PA more accessible).
One will also need certain concepts from this chapter if one wishes to completely understand certain flaws in some of the theories detailed in the fifth chapter, “Flawed Theories and Bogus Marketing”. Most important among these is the “Center of Mass” (CM) concept, as applied to forces acting through the various wheels and cogs within a bicycle. To this author’s knowledge, this concept has previously been unknown in the bicycle industry.
About the third chapter, “Path Analysis”:
This is where the main theory is presented. We don’t consider any of the sections to be more then moderately difficult. We suggest that all readers read all sections, even if some things are not clear.
About the fourth chapter, “Wheel Path Analyses of Some Existing Models”:
This chapter contains the cad drawings by Peter Ejvinsson. These drawings are most informative in conveying information about what is out there at the present time.
Most of the major design types that are more then trivial to evaluate are covered. For the most part, the material in this chapter is extremely easy to understand, the one exception being parts of the “The Virtual Pivot Point (VPP)” section.
In addition, a “Linkage data” link to Gergely Kovacs’ “Linkage” suspension simulation program (see below) is provided in each frame’s section (for which ltx data files have been pre-made). This program displays the most important characteristics of each frame. Clicking on the link in each frame’s section will automatically bring up data on that frame (note that the Linkage program must first be installed, again, see below).
About the fifth chapter, “Flawed Theories and Bogus Marketing”:
The original motivation for the production of this work was the ubiquity of false theories emanating from bicycle manufacturers and industry magazines, and circulating in bicycle-related web sites. We have thus devoted considerable space to demonstrating the flaws in some well-known and widely accepted theories.
Some of the false theories and marketing are associated with well-known names. This has made the work somewhat controversial. However, we note here, as well as in the chapter, that in all cases involving false theories, vigorous efforts were made to contact and discuss matters with the associated parties, before the release of this work.
One of the oldest and most respected of full suspension frame manufacturers has warned this author that the bike industry is very small and generally not kind to “realists”. He also warned that some “retaliation” should be expected and indeed, there has been some.
We are committed to exposing industry hype and nonsense, and to giving the public the best possible chance to make informed decisions, so we will not be deterred by retaliation. While we feel it unfortunate that some of this information has caused a good deal of consternation to some who have already made some very expensive purchases, we will continue with the circulation of this information for the greater public good.
We also note that, generally, the feedback from the industry has been positive; including, we are told, positive comments from one of Renault’s senior suspension engineers.
About the “Glossary”:
At this time, the “Glossary” has been done to explain terms in this first “Primary Concerns” chapter that may not be familiar to those new to mountain biking. We have not provided a detailed account of scientific terms in the later sections because of time constraints. We hope that those venturing into these sections will have adequate prior knowledge or know how to obtain such knowledge from more fundamental sources, or that the bold-written essential information will suffice to give a reasonable understanding. In the future, we hope to provide a more detailed account of scientific terminology.
About the “Linkage” suspension simulation program:
Linkage has been created by Gergely Kovacs to produce the most important information about any 4-bar rear suspension that one might want to concider.
To use Linkage, one must first download the self extracting zip file and instal the program. This can be done by clicking on any of the “Linkage” links in this page. One may then view suspension designs that are currently on the market or input the dimensions for any other linkage configuration that one desires.
The combination of theory presented in the text here and this program should allow any user to develope a keen intuition for comparing the pedaling and shock absorbtion characteristics of almost all full suspension designs.
To install Linkage, click on one of these “Linkage” links. You will be guided through a series of dialogue boxes. The installation defaults will install the Linkage folder, containing the program and ltx data files to C:\Program Files\Linkage2. If you like, you can specify another location. Shortcuts to various Linkage entities, as well as the PA web page will also be installed to the “Start” menu, under “Programs”.
After the Linkage program has been installed, Linkage data may be called up in three different ways:
1) As noted above, the Linkage program has been integrated into the text in each frame’s section in Chapter IV, for which an “ltx data file” (see the instructions) has been made. By clicking on the “Linkage data” link, the most important characteristics of the frame in question will be shown.
2) One may go into the Linkage2 directory, which is created on one’s computer upon installation, and call the program by clicking on the Linkage.exe icon. One may then open an existing ltx file by clicking the “Open” button or create a new file by clicking the “New” button.
3) One may go into the Linkage2 directory and click directly on an ltx data file icon for a frame of interest.
The authors are all avid bikers, who also have technical and/or language skills. We have provided this work freely to the public with the hope that it will benefit consumers and others interested in the workings of bicycles. A short biography and picture may be found on the “About the Authors” page, for those authors who have provided the information.
The authors wish to thank Prof. Curtis Collins, Ola Helenius (Ola H.), and Ray Scruggs (Derby) for their kind suggestions and help in finding errors. Thanks also to Drakon El Elfo for working on the link structure to the Spanish version.
The authors would like to especially thank J.I. Baeza (aka Sikander) and Jose R. Rubio, the editor of "http://www.mundobiker.es/, for hosting both the English and Spanish versions of this work.