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}
Read this section.
This is the central point of the entire work.
This section is moderately difficult.
1) All measures of suspension performance depend almost entirely on the paths of the following specified components relative to any reference frame defined by one of the bicycle frame members: Handlebars, seat, bottom bracket (BB), front and rear wheel axles, shock mounts, and rear brake.
As is explained in the “Reference Frames” section, establishing a frame member as our non-inertial reference does not mean that it will not move. It will translate and rotate, and our reference frame will move with it.
The above “specified” components will always move along paths or one-dimensional spaces in the reference frame of one of the supporting bicycle frame members, as a practical matter. The path tangents determine how any bike will behave at any point in time. The path curvatures determine how the bike will behave over time.
If we wish to compare two designs, we should identify a frame member common to both designs. The more alike the paths are in any two suspensions, in the common reference, the closer will be the performance of the frames that produce them. In practice, the bars and seat will always define the best reference and this will be the reference for all analysis in this work (though sometimes it can be interesting to see how paths compare from reference to reference).
Mass and its distribution play an important role in any mechanism. However, the main triangle and rider are usually about 60 times as massive as the suspension members (not including the shock). The movement of rider/main triangle mass will depend on the movements of the main triangle components (seat, bottom bracket, and handlebars), even with a non-integrated main triangle (bottom bracket moving with respect to the bars and seat). In addition, the differences in mass movement of the suspension members between different designs with similar component paths are relatively small. This makes the ground and the rider/main triangle the only two significant masses in bicycle physics.
These mass considerations are what allow for PA. We have covered mass approximations in the “Approximation” section of “Some Important Concepts.”. However, when and how to apply approximation can be a very difficult issue, so in the “Mass Approximation” section below, we will explain in detail how mass approximation allows for PA.
Naturally, each individual rider will produce a unique mass distribution. When we say that we can determine suspension performance by the paths, we mean that we can know the performance of the frame for any set of assumptions for relevant physical quantities, such as rider mass distribution or contributions from the suspension fork.
Friction in the suspension mechanism will always act to oppose the movement of components along their paths and will ultimately be directed tangent to the path. Friction magnitude can for the most part be controlled in one type of geometry as well as another. Thus, while we might find one particular suspension bike to have a favorable amount of friction relative to another, friction does not lend any advantage to one type of suspension over another.
Note that the forces between components are critical in determining suspension performance. However, all lines of force, whether they are through the rider, the chain, or external are equally producible in all designs. They thus do not distinguish one design from another. However, it is very helpful to understand how the forces and torques act on and within a bicycle.
Frame stiffness is an important factor in bicycle performance. However, it is much more an issue for handling (a topic not covered in this work), particularly high speed cornering, then anything else. With regard to pedaling, braking, and shock absorption, one only need be wary of the very lightest frames. It has been several years since the author has been aware of any new frames on the market that are so severely under-built as to cause real problems for pedaling, braking, and shock absorption, beyond bad choices and defects in materials and manufacturing, that lead to frame failure (also not covered in this work).
This leaves geometry as the overriding issue in suspension performance regarding pedaling, braking, and shock absorption.
In most cases, the full machinery of PA is not necessary since the paths of components may determine the orientations of their supporting structures (frame members, fork, etc.). For example, the BB and seat may fully determine the main triangle, so one could simply look at that body rather then the attached components.
However, in cases such as the i-Drive, the full machinery of PA is the only practical method of analysis. Analysis of the i-Drive by any other method would be extremely complicated. The power of PA will be revealed in the extreme simplicity of i-Drive analysis using this method.
We will give an analysis of the i-Drive theory, Ellsworth’s “Instant Center Tracking” (ICT) theory, and other erroneous theories at the end of this paper.