The next two theories we consider are examples of what I call “Internal Force” theories. (Actually, we have already discussed two examples of this sort of theory in “BISL theory #2” of the “‘Brake Induced Shock Lockout' (BISL).” section and also the “False Claims for Floating Brakes.” section.)
Suppose that we have a mechanism that has two parts connected by a pivot. An example is a URT bicycle. Internal force theories say that force interactions internal to one part, on one side of the pivot, do not influence the other part, across the pivot.
For example, it is sometimes thought that the chain force line between the crank and rear wheel in a URT does not have an effect on suspension reactivity to pedaling because the force is “internal” to the rear triangle (this is the second theory below). Another idea is that braking forces are “isolated” on the rear link of a Horst link suspension and thus do not activate the suspension (see “BISL theory #2” of the “‘Brake Induced Shock Lockout' (BISL).” section and also the “False Claims for Floating Brakes.” section). The same “isolation” on the rear link of a Horst link is said to be true for pedaling (we have not covered this, since we believe that it will be trivial for readers to repudiate, at this point). PA tells us that these ideas are false. In particular, “Nature Varies Smoothly” (NVS) and the “Coaxial Condition” establish that pivots do not “isolate” forces, as we have noted in numerous other places.
Mountain Bike Action (MBA), in particular, seems very taken with this false idea. The most convincing indication of this comes from the Richard Cunningham quotes below in the “‘i-Drive' – a Perpetual Motion Machine?!?!” section. Cunningham also makes some vague use of the terms “isolates” and “uncouples” in the context of chain stay pivot 4-bar suspensions [Page 70, Mountain Bike Action, May 2001]. For example, Cunningham says, “The Horst link isolates braking forces and chain tension in the seatstays and thus provides an active rear suspension.” Regarding “Parallel link” suspensions (a type of 4-bar), he goes on to state, “The wheel is mounted to the vertical rear link, which uncouples it from the swingarm and delivers a truly active ride. You can pedal or brake over rocks and roots and the rear wheel will follow the terrain exactly as it does when you are coasting.” (Here he assumes a disc brake mounted on the rear link.) It is not entirely clear what Cunningham means by “isolates” and “uncouples”, but it is clear that these terms are used to describe an effect of pivot location. These quotes, in conjunction with the Cunningham quotes in the “‘i-Drive' – a Perpetual Motion Machine?!?!” section, seem to indicate that MBA espouses internal force theories.
We will apply PA to the i-Drive first, since the analysis is extremely simple. We will then give a rigorous force vector treatment of the URT chain line as a test for Path Analysis.