The nonlinear spring placed in series with the guitar string serves to increase the movement of the motor and potentiometer for their desired range of string tensions to provide adequate resolution of pitch measurement. Pitch is generally a squared function of string tension and if a standard spring were used for this purpose, having a generally linear spring function, the resolution provided by the potentiometer would vary widely over the pitch range providing pitch errors at low pitches. This nonlinear relationship between pitch and tension is corrected, somewhat, by the use of a nonlinear spring which requires increased force to deflect at higher forces thus providing a linearized tension sensor output that provides for more consistent pitch resolution and thus reduced total pitch error over the desired tuning range.
The non-linear springs are produced by two series connected helical extension springs one of which is wrapped loosely with a nylon cord. When a given extension is reached, the cord stops further extension of the wrapped spring, causing the spring constant to abruptly increase.
The springs for the Milwaukee Guitar Design are cut from standard screen door springs. The following calculator provides a spring constants and yield forces for springs of this approximate diameter and material. I have estimated the torsional modulus of the material and the yield fiber stress of the material from the local hardware store (ACE) which I expect would be consistent for low-cost door springs. Information from a spring expert would not be turned away.
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