  Backlash, also known as mechanical play, is a piecewise differentiable
nonlinearity which exists in several actuated systems, comprising, e.g.,
rack-and-pinion drives, shaft couplings, toothed gears, and other machine
elements. Generally, the backlash is nested between the moving parts of a
complex dynamic system, which handicaps its proper detection and
identification. A classical example is the two-mass system which can
approximate numerous mechanisms connected by a shaft (or link) with relatively
high stiffness and backlash in series. Information about the presence and
extent of the backlash is seldom exactly known and is rather conditional upon
factors such as wear, fatigue and incipient failures in the components. This
paper proposes a novel backlash identification method using one-side sensing of
a two-mass system. The method is based on the delayed relay operator in
feedback that allows stable and controllable limit cycles to be induced and
operated within the (unknown) backlash gap. The system model, with structural
transformations required for the one-side backlash measurements, is given,
along with the analysis of the delayed relay in velocity feedback. Experimental
evaluations are shown for a two-inertia motor bench that has coupling with
backlash gap of about one degree.
