SOLUTION

Backlash or gear play arises in the mechanical system involving gear trains.

1. If an input sinusoid is used, then the output of a backlash will be periodic, but the output will remain constant whilst the input changes from being increasing to decreasing.
2. The main difficulty is the phase shift which is introduced by the backlash that can cause stability problems in feedback control loops.
3. An interesting feature of backlash is its multi-valued behaviour, since for each input there are two possible values for the output of the nonlinearity.
4. The output that is appropriate depends upon the previous motion of the input signal, and hence the output depends upon the history of the input signal movements.
5. If backlash occurs the analysis will be non-linear because the backlash can cause undesired low-level oscillation in the feedback control system.

Note:- The gear meshes are manufactured for minimal backlash, but the resulting increase in the friction between gear teeth thus reduces the efficiency of the system. Backlash can be useful sometimes as it increases the damping.