= Backlash
\b[Backlash] is free play in a mechanical coupling that can produce lost motion when the direction of drive reverses. In a <lead screw>, clearance between the <screw thread> and <nut (hardware)> permits relative movement before the opposite contact surfaces carry the load.<Selecting the Optimal Screw Technology by Tolomatic>[Screw Terminology, printed p5; Backlash, printed p18]{ref}
Consider an ideal screw with <screw lead> $L=4\,\mathrm{mm}$ per revolution and axial backlash $b=0.05\,\mathrm{mm}$. Suppose one thread flank initially carries the load and a small opposing <force> holds the carriage still while the screw reverses through the clearance. The angular movement required to take up the gap is
$$
\theta_b=\frac{2\pi b}{L}
=\frac{2\pi(0.05)}{4}\,\mathrm{rad}
\approx0.0785\,\mathrm{rad}
=4.5^\circ.
$$
During that interval, screw rotation need not produce carriage movement. A commanded reversal of $6^\circ$ corresponds geometrically to $4(6/360)=0.0667\,\mathrm{mm}$, but this simple gap model leaves only about $0.0167\,\mathrm{mm}$ of carriage travel after taking up the backlash.
The example assumes a particular contact state and holding force. If another <force> keeps the same thread flanks in contact, or moves the carriage across the gap, the observed reversal can differ. Thus backlash must be associated with a load condition, rather than inferred from every mismatch between commanded and measured position.
A useful measurement records screw angle and carriage position while approaching a chosen position from both directions. Direction-dependent results can reveal <backlash> even when repeated approaches from one direction agree. Separately changing the applied <force> helps distinguish free play from <mechanical compliance>: elastic deformation changes with force after contact is established, while clearance permits a gap before that load path engages. Both effects can contribute to a path-dependent relation and <hysteresis>.
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