= Caliper jaw tilt error
{title2=$e\simeq h\theta$}
\b[Caliper jaw tilt error] is a change in the indicated dimension caused by rotation of a <caliper>'s moving jaw relative to its reference geometry. If a contact lies distance $h$ from the displacement reference, a small rotation $\theta$ gives a signed offset contribution
$$
e=h\tan\theta\simeq h\theta.
$$
The sign depends on the direction of rotation and contact geometry. The approximation requires small $|\theta|$; it describes this angular contribution rather than every possible <measurement error>.
Mitutoyo gives a concrete geometry: a jaw slope of $0.01\,\mathrm{mm}$ over $50\,\mathrm{mm}$ and a contact depth of $40\,\mathrm{mm}$ produce a tip error of $0.008\,\mathrm{mm}$. Excessive contact force and wear of the guide can cause the moving-jaw rotation.<Quick Guide to Precision Measuring Instruments: Calipers by Mitutoyo>[printed p. 17, Moving Jaw Tilt Error and its numerical example]{ref}
An original diagnostic repeats a <gauge block> comparison at contact depths $h_1=10\,\mathrm{mm}$ and $h_2=40\,\mathrm{mm}$. With stipulated constant $\theta=2\times10^{-4}\,\mathrm{rad}$ and other effects unchanged, the angular contributions are approximately $2\,\mathrm{\mu m}$ and $8\,\mathrm{\mu m}$. Their $6\,\mathrm{\mu m}$ difference isolates a depth-dependent effect that a single closed-jaw zero reading could miss. Real contacts may also change force or deformation, so this comparison does not uniquely identify rotation without controls.
A <Vernier zero correction> removes an estimated constant offset; it cannot generally remove an error proportional to contact depth or varying force. Use consistent light contact, a clean reference and a stable <temperature>, and compare several separations and contact positions. A fine <Vernier scale> improves reading increments without guaranteeing that these mechanical contributions are small.
This lever-arm mechanism is distinct from merely projecting a fixed length onto a tilted measurement axis: the latter involves $\cos\theta$ and has a quadratic small-angle change, whereas the offset term above is linear in $\theta$. Keeping the geometry in the <measurement model> prevents applying the wrong angular correction.
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