Telecentric Lens for Gear Pitch and Bearing Dimensions

Small gears and bearing rings are flat, round, and mostly measurable — which is why they are also where telecentric measurement gets oversold. A silhouette gives you pitch and tip diameter reliably. It does not give you the involute profile, and it does not give you runout.

What a silhouette resolves on a gear

• Tooth pitch — angular spacing of tooth centres, or the chordal distance between corresponding points. Robust, because it is a relative measurement across many features.
• Tip diameter — outermost extent of the silhouette. Robust, and usually the tightest-tolerance dimension that is genuinely measurable.
• Root diameter — innermost extent. Measurable if the root is not occluded, which on fine-pitch gears with a shaft or a hub it often is.
• Bore diameter and its concentricity to the tip circle — both from circle fits, both reasonably robust.
• Tooth count and missing teeth — trivially robust.

What it does not resolve

• Involute profile. The flank shape is visible in a silhouette only as an outline, and the outline of a helical gear is not the involute. Profile measurement belongs to a gear tester.
• Tooth thickness at the pitch circle. The pitch circle is a construct, not a visible feature.
• Runout and eccentricity in Z. A gear that is not flat on the fixture produces an elliptical silhouette that reads as eccentricity. Check flatness before believing an eccentricity reading.
• Helix angle, lead, and backlash. Not 2D lateral measurements.

See when a telecentric lens is the wrong choice.

Telecentric models for gears and rings in this size band

Magnification from 0.3X to 1.0X covers tip diameters from roughly 11 mm to over 100 mm on 2/3″ and 1″ sensors. Ordered by resolution, finest first — tip diameter is usually the tightest tolerance in the set, and it is the dimension that benefits most from a well-sampled edge.

The flatness prerequisite

Every gear measurement from a silhouette assumes the gear plane is parallel to the sensor plane. A gear resting on a burr or on a chip is tilted; a tilted circle projects as an ellipse; and the ellipse is then fitted and reported as tip diameter and eccentricity. The numbers are self-consistent and wrong.

Telecentricity does not save this. It stabilises magnification against object distance; it does not project a tilted circle as a circle.

Magnification from tip diameter

The field of view must contain the tip circle plus margin. A 30 mm gear on a 2/3″ sensor needs about 11 / (30 × 1.25) ≈ 0.29X. Whether the individual teeth are adequately sampled is then a separate question: at 0.29X a 3.45 μm pixel resolves about 11.9 μm, and a 1 mm module tooth is roughly 84 pixels across — comfortable. A 0.2 module tooth is about 17 pixels, which is marginal for pitch but usable.

Use the FOV and magnification calculation rather than approximating.

Bearing rings: a slightly easier case

Bearing rings have no teeth, so the measurable set is larger: inner and outer diameter, wall thickness, raceway visibility depending on geometry, and concentricity between bore and outer diameter all fall out of circle fits. The hard part is not optics — it is that a ring resting on a flat surface hides the bore edge where it contacts, and that chamfers make the "diameter" depend on where along the height it is measured.

Lighting

Collimated backlight. Gears and rings are usually ground steel: a diffuse backlight produces a bright halo at the tooth tips that pulls the extracted tip circle inward, and the error varies with surface finish. The lighting guide covers collimated versus diffuse selection.

Questions engineers ask about this setup

Can a telecentric lens measure gear tooth profile?

No. A silhouette shows the outline, and for a helical gear that outline is not the involute. Profile, lead and helix angle belong to a dedicated gear tester.

Why does my tip diameter reading drift between parts?

The most common cause is the gear not lying flat — a tilted circle projects as an ellipse, and the fit then reports both a wrong diameter and a spurious eccentricity. Check for burrs and debris on the fixture before adjusting the optics.

Is eccentricity measurable?

Concentricity between two fitted circles is measurable, but only if the part is parallel to the sensor plane. Any tilt is absorbed into the eccentricity result, so a flatness check has to come first.

What magnification do I need for a small gear?

Set it from the tip circle plus margin, then check that a single tooth spans enough pixels. A 1 mm module tooth at 0.29X spans roughly 80 pixels, which is comfortable; a 0.2 module tooth spans under 20, which is marginal for pitch.

Can root diameter be measured?

Only when the root is visible. On fine-pitch gears with a hub or shaft, or on gears where the mating tooth occludes the root in projection, it is not.

Do bearing rings need a different setup?

A simpler one — no teeth means circle fits carry most of the measurement. The difficulty is presentation: a ring lying flat hides its bore edge at the contact point, and chamfers make the measured diameter depend on the height at which it is taken.

Related reading

• Telecentric lens selection guide
• Magnification and FOV calculation
• Lighting for telecentric measurement
• What a telecentric lens is and when to use one
• When a telecentric lens is the wrong choice
• Shaft and sleeve outer diameter
• Lead-frame coplanarity
• Machined parts: contour and spacing

Send one part and we will tell you what the measurement can hold

Specification arithmetic gets you to a shortlist, not to a verdict. Send one part with the drawing and the tolerance you have to hold, and we will run it and report what the system returns — including the features that come back as unmeasurable. A written feasibility note is worth more than another datasheet.