Pick approach for rotationally symmetric objects: wrap the angle

A wrist or cell camera reports a rotationally symmetric part at a different angle every cycle: twelve identical teeth give twelve equally valid answers, and the vision tool has no reason to prefer one. Left unwrapped, the gripper sweeps in from a different direction each pick — cycle time drifts, the dress pack flexes unevenly, and a downstream station sees random clocking. The fix is one line of arithmetic. Wrap the reported angle to the part's symmetry step, teach the pick once at a canonical angle, and every approach runs from the same taught direction. This guide gives the rule, a worked 12-tooth gear example with its error budget, a five-step teach procedure, and the camera and field-of-view decisions behind it.

Why the camera reports a different angle every time

The pattern matcher locks onto whichever tooth scores best in the current image. On a part with true rotational symmetry — a shape that looks the same after a partial turn — every tooth produces the same score, so the winner changes with a pixel of noise, a fingerprint or the part's position in the field. Each reported angle describes the part correctly. None of them is the pick angle until you impose a convention, and that convention is the wrap.

Two details matter before the arithmetic. First, the angle is measured against the working-plane reference you define, so a tilted fixture skews every reading by the same tilt. Second, the object reference the tool reports is usually anchored at the mass center of the detected edges; on a gear with an uneven hub that sits a few millimeters from the geometric center. Reading the object orientation angle from a camera covers how that measurement is produced; the teach procedure below absorbs the center offset.

The rule: wrap the angle to the symmetry step

Count the identical orientations per full turn — call it N — and compute the symmetry step s = 360° / N. Subtract whole steps from the reported angle until it falls inside one step, then command the wrist by the difference between the wrapped angle and the angle you taught:

The wrapped angle points at the same physical orientation as the raw one. Rotating the part by s degrees changes nothing about it, so gripping at θwrap is mechanically identical to gripping at θcam — but the approach direction is now deterministic, and every cycle looks the same to the wrist, the cables and the station downstream.

When the part is only partly symmetric, or the process defines how much clocking error it accepts, symmetric part orientation matching sets the tolerance framework. The wrap is that idea taken to its limit: zero tolerance against the symmetry group.

Worked example: a 12-tooth, 120 mm gear reported at +38°

One gear, one camera, one gripper — the numbers and where each comes from:

• N = 12 teeth — part drawing.
• 120 mm outside diameter — part drawing.
• θcam = +38° — vision tool output in the working-plane reference, in degrees.
• θtaught = 0° — the operator taught the pick on a canonical picture, so the taught angle is zero by construction.
• 1,600 px across the part — the image scale at the chosen field of view, 0.075 mm per pixel.
• 12 mm jaw width — gripper data sheet.

The rule in words: divide the circle by the tooth count, remove whole steps from the reported angle, and command the wrist by the difference from the taught pose.

s = 360° / 12 = 30°. θwrap = 38° − 30° × floor(38° / 30°) = 38° − 30° = 8°. The centered variant leaves 8° unchanged, because 8° ≤ 15°. The wrist command is θcmd = 8° − 0° = +8°. Every pick now lands within ±15° of the taught pose, and the jaws meet exactly the taught picture — not approximately, but identically, since 38° and 8° are the same part.

Three checks size the margin. Measurement: 120 mm across 1,600 px gives 0.075 mm per pixel; at the 60 mm rim radius that is 0.075 / 60 = 1.25 mrad ≈ 0.072° per pixel, so a 5 px pattern-fit error is 0.36°. The wrap itself loses nothing: one 30° step spans π × 120 / 12 = 31.4 mm of rim arc, about 419 px. Robot: 0.1 mm of linear repeatability at a 100 mm jaw radius is 0.1 / 100 = 1 mrad ≈ 0.06°. Clearance: pitch arc 31.4 mm minus the 12 mm jaw leaves 19.4 mm of free arc; half of it, 9.7 mm at a 60 mm radius, is 9.7 / 60 = 0.162 rad ≈ 9.3° of angular slack.

Expected error ≈ 0.36° + 0.06° = 0.42° against 9.3° of clearance — a margin above 20×. Decision: the wrap-only approach holds for this gear, and no secondary feature is needed. Run the same four numbers whenever the parts change. When the arithmetic puts clearance below a few degrees — fine-pitch gears with wide jaws do this — stop trusting symmetry and match a real feature instead.

Teach the canonical pick in five steps

1. Define the working plane in the tool, and mount or square the fixture to it. Every angle reads against this plane.
2. Trigger one detection and note the reported object reference. Its origin is the edge mass center, not necessarily the part center.
3. Jog the wrist to the true pick center and record the offset from the reported origin. Done once, this absorbs the eccentric-origin error for every future pick; tool-frame offsets for a gripper-mounted camera explains which offsets survive part-to-part variation.
4. Rotate the wrist until the picture is canonical — a tooth centered under the jaw axis, for instance — and record the taught angle θtaught and the approach pose above the part.
5. In the runtime path: read θcam, wrap it, add the recorded offsets, approach. Keeping the tool orientation fixed on round parts applies the same discipline to the grip itself.

A slide-table bench makes the teach repeatable when the same sensor moves between stations or comes back after maintenance. The LS-MNT-0040 gives a 700 mm column and a 400 x 450 mm base for an overhead teach camera; the rest of the camera stands range covers smaller footprints.

Cell camera or wrist sensor

Two placements work, and they trade cycle time against flexibility. A cell camera fixed above a presented pick point images while the robot retires, so it adds almost no cycle time; that is the standard layout in how a 2D vision-guided pick-and-place cycle works, and picking a full tray in one snapshot extends it to many parts per image.

A wrist sensor rides the gripper and sees the part at the last moment, absorbing rack-to-rack variation at the cost of an image-plus-move every cycle. Before committing the layout offline, a wrist-mounted camera simulation checks what the sensor will actually see from the taught poses. If the controller runs the approach from a sensor interrupt instead of a blocking vision call, the same wrap plugs straight in — an interrupt-based approach-control pattern for sensor-guided picking shows the structure.

Whichever placement you choose, a fixed-focus M12-mount vision sensor is the usual instrument, and the choice between them comes down to resolution and color:

All 3 share: Sensor type CMOS, global shutter; Pixel size 3.45 μm × 3.45 μm; Data interface Fast Ethernet (100 Mbit/s); Humidity 20% RH to 95% RH (no condensation); Client software SCMVS; Certification CE, KC. Values as printed in each product's data sheet; open a part for its drawing and full specifications.

Pick by tooth size and contrast. For small teeth or a wide cell view, the MV-SC3050XC-16M-ATN-H brings 5 MP, a color sensor, a global shutter and an M12 mount. For wrist duty, the MV-SCB007EC-12S-WBN and the HK-TD032-12-WBN are 1.6 MP Fast Ethernet sensors; the mono one is the default on bare metal, where color adds nothing. Both run inspection on board, so no PC sits in the loop. The smart cameras category and the camera finder filter these by resolution, interface and mount.

Lighting is the other half of the cell: bare metal teeth flare under a bare ring, so give the sensor polarized or low-angle light from the machine vision lighting finder. And parts arriving jumbled in a bin take a different strategy entirely — that is a 3D sensors and bin-picking problem, not an angle-wrap one.

Field of view and working distance

Size the field to the part plus background for the pattern model: 10–20% of the diameter per side is the practical band. For the 120 mm gear this case uses 20 mm per side, so the target field of view is 120 + 2 × 20 = 160 mm. Tighter than that and the matcher runs out of background; much wider and you spend pixels on empty belt.

Convert the field to a focal length with the small-magnification estimate f ≈ sensor width × WD / FOV, valid when the field is far wider than the sensor, which holds here. A 1/2.9-inch-format sensor is about 5 mm wide — the usual figure for that format class. At a 250 mm working distance and the 160 mm field, f ≈ 5 × 250 / 160 ≈ 7.8 mm, so an 8 mm-class M12 lens is the fit.

The MV-SCB007EC-12S-WBN ships with a 12 mm lens. At a 250 mm working distance that covers about 5 × 250 / 12 ≈ 104 mm — too tight for the 160 mm target. Either set the working distance to 160 × 12 / 5 = 384 mm, or fit an 8 mm-class lens, which covers about 5 × 250 / 8 ≈ 156 mm at 250 mm. Both reach the same image scale; pick by wrist clearance.

For wrist duty at that field, the MV-SCB007EC-12S-WBN is the compact option with its 12 mm lens.

When the wrap is not enough

Three situations break the trick. Look-alike is not identical: a keyway on one face, one ground tooth or a chamfered lead-in makes the part symmetric to the camera but not to the gripper. The bench test settles it — command one extra symmetry step, re-image, and if the picture moves, there is no symmetry to wrap.

Downstream clocking overrides pick symmetry. A gear may be 12-fold for the jaws yet 1-fold for the keyway it must land on: wrap for the grip, then re-orient after the pick, or grip on a defined feature. And when the clearance arithmetic lands below a few degrees, vision-guided repeatability on round symmetric parts shows where the remaining error actually comes from; self-centering V-jaws or a compliant jaw insert buy the margin back mechanically.

The decision rule is short. True symmetry and clearance above a few degrees: wrap. Look-alike features or tight clearance: match a real feature. Clocking downstream: wrap at pick, control orientation at place.

Pre-run checks

Six checks, each with the reason it exists:

• Step-and-reimage test passes — otherwise the symmetry order is wishful.
• Angle unit and range confirmed with a known 90° turn — the wrap routine cannot fix a radians answer treated as degrees.
• Taught picture recorded at θtaught = 0 with the canonical tooth centered — the whole convention hangs on this one pose.
• Center offset from the edge mass center jogged and stored — without it every pick lands off-center by the hub's eccentricity.
• Wrap arithmetic unit-tested on +38°, −38°, +359° and −359° — the negative and wrap-around branches are where floor functions bite.
• First ten picks logged with raw and wrapped angles at reduced speed — the log is the evidence the margin is real.

For a specific cell, send the part, its diameter, tooth count and jaw style, and we will size the sensor, field and light together — start at the contact page with those four numbers. More application walkthroughs sit on the applications topic page.