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20-Bio-B7 Ergonomics · May 2016

Question 5 of 6: Machine Vision — Resolution and Field of View

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams May 2016 — 04-Bio-B7, 3 hours, closed book (one aid sheet allowed, written on both sides; approved Casio/Sharp calculator only). Six questions are printed; the first five as they appear in the answer book constitute a complete exam paper (all six are answered here as a complete study resource). Each question is of equal value; some require an essay-format answer.

This solution follows the paper's true subject and cites robotics/manufacturing references accordingly.

Reference texts: M. P. Groover, R. Weiss, R. N. Nagel & N. G. Odrey, Industrial Robotics: Technology, Programming, and Applications (2nd ed. — robot configurations, end-effectors/grippers, machine vision, sensors and transducers); M. P. Groover, Automation, Production Systems, and Computer-Integrated Manufacturing (5th ed. — Geneva mechanisms/dial indexing, PLC ladder logic, production-rate and line-efficiency analysis).

Question 5: Machine Vision — Resolution and Field of View (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

QuantitySymbolValue
Camera height above the belt (taken as working distance)$WD$100 cm = 1000 mm
Lens focal length$f$15 mm
Sensor width × height$s_x\times s_y$6 mm × 4.5 mm
Pixel array$p_x\times p_y$640 × 480 px

Find. (a) the minimum resolvable feature size (per-pixel spatial resolution); (b) the field of view $FOV_x\times FOV_y$ on the conveyor; (c) a labelled system diagram.

conveyor belt (direction of travel to the right)stamped partcamera640x480 sensor15 mm lensFOV approx. 394 mm x 296 mm on the beltlight sourcelight source100 cmpart-present sensor (trigger)vision processor / PCimage analysis + decisionPLC / rejectactuator
Fig. 5 — part (c): side view of the machine vision system, showing the camera and lens, lighting, part-present trigger, vision processor, PLC/reject actuator, and the field of view on the conveyor.

Approach. Use the thin-lens magnification $m=f/(WD-f)$ to project the sensor's physical size onto the object plane (the field of view), then divide the FOV by the pixel count to get the size each pixel represents on the part.

  1. Magnification. $$m=\frac{f}{WD-f}=\frac{15}{1000-15}=\frac{15}{985}=0.01523.$$
  2. Field of view. $$FOV_x=\frac{s_x}{m}=\frac{6}{0.01523}=394\ \text{mm},\qquad FOV_y=\frac{s_y}{m}=\frac{4.5}{0.01523}=295.5\ \text{mm}.$$ $$\boxed{FOV\approx 394\ \text{mm}\times295.5\ \text{mm}}$$
  3. Part (a) — spatial resolution. $$\text{res}_x=\frac{FOV_x}{p_x}=\frac{394}{640}=0.616\ \text{mm/px},\qquad \text{res}_y=\frac{FOV_y}{p_y}=\frac{295.5}{480}=0.616\ \text{mm/px}.$$ Both axes agree because the sensor and pixel array share the same 4:3 aspect ratio, so $$\boxed{\text{minimum resolvable feature}\approx0.62\ \text{mm (one pixel)}}.$$
ResultValue
Magnification $m$0.01523
Field of view394 mm × 295.5 mm
(a) Minimum resolvable feature≈0.62 mm/px
(b) Field of view $x,y$394 mm, 295.5 mm
Check — distance convention: the paper gives the height of the camera sensor (100 cm). The working above treats it as the lens-to-part distance in the thin-lens magnification, giving 394 × 295.5 mm. The common shortcut $FOV\approx s\cdot WD/f$ gives 400 × 300 mm (0.625 mm/pixel). An exact thin-lens solution with sensor-to-part = 1000 mm (object distance 984.8 mm, image distance 15.23 mm) gives 388 × 291 mm (0.606 mm/pixel). All three agree within 3%, so the answer to (a) is about 0.6 mm per pixel whichever convention is intended.

(c) System sketch and essential parts (Fig. 5). (1) The camera with its 640×480 sensor and 15 mm lens, mounted rigidly 100 cm above the belt and square to it. (2) Controlled lighting (diffuse, ring or low-angle lamps). This matters most for a reflective stamped sheet-metal part, because glare and shadows destroy edge contrast; a backlight is the choice for silhouette or hole-position measurements. (3) A part-present sensor (photo-eye) or belt encoder that triggers image capture when the part is inside the field of view, with a short exposure or strobe so that belt motion does not blur the image. (4) The vision processor / PC (frame grabber and image-analysis software: thresholding, edge detection, feature measurement, and comparison against tolerances). (5) The output interface: a PLC and a reject actuator (or robot) that acts on the pass/fail decision. (6) The conveyor, which carries each part through the field of view.