GATE 2023 ME – Question 54

Metrology and Inspection · Alignment and testing, tolerance analysis, coordinate-measuring machine · 2 marks · Numerical answer

A coordinate measuring machine (CMM) is used to determine the distance between Surface SP and Surface SQ of an approximately cuboidal shaped part. Surface SP is declared as the datum as per the engineering drawing used for manufacturing this part. The CMM is used to measure four points P1, P2, P3, P4 on Surface SP, and four points Q1, Q2, Q3, Q4 on Surface SQ as shown. A regression procedure is used to fit the necessary planes.

The distance between the two fitted planes is ___________ mm.
(Answer in integer)

a cuboid with the datum surface SP and the opposite surface SQ, and the measured points (in mm). P1: (4, 0, 3), P2: (3, 0, 6), P3: (1.5, 0, 7), P4: (2, 0, 2). Q1: (4, 6, 3), Q2: (1, 6, 3), Q3: (1.5, 4, 7), Q4: (4, 4, 6).

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Correct answer: 5

Explanation

All four points of SP have $y = 0$, so the fitted datum plane is $y = 0$. The points of SQ are at $y = 6, 6, 4, 4$. The least-squares plane through them passes through their centroid, whose $y$-coordinate is the mean $\frac{6 + 6 + 4 + 4}{4} = 5$. The distance from the datum plane (measured along its normal, the $y$-axis) to the fitted plane of SQ is 5 mm.