Computing a Linear Dimension
The coordinates at the two ends of a certain length dimension of a machined component have been measured by a CMM. The coordinates of the first end are (23.47, 48.11, 0.25), and the coordinates of the opposite end are (73.52, 21.70, 60.38), where the units are millimeters. The given coordinates have been corrected for probe radius. Determine the length dimension that would be computed by the CMM software.

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Accepted Answer

Using Equation (22A.2),

[latex]L=\pm \sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^{2}+(z_{2}-z_{1})^{2}}[/latex]

[latex]= \sqrt{(23.47 - 73.52 )^{2}+(48.11 - 21.70 )^{2}+(0.25 - 60.38)^{2}}[/latex]

[latex]= \sqrt{(-50.05 )^{2} + (26.41 )^{2} + (-60.13)^{2}}[/latex]

[latex]= \sqrt{2,505.0025 + 697.4881 + 3,615.6169}= \sqrt{6,818.1075}= 82.57[/latex] mm

Question 22A.1: Computing a Linear Dimension The coordinates at the two ends...

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