A work piece is to be firmly held in a fixture. It is to be machined by using a plain slab milling cutter as shown in the figure below. Which one of the following options is the most suitable value of height H of the fixture in mm?
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Set up a right triangle with the cutter radius as the hypotenuse and half the workpiece width as one leg to find H.
The fixture blocks need to be as tall as possible for good support, but their top corners must stay just inside the circle that the rotating cutter edge traces out, otherwise the cutter would gouge into the fixture.
Set up the right triangle: the cutter's centre line sits directly above the middle of the 100 mm wide workpiece, so each fixture corner is 50 mm off to the side. This 50 mm offset, the cutter radius of 205 mm (the hypotenuse), and the fixture height H form a right triangle.
Solve for H: $H = \sqrt{205^2 - 50^2} = \sqrt{42025 - 2500} = \sqrt{39525} \approx 198.8$ mm.
Compare with the options: 198.8 mm sits closest to 200 mm; the other choices (210, 150, 70) are all further away and would either clip the cutter path or waste usable support height.
So the most suitable fixture height is option (A), 200 mm.
