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.
Step 1: Identify what limits the fixture height.
The milling cutter sweeps out a circular path as it rotates, so the fixture blocks on either side of the workpiece must stay clear of that circle while still supporting the workpiece as high as possible.
From the figure, the cutter reaches down to the workpiece over a radius of \( R = 205 \) mm, and the workpiece width is \( 100 \) mm, so each fixture sits \( 50 \) mm to the side of the cutter's centre line.
Step 2: Apply the circle geometry at the fixture edge.
At the top inner corner of the fixture, the cutter's circular envelope must just clear that corner, so the corner lies on the circle of radius R centred on the cutter axis.
Using the right triangle formed by the radius, the 50 mm horizontal offset, and the vertical clearance height H:
\[ H = \sqrt{R^2 - (w/2)^2} = \sqrt{205^2 - 50^2} \]
Step 3: Evaluate the height.
\( H = \sqrt{42025 - 2500} = \sqrt{39525} \approx 198.8 \) mm.
Final Answer:
Rounded to the nearest listed value, the most suitable fixture height is about 200 mm, matching option (A).
\[ \boxed{H \approx 200 \text{ mm}} \]
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