A workpiece is taper turned using lathe, where large diameter of workpiece is D and small diameter d. If the length of this workpiece is L, then half angle a is given by: 

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  1. \(\rm \tan \alpha=\frac{(D-d)}{2L}\)
  2. \(\rm \tan \alpha=\frac{(D-d)}{3L}\)
  3. \(\rm \tan \alpha=\frac{(D-d)}{L}\)
  4. \(\rm \tan \alpha=\frac{(D-d)}{4L}\)

Answer (Detailed Solution Below)

Option 1 : \(\rm \tan \alpha=\frac{(D-d)}{2L}\)
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Detailed Solution

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Concept:

When the diameter of the bar either increases or decreases along the length of the bar then it is called a taper.

This operation is performed on a lathe machine with the help of a taper-turning attachment.

The formula for half taper angle α is

F1 Tabrez 2.7.21 Pallavi D1

\(\tanα = \frac{{D \ - \ d}}{2L}\)

where, α = half taper angle, D = large diameter of the bar, d = small diameter of the bar, L = length of the bar.

The amount of taper is given by,

\(Taper = \frac{{D \ - \ d}}{L}\)

F1 Tabrez 11.11.20 Pallavi D1

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