Question

Two rollers of diameters $D_1$(in mm) and $D_2$ (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights $H_1$(in mm) and $H_2$(in mm) are measured by using a height gauge after inserting the rollers into the same V-groove as shown in the figure.


Which one of the following is the correct relationship to evaluate the angle $\alpha$ as shown in the figure?

• A. $sin\alpha =\frac{(H_1-H_2)}{(D_1-D_2)}$
• B. $cosec\alpha =\frac{(H_1-H2)-(D_1-D_2)}{2(D_2-D_2)}$
• C. $cos\alpha =\frac{(D_1-D_2)}{2(H_1-H_2)-2(D_1-D_2)}$
• D. $sin\alpha =\frac{(D_1-D_2)}{2(H_1-H_2)-(D_1-D_2)}$

Answer 1

The correct option is D $sin\alpha =\frac{(D_1-D_2)}{2(H_1-H_2)-(D_1-D_2)}$


$\text{As per given data:}$

$OB=(H_1-\frac{D_1}{2})-(H_2-\frac{D_2}{2})$

$=(H_1-H_2)-\left(\frac{D_1-D_2}{2}\right)$

$OA=\frac{D_1-D_2}{2}$

$sin\alpha =\frac{\frac{(D_1-D_2)}{2}}{(H_1-H_2)-\frac{(D_1-D_2)}{2}}$

$sin\alpha =\frac{(D_1-D_2)}{2(H_1-H_2)-(D_1-D_2)}$