Two rollers of diameters D1 (in mm) and D2 (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights H1 (in mm) and H2 (in mm) are measured by using a height gauge after inserting the rollers into the same V-groove as shown in the figure.Which of the following is the correct relationship to evaluate the angle α as shown in the figure?

Question

TuteeHUB · Accepted Answer

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

TuteeHUB · Answer

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

TuteeHUB · Answer

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

TuteeHUB · Answer

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

1.	Two rollers of diameters D1 (in mm) and D2 (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights H1 (in mm) and H2 (in mm) are measured by using a height gauge after inserting the rollers into the same V-groove as shown in the figure.Which of the following is the correct relationship to evaluate the angle α as shown in the figure?
A.	\(\sin \alpha = \frac{{\left( {{D_1} - {D_2}} \right)}}{{2\left( {{H_1} - {H_2}} \right) - \left( {{D_1} - {D_2}} \right)}}\)
B.	\(\cos \alpha = \frac{{\left( {{D_1} - {D_2}} \right)}}{{2\left( {{H_1} - {H_2}} \right) - 2\left( {{D_1} - {D_2}} \right)}}\)
C.	\(cosec\;\alpha = \frac{{\left( {{H_1} - {H_2}} \right) - \left( {{D_1} - {D_2}} \right)}}{{2\left( {{D_1} - {D_2}} \right)}}\)
D.	\(\sin \alpha = \frac{{\left( {{H_1} - {H_2}} \right)}}{{\left( {{D_1} - {D_2}} \right)}}\)
Answer» B. \(\cos \alpha = \frac{{\left( {{D_1} - {D_2}} \right)}}{{2\left( {{H_1} - {H_2}} \right) - 2\left( {{D_1} - {D_2}} \right)}}\)

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