Question #306283

3. Two shafts, having axes in the same plate intersecting at an angle of 45°, turn in opposite senses at 30 rpm and 90 rpm. Draw a pair of cone to be located on these shafts and turn in pure rolling contact. Diameter of base of smaller cone is 1 in. Calculate the cone angles.


1
Expert's answer
2022-03-07T17:12:04-0500

Solution;


From the diagram;

r1sin(45γ2)=r2sinγ2\frac{r_1}{sin(45-\gamma_2)}=\frac{r_2}{sin\gamma _2}

To find r,we can use the relation;

N2N1=r1r2\frac{N_2}{N_1}=\frac{r_1}{r_2}

r2=9030×1=3inchr_2=\frac{90}{30}×1=3inch

Hence;

345γ2=1sinγ2\frac{3}{45-\gamma_2}=\frac{1}{sin\gamma _2}

From which;

γ2=10.79°\gamma _2=10.79°

γ1=4510.79=34.21°\gamma _1=45-10.79=34.21°


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