Q$3.[6$ marks$]$

A non$-$standard spur gear having $87$ nos. of teeth has to be produced in a horizontal arbour

milling machining. For the differential indexing $($DI$)$ purpose, one operator has an option to

use Brown and Shaper Plate $1($having $15,16,17,18,19$ and $20$ hole circles$)$ while the other one

has to use Plate $2($having $21,23,27,29,31$ and $33$ hole circles$).$ Determine the teeth number

of the gears in the DI$-$assembly to be used for the said purpose. Draw the schematic of the

differential indexing assembly with appropriate gear tooth numbers. Separate drawings are to

be sketched for two different conditions.