When in mesh, two gears with $95$ and $20$ teeth of involute form rotate in opposite directions and operate with a pressure angle of $20\backslash$deg $,$ a module of $4$ mm and a contact ration of $1\mathrm{.}5.$ The arc of recess is $1\mathrm{.}2$ times the arc of approach. The smaller wheel runs at $2000$rpm and transmits $4$kW to the larger wheel. Determine:

$1.$ The pitch circle diameter of gear of the larger gear $=$ Answer

mm and the pitch circle diameter of the smaller gear $=$ Answer

mm$.(2)$

$2.$ The circular pitch of the gears $=$ Answer

mm$.(1)$

$3.$ The Arc of Contact $=$ Answer

mm$.(1)$

$4.$ The Path of Contact $=$ Answer

mm$.(1)$

$5.$ The path of approach $=$ Answer

mm$.(3)$

$6.$ The path of recess $=$ Answer

mm$.(3)$

$7.$ The outside diameters of the two gears, larger gear $=$ Answer

mm and smaller gear $=$ Answer

mm$.(2)$

$8.$ The addendum of the larger wheel $=$ Answer

mm and the addendum of the smaller wheel $=$ Answer

mm$.(2)$