Question $5.$

$5\mathrm{.}1$ An epicyclical gear train shown in figure $4$ in the addendum consists of an annulus $\backslash ($ A $\backslash )$ having $130$ teeth, a sun gear B having $40$ teeth and a planetary gear C having $50$ teeth that are mounted on arm D$.$

Make use of the conditions given in the table above to calculate the following:

$5\mathrm{.}1\mathrm{.}1$ The velocity ratio of sun gear B

$5\mathrm{.}1\mathrm{.}2$ The velocity ratio of planetary gear $\backslash ($ C $\backslash )$

$5\mathrm{.}1\mathrm{.}3$ The speed of planetary gear C when annulus $\backslash ($ A $\backslash )$ is fixed and arm D rotated at $\backslash (50\backslash$mathrm$\{$r$\}/\backslash )\backslash (\backslash$min $\backslash ).$

$5\mathrm{.}1\mathrm{.}4$ The speed of annulus $\backslash ($ A $\backslash )$ when sun gear $\backslash ($ B $\backslash )$ is fixed and arm D rotates at $\backslash (30\backslash$mathrm$\{$r$\}/\backslash$mathrm$\{$min$\}\backslash ).(4)$

$5\mathrm{.}2$ A set of spur gears have a velocity ratio of $\backslash (5$: $3\backslash )$ and a module of $6$ mm if the pinion has $30$ teeth. Calculate the pitch diameter of both gears.