Question #$1$

The double$-$reduction helical gearset shown in the figure above is driven through

shaft $a$ at a speed of $1200\frac{\text{r}\text{e}\text{v}}{\text{m}\text{i}\text{n}}.$ Gears $2$ and $3$ have a normal diametral pitch of

$12$ teeth$/$in$,$ a $30$@ helix angle, and a normal pressure angle of $20.$ The second pair

of gears in the train, gears $4$ and $5,$ have a normal diametral pitch of $6$ teeth$/$in$,$ a

$25$ helix angle, and a normal pressure angle of $20.$ The tooth numbers are: $N_2=$

$14,N_3=54,N_4=16,N_5=36.$ Find:

$($a$)$ The directions of the thrust force exerted by each gear upon its shaft

$($b$)$ The speed and direction of shaft $c$

$($c$)$ The center distance between shafts