Answer:
Number of teeth on pinion = [tex]N_{p}[/tex] = 12
Step-by-step explanation:
Given:
Gear ratio = 3 : 1 = 3
Diametral Pitch = P = 4
Center distance = c= 6 in
No. of teeth on Pinion = [tex]N_{p}[/tex] =?
Gear ratio =[tex]\frac{ Number. of. teeth. on. gear}{ Number. of. teeth. on. pinion}[/tex] = [tex]\frac{N_{g} }{N_{p}}[/tex] = 3
As Gear ratio = 3, so
Diameter ratio = [tex]\frac{d_{g} }{d_{p}}[/tex] = 3
(Note : Diameter Ratio = Gear ratio )
[tex]d_{g} =3d_{p}[/tex] Equation 1
Center Distance = c = [tex]\frac{d_{g} + d_{p}}{2}[/tex] = [tex]d_{g} + d_{p}[/tex]= 2 (c)
[tex]d_{g} + d_{p}[/tex] = 2 (6) = 12 in
substitute [tex]d_{g} [/tex] from equation 1, here
[tex]3d_{p} + d_{p}[/tex] = 12
[tex]4d_{p} [/tex] = 12
[tex]d_{p} [/tex] = [tex]\frac{12}{4}[/tex] = 3
[tex]d_{p} [/tex] =3in
Now : Diametral Pitch =P= [tex]\frac{N_{p} }{d_{p} }[/tex]
[tex]N_{p}[/tex] = [tex]d_{p}(P)[/tex]
[tex]N_{p}[/tex] = 4 (3)
[tex]N_{p}[/tex] = 12
Which are the number of teeth on pinion
