Two gears in a 3: 1 ratio gearset and with a diametral pitch of 4 are mounted at a center distance of 6 in. Find the number of teeth on the pinion. (please note that the smaller gear is the pinion, and the larger gear is the gear)

Answer:Number of teeth on pinion = [tex]N_{p}[/tex] = 12 Step-by-step explanation:Given:Gear ratio = 3 : 1 = 3Diametral Pitch = P = 4Center distance = c= 6 inNo. 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] = 3As Gear ratio = 3, soDiameter ratio = [tex]\frac{d_{g} }{d_{p}}[/tex] = 3   (Note : Diameter Ratio = Gear ratio )[tex]d_{g} =3d_{p}[/tex]                                     Equation 1Center 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 insubstitute [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] =3inNow : 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