Kinematics Please Help In the mechanism shown let the input

Kinematics Please Help

In the mechanism shown, let the input be gear 2 and assume that all of the gear tooth numbers (N2, N3, N4, N5, N6, N7, and N8) are known. Derive an expression for the angular velocity of gear 8. (Stages, angular velocity expression)

Solution

Gear 2 is input gear having angular velocity ₂.

Gears 3 and 4 are compound gears mounted on the same shaft.

Apply law of gearing between mating gears

(2-3) (₂/₃) = (N₃/N_{2) ........equation 1}

(4-5)   (₄/₅) = (N₅/N4) ....... equation 2

(5-6) (₅/₆) = (N₆/N₅) ..........equation 3

(6-7) (₆/₇) = (N₇/N₆) ......... equation 4

(7-8) (₇/₈) = (N₈/N₇) .............equation 5

multiplying the above equations

Note: ₃=₄ since mounted on same shaft.

(₂/₈) = ((N₃xN₈) / (N₂xN₄))

Thus the final expression for ₈ is

₈ = (( ₂ x N₂ x N₄ ) / (N₃ x N₈))