Gear - Wing Spar Linkage

Hi All,

I am building a robotoc bird and have drive mechanism with a gear that has a linkage attached to it at some distance (L) like in the picture (#2 and #3). I am trying to find the vertical component of force given a torque for each cycling period. 

I have derived the free body diagram (#3) with the following equation to get the vertical component.

F_v = F*cos(90-theta)

Theoretically this makes sense but intuitively thinking about it, at 90 deg, FV should equal F as the force from the gear acts tangentially to the moment arm L

Any help would be greatly appreciated, maybe I need to draw a simpler free body diagram, been staring at this for hours and can't figure out what I am missing.


Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
  • Let me know if you have any questions.

    • Hi Savionf Thank you for taking the time to answer. Would you say this free body diagram is the best representation of the system. I am skeptical that this representation actually represent the forces acting at point at which the linkage is attached to the wing spar. (Upper most point on (#1) but rather that it is representative Soley of the vertical component of force at the gear. Does this make sense??

    • It is hard to answer your questions in general as it could depend on what you really want to do, but the formula you have for F_v seems reasonable, both mathematically and intuitively. F_v is the force which makes the gears to rotate. As you can see, the force results in minimum rotation when theta=0 and maximum rotation when theta=90 degrees.

The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.