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Deflection angle for idle gear development

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   When I develop the machine, I used to use some formulars in textbook which I studied at my university. I used the Castigliano's theorems so often and several cases were already solved so I just needed to apply it to my real case. But below case was not in my textbook, which I needed this case for my idle gear development so I made it by myself. M A B = − M ′ − F a c l M B C = − M ′ + F ( c − l − a ) M_{AB} = -M' - \frac{F a c}{l} \qquad M_{BC} = -M' + F(c - l - a) ∂ M A B ∂ M ′ = − 1 ∂ M B C ∂ M ′ = − 1 \frac{\partial M_{AB}}{\partial M'} = -1 \qquad \frac{\partial M_{BC}}{\partial M'} = -1 θ A = ∫ 0 l + a M ( ∂ M ∂ M ′ ) d c E I , (where M ′ = 0) \theta_A = \int_0^{l+a} M \left( \frac{\partial M}{\partial M'} \right) \frac{dc}{EI} \quad,\quad 2M' = 0 = ∫ 0 l − F a c l ( − 1 ) d c E I    +    ∫ l l + a F ( x − l − a ) ( − 1 ) d c E I = \int_0^l -\frac{F a c}{l} (-1) \frac{dc}{EI} \;+\; \int_l^{l+a} F(x - l - a)(-1)\frac{dc}{EI} ​ = F a E I ∫ 0 l x l d ...

Profile shifted gear addendum and tip diameter

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 I worked in R&D for transmission development. I used to study by myself to prove any formular for better understanding. Sometimes I look back my documents and surprised to myself how I did this all. Below is to find the reason why profile shifted gear addendum and tip diameter is decided by center distance correction coefficient and profile shift coefficient of partner gear. I was wondering why some gear specs is decided by partner gear's specification so I calculated to see it. Addendum and Dedendum based on gear 1's reference circle is as below. Addendum = ( 1 + y − x 2 )   m (1 + y - x_2)\,m Dedendum = ( 1.25 − x 2 )   m Total depth = Addendum + Dedendum = ( 2.25 + y − ( x 1 + x 2 ) )   m The clearance between 2 gears are same as length of AB. A  ⁣ B = ( 1.25 − x 2 ) m − { ( 1 + y − x 2 ) m − y m } A\!B = (1.25 - x_2)m - \{(1 + y - x_2)m - y m\} = 0.25   m = \boxed{0.25\,m} ​ ​ This proves that even after profile shift is applied, to meet the clearance (0.25m) between...

Gear working pressure angle

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For beginner member in R&D, I always used to recommend to prove some formulars by themselves. By doing so, they can remember it better and apply it to another area better.  Regarding gear in machine, pressure angle and correction coefficient of center distance can be obtained from the following calculation. Note that even when gear has profile shift, base diameter doesn't change. d ′  cos α ′  =  d b (base diameter) ​ d  cos α  =  d b (base diameter) ​ ​ \Rightarrow\ d' \cos \alpha' = d \cos \alpha ⇒    d ′  cos α ′  =  d  cos α cos ⁡ α ′ = d d ′  cos ⁡ α = cos ⁡ α ⋅ a 0 a a : actual center distance a0 : standard center distance where a 0 = r 1 + r 2 2  m a_0 = \frac{r_1 + r_2}{2} \text{ ?} Finally then I can get, ∴   α ′ = cos ⁡ − 1 ( cos ⁡ α 2 λ z 1 + z 2 + 1 ) \therefore\ \alpha' = \cos^{-1} \left( \frac{ \cos \alpha }{ \frac{2\lambda}{z_1 + z_2} + 1 } \right) This working gear pressure angle is us...

Ads not showing and debugging

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This project was based on below environment. Expo bare project ( npx expo prebuild ) with template TypeScript. expo: 54.0.23 react-native: 0.81.5 react-native-google-mobile-ads: 16.0.0 Suddenly Ads were not working! Yesterday they were all fine, all ads were showing correctly. But now Banner area empty, rewarded ads not loaded (if not loaded, gray inactivated button)  I didn't change anything from yesterday. No package added, no coding editied, it was same as before, but just 1day after, it's not working. I have banner, interstitial, rewarded ads but they all are not showing. The first thing I tried was making bare project again. Simply erase android, ios folder and make it again with expo prebuild. $ rm -rf android ios $ npx expo prebuild $ npx expo start:android Ads still not showing. So this time I tried to wipe data in simulator and even delete the simulator and made it again. Not working. I started to doubt about some AdMob server error, since I heard rec...

Rewarded Ads logic and debugging

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  This writing is about how I make some logic to show the correct hint in Sudoku after watching Google AdMob rewarded ads. The project is based on expo bare project with package, react-native-google-mobile-ads. This project was based on below environment. Expo bare project ( npx expo prebuild ) with template TypeScript. expo: 54.0.23 react-native: 0.81.5 react-native-google-mobile-ads: 16.0.0 What I was trying to achieve is that in the hint modal, if I touch the WATCH AD button, it shows rewarded ads from Google AdMob. After watching it, hint modal should be closed automatically and 1 hidden sudoku number should appear in random as a reward. The first challenge that I encounter was that the reward action was not carried out at the first ads watch. From the second ads watch reward action was carried out well, but not the first one. After several trial and error I found that it was because when reward action function was called it referred old status of the function so first reward w...