Tutorial: How to Derive the Formula for the Planetary Mechanism Gear Ratio

O.T. Vinta
O.T. Vinta
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Published 2018-01-09
The gear ratio formula for two meshing gears is simple and intuitive, while the gear ratio formula for the planetary mechanism is not. In this tutorial, we will show you an original and easy-to-understand approach to deriving this formula.

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All Comments (21)
  • @avivzaberko5217
    Awesome video, thank you so much! There aren't many channels out there who post good and clear tutorials about the mathematics behind mechanisms.
  • @user-ds7dx5dh9j
    Thank you very much! This is the clearest explanation that tells how the gear ratio is derived. It's really helpful for me to understand my textbook.
  • @arturoaramburo9365
    Beautifully Emplaned!! These 2 concluded formulas to determine the ratio, apply well when the input is the sun and the output is the carrier as mentioned in the video. What about a scenario in which the input is the sun with the carrier arrested and the output is the ring? How can that ratio be determined?
  • @LuxBacelo
    Learning with GLaDOS. Awesome video!
  • @sivaprabha8681
    Thanks for a clear explanatin. Can any body explain, if the sun gear has 30 teeth, panatary has 15 teath, and ring has 90 teath what will be the RPM of the carrier if the sun gear is rotated at 1000 RPM, under the following conditions. Sun gear is the driver and carrier shaft is the driven connected to a load. 1. The ring gear is held stationary. 2. The ring gear is free to rotate, and the carrier shaft is loaded.
  • @muhah95
    I want to ask For example Sun 12 teeth Planet 24 teeth Ring 60 teeth If the sun gear turns 360° 12 teeth, the planet gear will turn 12 teeth 180° If the planet gear turns 12 teeth 180°, the ring gear will turn 12 teeth 72° But if we calculate this by using this formula we get 360÷((60/12)+1)=60° How it can be? (The formula is true, i dont say it is wrong) but What is my mistake?
  • @mekanikaengineerikatv
    A very interesting explanation, Now your calculation is only true if the ring is static!
  • @danielcalvo9254
    Me ha gustado mucho la explicación. Lo he comprendido bien.
  • @makerEmber
    Perfect instructions!!! I got full understand for my planetary gear system. And I have one question for compounnd planetary gear such that one tooth of planetary gear meshes with sun gear and other tooth meshes with ring gear. From googling, I understand both tabular method and algebraic method can be used. But I couldn't solve gear ratio formula for compound planetary gear using your method ... Vc and zero velocity at the ring contact point and instantaneous velocity at the sun contact point and so on. Please could you give me some directions?
  • @albertousman7624
    Me.encanto. Entiendo el inglés y la explicación. Desde ya agradezco , es muy útil, interesante . Pero sería conveniente que estuviera los subtítulos, por lo menos en castellano. Muchos que se beneficiarían de esta información, y no tienen PC, deben verlo por el celular. Yo, de mi parte estoy agradecido por estos tips. Atte. Alberto.
  • @jamesmatheson9624
    A planetary gear calculation is ring divided by sun So. 46 ring.9sun=5.1
  • @joandar1
    I was falling into the mistake of thinking it was as simple as the ratio of the sun gear tooth No. and the ring gear tooth No. I can now see why I was always wrong until now! Great educational tutorial!!! By the way I have also heard the ring gear referred to as an Annulus, has anyone else heard of this or used this term! Just curious. John, Australia. https://en.wikipedia.org/wiki/Annulus_(mathematics)