What is the relationship between the Byakugan, Rinnegan, and Sharingan? Can anyone brief a little about the link between the Byakugan, Rinnegan, and Sharingan? I know the meanings, but I don't know the relationship between the eyes.
The progenitor of chakra, Kaguya Otsutsuki, was the first character (historically) to have Byakugan on Earth. 

After eating the Chakra Fruit, she awakens a third eye on her forehead, the Rinne Sharingan.



Now the Rinne Sharingan is completely independent of the Byakugan's influence. This is because the Rinne Sharingan is the result of the manifestation of the powers of the Chakra Fruit on a person. 


  The Rinne Sharingan possesses the ocular power of the Sharingan, and can be used to cast the Infinite Tsukuyomi, an extremely powerful genjutsu which can only be countered by the Rinnegan and the chakra of the nine tailed beasts.


When her two sons, Hagoromo and Hamura were born, they had their mother's Byakugan. As time progressed, Hagoromo awakens a new dojutsu, the Sharingan. In the anime, Hagoromo awakened the Sharingan after finding the corpse of his love interest Haori.



The Sharingan is a derived form of the Rinne Sharingan, meaning, weaker. But powerful nevertheless. He goes on to attain the Mangekyou Sharingan also, but that is not shown on screen.

Hagoromo then achieves the Rinnegan, after nearly killing his brother (and thereby freeing him from his mother's control). 



The Rinnegan is a much more advanced form of the Sharingan and it has a wide range of powers. The Rinnegan is stated to be something that is unique to the Sage of Six Paths, which is why, to obtain the Rinnegan, shinobi mix the chakra of Ashura and Indra (thereby getting Hagoromo's chakra).

While the Byakugan doesn't have any direct link to the Rinnegan and Sharingan, it does play a significant role in their creation, along with the Rinne Sharingan.