How did Kamasutra originate in India?

Kama Sutra isn't a concept to have originated.

It is the name of a book written by Vatsayana that's now considered to be the standard compilation of human sexual behavior

If you are asking how Vatsayana came with that idea, I believe that Indians were open about sex than anyone else. Indians associated sex with spirituality, pleasure and that which everyone is open about. We even have a dedicated God of Love (Kamadeva).

Kama sutra (Formulas of desire), written more than 1500 years ago by Vatsyayan is still an international bestseller and one of the most downloaded books from Internet. “Kama sutra” could be called as a “ Gift of India to the world” because neither any ancient nor any modern book have written anything like this on one of the most controversial and marketable subject on the earth- “Sex”. The book is not only about the copulation between male and female but it also deals with romance, codes & conduct, interaction, marriage, lifestyle and entertainment. Kama sutra had a deep impact on society and more importantly even on religions. Later on, Tantric sect in Hinduism and Vajrayan sect in Buddhism emerged, developed and dominated the society which emphasized on “Sexual or Materialistic way of life”. Even during medieval period, Kama sutra was very popular in royal houses. In modern times too, when it reached to the world, it created a sensation. But the main point of discussion of my topic is that how this remarkable book was made? Because the book is very vast, complex, critical and versatile as well. It’s author either had studied a vast literature on this topic or he had been a “Great genius” who wrote first time on a new topic? Here, the first opinion is correct i.e. he studied a vast literature on this topic written by his early authors. A.T. Kama sutra, the Kama shastra(science of Desire) is as ancient as the Indian civilization itself. But I have arose this topic because people in India as well as in the world know that Kama sutra is the first book on this subject, which is not correct. Through this article, I would show you that how ancient is the tradition of Kama shastra in India.

It’s very widely described in Kama sutra as :-

 Prajapati(Creator) after Creating people, wrote a book “Trivarga” [“Three subjects” which are Dharm (Righteousness), Arth(Economy and policy) and Kam(Desires)], composed on 1 lakh couplets  for better living of the people – (1.1.5.)

•     Manu took the “Dharm” part of this book and made an independent subject “Dharm shastra” Brihaspati took the “Arth” part of it and developed “Arthshastra” from it. Nandi, follower of Mahadev extracted “Kamasutra (or Kama shastra) from it, which was composed of a 1000 chapters(The story is also found in Mahabharat)– (1.1.6-8)

•   Shvetketu, son of uddalak summarized  “Kama shastra of Nandi” into 500 chapters (just half)  - (1.1.9.) 
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•   Then, Babhravya, resident of Panchal (Western uttar Pradesh) after intense study and revision shortened that  book into 100 chapters which composed of 7 books or units :- (i) Sadharan (ii) Samprayogik (iii) Kanya samprayuktak (iv) Bharyadhikarik (v) Pardarik (vi) Vaishik and (vii) Aupnishdik – (1.1.10) 
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•   Then “Duttak” on the request of courtesans of Patliputra, wrote on “Vaishik”(About Courtesans), the 6^th unit of Babhravya’s             Kama shastra – (1.1.11)

 Following the trend, separate books were written on each unit of the book:-

# “Charayan” wrote on Sadharan (Introduction into subject, .. lifestyle)

# Suvarnanath wrote on Samprayogik (Pre-sex experiments or enjoyement)

# Ghotak much wrote aon kanya samprayukt (Selection of life partner)

# Gonordiya (Patanjali) wrote on Bharyadhikaran (About wife)

# Gonika putra on Pardarik (Extra married relation)

# Kuchumar on Aupnishdik (Artificial uses for better sex-life)-(1.1.12)

  Thus with the authorship on different subjects by different masters, the main subject “Kama shastra” was divided and scattered. Every book like “Vaishik” of Duttak, were only fragments of the main subject. On the other side, the main book of “Babhravya”  was inaccessible for the masses due to it’s vastness (Made of 100 chapters). That’s why I (Vatsyayan) have summarized the great book of Babhravya with all it’s subjects (for mass readers). – (1.1.13-14)

TRADITION OF KAMA SUTRA

                 Thus, Vatsyayan describes the story of the tradition of the Kama shastra but in the last chapter of his book, he reveals some more important facts behind the composition of this book. These are :-

1. He experimented what he wrote:- He says (7.2.52.) that he gathered books of ancient authors, deeply studied them and experimented the written things. Then after great effort, he summarized the experimented facts and main points into his book “Kama sutra”

2.      Special tribute to Babhravya:- After analyzing the meaning of formulas especially of Babhravya, Vatsyayan wrote the “Kama sutra” in a systematic way (7.2.56)