The origin of Charkha has been a point of contention between many historians. While some believe the spinning wheel was invented in India between 500 & 1000 A.D., other school of thought denies the same (and claim it was only hand spinning) and believe that there is a high probability of Charkha being invented in Islamic world in early 11th Century. Etymology also points at the place of origin being either of the two. While in Persian and Urdu the word Charkha seem to have evolved from Charka which means wheel, in Sanskrit it is closely related to Cakra which means circle. Also, in Iran the Spinning wheel was/is called Charkhu. There are however, two specific evidences which favor Islamic world as the place of Origin. Firstly, the earliest illustration comes from Baghad from 1237. Secondly, the earliest Indian reference is dated to 1350 pointing at the fact the Charkha arrived in India from Iran.
You'd question that these mentions are from 11th century broadly, what happened before that? The answer is simple and straight- handspinning with a spindle. A little reading into the topic actually made us realise two very interesting facts. For one, spinning with spindle has been in practice since stone age. And spindle were commonly used in parts of Europe as late as mid-18th Century.
Another interesting thing to learn about origin of Spinning wheel or rather anything, is the fact that, things are not created overnight. The continuous improvement to the design and addition of features created what we see today as a Charkha, the Great Wheel or the Treadle Wheel. This process of design improvement is still on. While, we might have different definitions for what qualifies as handspun, it cannot be denied that Spinning wheel further evolved into present day NMC (New Model Charkha). Further on the basis of variety, ethics, taste requirement, the definition as well as the spinning wheel shall keep evolving.
Sources: Wikipedia, Friends from Khadi Sector & Our knowledge from our days at College.