Traditionally, from Moses and on there was always only one head of the Sanhedrin, the president, the prince, the king, the Supreme Judge, Av Beis Din, etc. No other members or titles or names are ever mentioned IIRC, (to prove the point that all courts are equally authoritative).
After the Hasmonean revolt, the age of the Rabbinic Pair (Zugot) commenced and presented a sudden change in the pattern: two heads of the Sanhedrin functioning alongside each other - Nassi AND Av Beis Din.
What exactly happened here - was it the position of Nassi invented or of Av Beis Din? And what were their duties and responsibilities?