The word Vidangam means something which is not chiseled or created by hand. The whole Lingam i.e the base and the top elliptical portion are in one piece i.e. Swayambhoo. There are 7 temples in South India around Thanjavur which are together known as Saptha Vidanga Sthalam. In all these places the Linga is made of either Emerald or Jade. The main deity in all these temples is Lord Shiva known as Thyagaraja.
Vidanga is a Sa-Uma-Skanda murti known as Somaskanda murti or Thyagaraja murti. Originally it was also known as Thyagaraja murti. It is also represented by a linga. The top portion of the linga which is elliptical in shape is believed to be a swayambhu while the base (avudayar in Tamil) is made by hand. In sapta vidangam represented by seven lingas, the base as well as top are in the single piece. They are made of same material (emerald or jade) but are of different sizes. The biggest is at Thirunallar whereas medium sized one is at Thiruvalur. It is believed that Lord Indra performs evening worship of the vidanga at Thiruvarur. Hence it is considered to be more auspicious. The murtis are generally kept in a separate shrine. The abhishek of these sapta lingas are done twice a day. After the rituals the lingams are kept in a safe place under lock and key as they are most valuable and priceless. Generally we observe Nandi to be in a seated position in front of Shiva linga in shiva temples. But in the sapta vidanga sthala we will find that the Nandis are in standing position in front of the shiva lingas.
Details of Sapta Vidanga from Puran:
According to Puran, once a monkey on a tree was plucking the leaves and dropping it to the ground where Lord Shiva and Goddess Parvati were relaxing under the tree. At that time Goddess Parvati who was disturbed asked Lord Shiva to drive the monkey away. As it happened to be a shiva ratri day, Lord told Parvati that the money has worshiped him with bilva leaves, hence he was pleased by his worship. He manifested before the monkey and asked him to ask for a boon. The monkey which did not desire anything worldly requested that it wishes to be born as a king with a monkey face and conquer the world (wanted to become famous). Later on this boon was granted by Lord Shiva. So the monkey was born as a Chola king named Muchukunda chakravarti with a monkey face.
As legend goes, to beget a son, Lord Vishnu prayed on an idol (moorthy) of Somaskanda (Shiva, Parvati and Skanda together). As a result He got Manmada (Kaama) as his son. During this period he also prayed on a Vidanga. Later on Lord Brahma got the Somaskanda moorthy along with Vidanga from Lord Vishnu who in turn gave it to Lord Indra. King Muchukunda (who has a face of monkey) helped Indra in defeating the asura Vaalasur in indraloka. Extremely pleased with Muchukunda’s help and full of gratitude, Indra wished to give a gift to Muchukunda for the help rendered by him. Being a staunch devotee of Lord Shiva, Muchukunda knew about the Thyagaraja moorthy (Vidanga Lingam) and asked for the same from Indra. Indra did not want to part with the same. So he made 6 more identical Vidangas and placed them before King Muchukunda and asked him to choose the real one from the lot. The King prayed to Lord Shiva and identified the correct one. So Indra gave all the 7 Vidangas to King Muchukunda. King decided to install them in and around Thiruvarur. Though Muchukunda was from Kongu region, he decided to install them around Thiruvarur because he knew spiritual greatness of Kaveri region. So he installed the original vidanga at Thiruvarur. The maragada (emerald) linga installed at Thiruvarur is known as Thyagaraja or maragada Nataraja. The place where these seven lingas were installed are together known as Sapta Vidanga. Thyagaraja is name given to the manifestation of Shiva at Thiruvarur and six other places is called as Somaskanda.