Lord Surya Narayana's Ratha Saradhi (Charioteer) Aruna doesn't have both legs. What exactly is the story behind losing his legs and becoming ratha saradhi of lord Surya?
Birth story of AruNa is described in SECTION XVI Astika Parva- Adi Parva of Mahabharata.
"Sauti said, ' O Brahmana, in the golden age, Prajapati had two daughters. O sinless one, the sisters were endowed with wonderful beauty. Named Kadru and Vinata, they became the wives of Kasyapa. Kasyapa derived great pleasure from his two wedded wives and being gratified he, resembling Prajapati himself, offered to give each of them a boon. Hearing that their lord was willing to confer on them their choice blessings, those excellent ladies felt transports of joy. Kadru wished to have for sons a thousand snakes all of equal splendour. And Vinata wished to bring forth two sons surpassing the thousand offsprings of Kadru in strength, energy, size of body, and prowess. Unto Kadru her lord gave that boon about a multitude of offspring. And unto Vinata also, Kasyapa said, 'Be it so!' Then Vinata, having; obtained her prayer, rejoiced greatly. Obtaining two sons of superior prowess, she regarded her boon fulfilled. Kadru also obtained her thousand sons of equal splendour. 'Bear the embryos carefully,' said Kasyapa, and then he went into the forest, leaving his two wives pleased with his blessings.'
"Sauti continued, 'O best of regenerate ones, after a long time, Kadru brought forth a thousand eggs, and Vinata two. Their maid-servants deposited the eggs separately in warm vessels. Five hundred years passed away, and the thousand eggs produced by Kadru burst and out came the progeny. But the twins of Vinata did not appear. Vinata was jealous, and therefore she broke one of the eggs and found in it an embryo with the upper part developed but the lower one undeveloped. At this, the child in the egg became angry and cursed his mother, saying. 'Since thou hast prematurely broken this egg, thou shall serve as a slave. Shouldst thou wait five hundred years and not destroy, or render the other egg half-developed, by breaking it through impatience, then the illustrious child within it will deliver thee from slavery! And if thou wouldst have the child strong, thou must take tender care of the egg for all this time!' Thus cursing his mother, the child rose to the sky. O Brahmana, even he is the charioteer of Surya, always seen in the hour of morning!
Since Aruna was upper part of embryo, he doesn't have legs.
After churning of ocean, Surya and Chandra caught Danava Rahu drinking nectar or Amrita in disguise. Though Lord Vishnu used His Sudharshana Chakra to sever his head, Nectar had already reached his throat and severed parts Rahu and Ketu attained immortality. Now as an act of retaliation, Rahu and Ketu started devouring (hiding) them for some time (what we call eclipses). Lord Surya thought Devas were acting as mere spectators to these events and decided to burn three worlds. Aruna stopped this intensity and became his Ratha Saradhi.
This story is described in SECTION XXIV Astika Parva- Adiparva of Mahabharta
"And Garuda said, 'Let no creature be afraid; as ye are in a fright at the sight of my terrible form, I shall diminish my energy.'
"Sauti continued, 'Then that bird capable of going everywhere at will, that ranger of the skies capable of calling to his aid any measure of energy, bearing Aruna on his back, wended from his father's home and arrived at his mother's side on the other shore of the great ocean. And he placed Aruna of great splendour in the eastern regions, just at a time when Surya had resolved to burn the worlds with his fierce rays.'
"Saunaka said, 'When did the revered Surya resolve at the time to burn the worlds? What wrong was done to him by the gods that provoked his ire?'
"Sauti said, 'O sinless one, when Rahu was drinking nectar among the gods at the time of the churning of the ocean he was pointed out to the gods by Surya and Soma, and from that time he conceived an enmity towards those deities. And upon this Rahu sought to devour his afflictor (Surya), became wroth, and thought, 'Oh, this enmity of Rahu towards me hath sprung from my desire of benefiting the gods. And this dire consequence I alone have to sustain. Indeed, at this pass help I obtain not. And before the very eyes of the denizens of heaven I am going to be devoured and they brook it quietly. Therefore, for the destruction of the worlds must I strive.' And with this resolution he went to the mountains of the west.
"And from that place he began to radiate his heat around for the destruction of the world. And then the great Rishis, approaching the gods, spake unto them, 'Lo, in the middle of the night springeth a great heat striking terror into every heart, and destructive of the three worlds.' Then the gods, accompanied by the Rishis, wended to the Grandsire, and said unto him, 'O what is this great heat today that causeth such panic? Surya hath not yet risen, still the destruction (of the world) is obvious. O Lord, what will happen when he doth rise?" The Grandsire replied, 'Indeed, Surya is prepared to rise today for the destruction of the world. As soon as he will appear he will burn everything into a heap of ashes. By me, however, hath the remedy been provided beforehand. The intelligent son of Kasyapa is known to all by the name of Aruna. He is huge of body and of great splendour; he shall stay in front of Surya, doing the duty of his charioteer and taking away all the energy of the former. And this will ensure the welfare of the worlds, of the Rishis, and of the dwellers in heaven.'
"Sauti continued, 'Aruna, at the behest of the Grandsire, did all that he was ordered to do.