Think of the perfect Impressionist image and chances are that it would be either one of Edgar Degas's pictures of ballerinas or a Monet view of lilies or haystacks.

Degas was as obsessed with dancers and capturing the way they moved as Monet was with capturing the light through the day on haystacks, buildings and his garden.

Not that they were that similar as artists. Where most of the impressionist group – whose exhibitions Degas showed in from their beginning in 1874 to their last in 1882 – were concerned with colour and the play of light on landscape and the life of the new world they championed, Degas, who was also concerned with capturing the life of the new world, did so in a far more studied way, interested at first less in colour than form and technical experiment. The "en plein air" painting so beloved by most of his colleagues he openly derided, nor was he much taken by the efforts of his fellow impressionists to achieve effect through the spontaneity of brushwork directly on canvas. And then there was the question of personality. Most of the Impressionists felt themselves part of a group pioneering modernity in good spirits. Degas was a loner with an acerbic wit and a habit of losing friends. The older he got, the more right wing and the more openly anti-semitic he became. Over the Dreyfus affair – that litmus test of intellectual liberalism in his day – he sided with the government. "All his friends had to leave him," commented Jean Renoir. "I was one of the last to go, but even I couldn't stay till the end."

But if Degas was on the wrong side of history, he was on the right side of art. His radical approach to technique, his efforts – through painting, print, photography and sculpture – to pursue his chosen themes, his startling compositions and, above all perhaps, his pastels and work in oil on paper earned him far greater influence on his successors and on modern art than any of his colleagues in the movement.

Nowhere more so than in his paintings of ballerinas, a theme he pursued throughout his long working life: drawing, modelling, photographing and painting them in almost every gesture and movement from the early 1870s until the time he ceased working in the first decade of the 20th century.

All the more extraordinary, then, that we in Britain have had to wait until now – with a major exhibition on Degas and the dance opening this week at the Royal Academy – to see his most committed theme in all its aspects and over its full development, from the first precise paintings of the rehearsal to the final studies of dress and movement.

Why this obsession with the dance in general and the ballerinas in particular? He himself always evaded a clear answer, talking at one time of the classical tradition going back to Greece, at other times of its suitability as a subject of drawing. "They call me the painter of dancers," Ambroise Vollard, the art dealer, later recalled him as saying, jokingly. "They don't understand that for me the dancer was a pretext for painting pretty fabrics and rendering movement."

It is the movement part of that explanation which the Royal Academy is emphasising. Indeed its show is titled Degas and the Ballet: Picturing Movement. Eschewing the "chocolate box" fame of his art they are determined to stress instead his seriousness and his radicalism, through photography as much as drawing. Capturing motion certainly challenged Degas in a peculiarly obsessive way. All his career he sought to present the human figure, not in repose or monumentality, but in action or preparation for it. Even his nudes had to be portrayed in the process of washing themselves, drying their backs or combing their hair.

Going backstage at the Paris Opera and hiring dancers to hold poses in his studio, he made endless studies in his sketchbook of their actions and dress.

Starting with a preliminary sketch of the central figure of his composition, he would then expand it with added drawn sheets until he had the full picture prepared, which he then transferred by canvas, often using the grid system used by the Italian fresco artists of the Renaissance, whose work he spent two years copying as a young man. Once worked up, he would then keep retouching and making slight changes until the canvas was taken from him.

It was the same with pastels and his painting in thinned oils on paper ("essence" as it was called). The paint or pastel lines were looser, the colours bolder, particularly as his eyesight started fading in his seventies and oil on canvas became more laborious. But the preparation was as exacting and his effort to build up colour and texture by fixing one layer and then adding another was an invention of his own, as was his development of monotype engravings, in which he painted directly on to the plate and then soaked a paper upon it. He used them not just to experiment with composition but also as the foundation on which he could then add pastel or oil.

But there was also something peculiarly compulsive about the way he sought, in the most concentrated fashion, to examine the female figure, in nudes as in dancers.

He also wanted, in his dance pictures, as in his nudes, to delineate the female figure with scientific accuracy, to the point that critics complained (and he himself conceded) that he was treating the human figure as if it were an animal, to be dissected and studied as a body rather than a person.

How much sex played a part in this is uncertain. Degas was a single man. Above his bed he hung an erotic Japanese print of some frankness. More than one of his contemporaries voiced the suspicion that his love of ballet and his frequent visits backstage and the invitations to model back in his studio, were not entirely artistic in their intention.

The members of the corps de ballet were mostly poor girls regarded as ready prey for the aficionados allowed access to the rehearsal rooms. He astounded the art world in the 1881 Impressionist Exhibition by showing the now-famous wax sculpture Little Dancer of Fourteen Years, with real hair, dress and ballet pumps.

It was a daring departure for sculpture, but the reference to the age of the girl and the position of the dancer, thrusting out her still unformed breasts worried some.

If sex was a driving force, however, the paintings don't betray it. Desire is not the undercurrent: sweat and poise are. So is froth and flounce. Degas may have been joking when he said that depicting dance was a "pretext for painting pretty fabrics" but he had a keen sense of texture and gathered a considerable variety of textiles to use as backdrops in his studios. Beside the figures of the dancers themselves, drawn with precise feeling for the body beneath, there are joyous swirls of tulle and colour. There is in his ballet works a vivacity; a playfulness even, that suggests a man who genuinely loved the art form and enjoyed the company of ballerinas; their chatter as well as their performance.

His early rehearsal paintings are still quite formal in their composition, the dancers painted in groups arranged against windows and staircases.

Like all the Impressionists, he was profoundly influenced by the Japanese woodblock prints becoming available at the time, with their use of bold, block colours, their fresh angles of vision and their drastically cropped figures. They also taught him to be unafraid of using large empty spaces in his compositions. His early pictures of the rehearsal rooms, of which the exhibition is showing several, are masterpieces of line and space.

As his work developed, however, so did his concentration on the dancers themselves and the flow of their limbs and costumes. It was the performance itself he wanted to capture, with quite startling viewpoints and close-ups, bringing not just movement to life but making the viewer into the audience.

And then with the late works of the 1890s, as his eyesight started to fail and he resorted more and more to pastel and the use of tracing paper to transfer design and even act as the underlay, he embarked on what he called "an orgy of colour".

Partly influenced by young painters such as Gauguin and Van Gogh (whose work he bought surprisingly early) he went for the sense of vivacity and swirl in his dancers, framing them in small groups of two and three as if they were one and the same person in different poses: in blues and oranges and yellows of vivid freshness.

It is these, of course (and the Academy show has a good selection, particularly of his long horizontal "panorama" pictures), for which he is best known and most loved by today's exhibition-goers. And how could you not be entranced by them? Of all artists, Degas warrants academic study of his methods – as an unforgettable small show at the National Gallery in its Artist at Work series six years ago and a bigger exhibition concentrating on his later work, Degas: Beyond Impressionism, a decade and a half ago, both illustrated.

Degas is the artist's artist of the Impressionists; the man younger painters looked to for ideas and novel experiment. With Monet and Renoir, you don't need X-rays of the canvas to understand what they were up to. Their approach was relatively simple, if the effect was complex. But with Degas, examination of the works does throw new light on how he achieved what he did.

Knowledge of his working methods does deepen your understanding and increase your respect for his work.

But then he's not a "chocolate box" artist for nothing. You can make too much of the perspiration behind his invention and not enough of the joy in the effect. The Royal Academy in this case seems intent on playing up the importance of photography of his life, presumably as an original contribution to understanding his work. But the thing about his dance pictures is that they sing. They're not dry exercises in method, for all their preparation. They are full of life. Indeed, by the end, when he painted several pictures of Russian dancers, Degas seems to be reaching for something beyond dance: actual ecstasy. Maybe his primary aim was an intellectual one of capturing movement. But I suspect something else was in play. Go to any ballet performance and you will find men who are there not to accompany their wives or to ogle the men in tights, but to feel something special and indefinable in the ballerina – the froth of femininity along with its grace.