I was learning about the Wright Brothers and I wondered why the first planes didn't have wings that would flap. You would think that humans would naturally try and mimic a bird's wings, so why were the first plane wings stationary?
Ornithopters
What your are referring to, using the correct terminology, is called a ornithopter, Whilst some of the first aviation pioneers, including Leonardo da Vinci indeed took inspiration from the flapping motion birds make, the path of aircraft development took a different direction.
The inherit problem with Ornithopters is that they are complex, in the sense that they use a lot of moving parts in order to mimic the motion birds actually make. And up until recently, with the modern day materials such as carbon fiber micro-electric engines and such, no one was able to accurately mimic the motion.
The step towards fixed wing aircraft as opposed to flapping contraptions was probably first undertaken by Sir George Cayley (b.1773-d.1857) around 1799. His 1799 design comprised of fixed wings and a cruciform tail plane, and a man powered “Flapper” propellor, designed to produce both lift and propulsion. This can be seen as a stage between the pure Ornithopter and the fixed wing aircrafts. He observed birds closely and discovered that the motion that previous Ornithopter designers tried to mimic was erroneous, and that the real motions bird wings make are vastly more complex. He decided that this would be hard, if not impossible to mimic and sought other means of generating lift, though persistently retaining “paddle propulsion”. He was probably also one of the first persons to become fully aware of the lifting capabilities curved wing designs posed, as this was also included in his design, though it was more or less a sail, and not the rigid form we became used to. He possibly took inspiration from the way in which ship sails curved with the wind, in addition to shape of bird wings. In 1804 he was the first to conduct research into the lifting capabilities of wing forms at various angles of attack on a revolving whirling arm, mill like contraption, on this he produced a model that we would recognize to be a glider / kite: a cruciform shape with wings at the front set at an incidence angle of 11,5 degrees (this is very close to the optimal angle of attack for most aerofoils !)
The logical next step was powering these gliders, but this was unfeasible given the technology of the early 19th century as Steam-engines have a power to weight ratio that is too poor for aircraft. This discouraged him from further developing his machines for the time being.
After a break from his aeronautical aspirations, and period in which he favoured the powered airship, he returned to designing mono winged gliders. He produced a prototype and demonstrated it’s gliding capabilities, and published his design in 1852, but sadly it was lost to the world until the new generation of pioneers came along towards the end of the 19th century, whom were indebted to him, including Otto Lillienthal, whom is often cited as the inventor of the glider.
Sources:
Charles H. Gibbs-Smith, Sir George Cayley: 'Father of Aerial Navigation' (1773-1857) Notes and Records of the Royal Society of London, Vol. 17, No. 1 (May, 1962), pp. 36-56 http://www.jstor.org/stable/531013
C. H. Biddlecombe, The Development of the Heavier-Than-Air Machine, Proceedings of the American Philosophical Society, Vol. 67, No. 3 (1928), pp. 297- 305 http://www.jstor.org/stable/984295