The pilot reported that he was performing touch and go landings. On the fourth traffic pattern, the controller requested that he turn inside of the airplane that was on final approach. The pilot stated that he delayed extending the landing gear until he turned the airplane onto the final approach leg. After he reduced the airspeed, he selected flaps and extended the landing gear. During the landing, the pilot “heard the sound of metal” and realized that the landing gear was not extended. The pilot reported that when he moved the landing gear handle, he did not see the unsafe landing gear warning light, nor was there a landing gear warning horn. The airplane sustained damage to the lower fuselage. The mechanic that recovered the airplane after the accident reported that the landing gear extended normally, and the landing gear warning horn was audible. Further, the pilot reported to the responding inspector that he had just forgot to extend the landing gear.