The pilot/builder was planning a short flight above the runway for the purpose of testing the newly built gyrocopter. During the takeoff roll, the nose wheel experienced a shimmy and the pilot was unable to maintain directional control. The gyrocopter rolled onto its left side and exited the side of the runway before coming to rest in the grass. During the rollover, the main rotor mast was substantially damaged. A postaccident examination of the gyrocopter revealed a loose bolt in the nose gear steering linkage which allowed the nose wheel to shimmy.