The purpose of the training flight was to practice autorotations with power recovery. The flight instructor reported that, as the helicopter descended through about 40 ft, he instructed the student pilot to increase the landing flare and roll on throttle for power recovery. As the helicopter continued to quickly descend to about 8 ft, they raised the collective, and the flight instructor felt resistance in the collective. The rpms began to drag down, and he tried rolling on the throttle to bring the rpms back up. The flight instructor reported that he believed that the student had tensed up on the throttle and collective as he tried to keep the helicopter level and cushion for the landing. The student pilot reported that, in hindsight, he was pulling up on the collective, but his hand (wrist) was locked, which prevented the governor to roll on and increase power. The helicopter subsequently landed hard, which resulted in substantial damage the fuselage. The flight instructor reported that there were no preaccident mechanical malfunctions or failures with the helicopter that would have precluded normal operation