We have proposed a velocity-based mechanical safety device for human-friendly robots in order to improve the safety of the robots. The device is attached to each of the robot's drive-shafts. If the device detects an unexpected drive-shaft's angular velocity, it locks the drive-shaft. The device works even when the robot's computer breaks down, because it consists of only passive components without actuators, controllers, or batteries. In the device, the rotational angle of the drive-shaft after detecting the unexpected velocity and before locking is important because an increase in the angle increases the risk of collision between the robot and humans. However, we have never analyzed the angle. In order to design the safety device efficiently, we need to analyze the angle. In this paper, we analyze the rotational angle of the drive-shaft. First, we review the velocity-based mechanical safety device. Next, we analyze the rotational angle. Lastly, we verify the effectiveness of the analysis by experiments using the velocity-based mechanical safety device which we developed.