Impulse force generator based on snap-through buckling of robotic closed elastica: Analysis by quasi-static shape transition simulation

In this paper, we investigate the property of an impulse force generator based on snap-through buckling of a robotic closed elastic rod which is considered as one of good examples of continuum robots. The impulse force generator considered here utilizes a snap through buckling of an elastic rod where its base end is pinned and driven by a rotary actuator forcibly while the tip end is pinned or clamped to the fixed point. One of the most fundamental design problems is to maximize the released elastic energy at each buckling state subject to limited ranges of driving torque and angle of a given actuator. From this design viewpoint, we show two findings obtained from quasi-static planar shape transition simulation of the closed elastica, which will be useful for a design of the robot, that is, the ratio of the elastica length and the endpoint distance decides 1) the buckling angle which relates to the range of an actuator driving angle, and 2) the released elastic energy per the maximum driving torque. We also provide a mathematical description of snap-through buckling based on which we can measure a distance to a buckling point.