Small aerial robots usually face a common challenge: they can only fly for a short time due to their limited onboard energy supply. To tackle this issue, one promising solution is to endow flying robots with perching capability so that they can perch or land on walls, trees, or power lines to rest or recharge. Such perching capability is especially useful for monitoring-related tasks since the robot can maintain a desired height for monitoring without flying. One of the major challenges for perching is to design a light-weight and energy-efficient perching mechanism. In this paper, we present a 3D-printed compliant bistable gripper which is easy to close, stable to hold, and easy to adjust for a palm-size quadcopter to perch on cylindrical objects. If installed on the bottom of aerial robots, it can also be used for aerial grasping. The gripper can be directly activated by the impact force during contact to switch from open state to closed state. It can also hold the quadcopter safely since the required force to open the gripper is larger than the robot weight. We analyze the required forces for closing and opening to provide design guidelines for the mechanism. Experimental results show that the designed gripper can successful make the quadcopter perch on cylinders as well as grasp objects.