Grasping is an essential task in robotic applications and is an open challenge due to the complexity and uncertainty of contact interactions. In order to achieve robust grasping, systems typically rely on precise actuators and reliable sensing in order to control the contact state. We propose an alternative design paradigm that leverages contact and a compliant bistable mechanism in order to achieve "sensing" and "actuation" purely mechanically. To grasp an object, the manipulator holding our end effector presses the bistable mechanism into the object until snap-through causes the gripper to enclose it. To release the object, the tips of the gripper are pushed against the ground, until rotation of the linkages causes snap-through in the other direction. This push-on push-off scheme reduces the complexity of the grasping task by allowing the manipulator to automatically achieve the correct grasping behavior as long as it can get the end effector to the correct location and apply sufficient force. We present our dynamic model for the bistable gripping mechanism, propose an optimized result, and demonstrate the functionality of the concept on a fabricated prototype. We discuss our stiffness tuning strategy for the 3D printed springs, and verify the snap-through behavior of the system using compression tests on an MTS machine. Acknowledgements Support for this project has been provided in part by NSF Grant No. 1138847 and DGE-1845298. We also thank Terry Kientz, Jeremy Wang, Peter Szczesniak, and Joe Valdez for their assistance with the fabrication, and Neal Tinaikar for assistance with initial prototypes. We are grateful.