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Flying robots capable of perch-and-stare are desirable for reconnaissance missions. Inspired by an adaptation that enables songbirds to sleep in trees without active muscle control, the research presented herein details the design for a passive mechanism that enables a rotorcraft to perch reminiscent of a bird perching on a tree branch. Perching is accomplished through the integration of a compliant, underactuated gripping foot and a collapsing leg mechanism that converts rotorcraft weight into tendon tension in order to passively actuate the foot. Analysis of mechanism behavior is presented, and stability tests were performed to characterize the ability of the system to reject disturbances. The results indicate that it is possible to passively perch a rotorcraft on multiple surfaces and support reasonable environmental disturbances. The analysis in this paper can enable passive perching design optimization in vertical take-off and landing systems.