To support the design of a mechanism with two opposing, underactuated, multi-segmented feet that enables a small UAV to grasp and perch upon a branch or similar structure, a hybrid empirical-computational model has been developed that can be used to predict whether the mechanism can kinematically grasp structures with a range of cross-section shapes and sizes in various orientations and to quantify the forces exerted by the grasp. This research was presented at the ASME 2018 International Mechanical Engineering Congress & Exposition (IMECE) with funding from a SAG award.