Aerial robots can perch onto structures at heights to reduce energy use or to remain firmly in place when interacting with their surroundings. Like how birds have wings to fly and legs to perch, these bio-inspired aerial robots use independent perching modules. However, modular design not only increases the weight of the robot but also its size, reducing the areas that the robot can access. To mitigate these problems, we take inspiration from gliding and tree-dwelling mammals such as sugar gliders and sloths. We noted how gliding mammals morph their whole limb to transit between flight and perch, and how sloths optimized their physiology to encourage energy-efficient perching. These insights are applied to design a quadrotor robot that transitions between morphologies to fly and perch with a single-direction tendon drive. The robot’s bi-stable arm is rigid in flight but will conform to its target in 0.97 s when perching, holding its grasp with minimal energy use. We achieved a 30% overall mass reduction by integrating this capability into a single body. The robot perches by a controlled descent or a free-falling drop to avoid turbulent aerodynamic effects. Our proposed design solution can fulfill the need for small perching robots in cluttered environments.