Abstract The need for a perching robot is increasing in the field of rescue and transportation. Accordingly studies on perching an object by attaching a robot arm to a perching robot have been conducted. However, almost all the studies related to perching have been conducted using an actuated or electric device. However, perching by using an electric device has several disadvantages, such as additional power consumption and an increase in the mass of the multicopter used to load the electric source. Instead of using an electric device, perching by using an underactuated gripper can effectively avoid these disadvantages. Accordingly, we developed an underactuated passive gripper that has the advantage of nonconsumption of electric power for perching. A method to confirm the available range for stable perching is one of the problems of using an underactuated passive gripper. Therefore, in this study, we analyze a multicopter carrying an underactuated parallel-link passive gripper for available plane perching. To enable perching on planes with different thicknesses and being embedded at different depths, we summarize the available perching range and limitations based on the friction cone theory. Our conclusion is supported by both theoretical and experimental results.