This paper presents an exciting and meaningful design to make mobile robots capable of adapting to various terrains. We designed a relatively simple and novel composite motion mechanism called the flexible spoked mecanum (FSM) wheel and created a mobile robot, LZ-1, with multiple motion modes based on the FSM wheel. Based on the motion analysis of the FSM wheel, we designed an omnidirectional motion mode for this robot, allowing it to move flexibly in all directions and successfully traverse rugged terrains. In addition, we designed a crawl motion mode for this robot, which can climb stairs effectively. We used a multilayer control method to move the robot according to the designed motion modes. Multiple experiments showed that these two motion modes for the robot are effective on various terrains.