A cycling rehabilitation robot is developed to assist in rehabilitation training for stroke patients. The robot can realize flexion movements of the patient’s hip, knee and ankle. First, based on physiological principles, the range for flexion motion angles of the lower limbs is presented. The mathematical modeling of the lower limb rehabilitation motion angles is established. The angular motion characteristics of the lower limb hip and knee joints are analyzed, and the relationship of the motion between the lower limb hip and knee joints is presented. To verify the correctness of the theoretical model, the structure of the lower limb rehabilitation training robot is designed. The experiments show that the rehabilitation robot can achieve flexion rehabilitation training of the lower limbs effectively, which proves the correctness of the proposed theoretical model. The results provide scientific guidance for patients using cycling rehabilitation devices.