With continuous improvements being made in science, technology, and production automation, robotics is becoming increasingly popular in the field of automation. Robotics has the potential to improve work efficiency, reduce production cost, protect humans from adverse conditions, and increase production scale. A three-dimensional (3D) printed amphibious spherical robot was designed to operate in various environments with a wide-range of complex conditions over a long period of time. The compact, fully waterproof design has the advantages of a reduced manufacturing time, high efficiency, good mobility, low noise, and reliable stability. This study considers how some of the more critical components of the robot, such as its leg brackets, circular middle plate, and spherical shell, respond to large dynamic stresses, shocks, and vibrations during operation; this can lead to reduced precision of the robot’s locomotion and may cause critical components to become damaged or fail. To design the robot with a more rigid structure and improved dynamic characteristics, 3D models of the critical components were constructed with SolidWorks. Using ANSYS WORKBENCH software, these models were incorporated into the robot design to determine the natural frequencies and the associated mode shapes of the first six orders. The procedure and analysis results are described in this paper. The fatigue life of these critical components was examined using the cyclic load spectrum and cyclic stress as a function of number of cycles to failure ( S – N curve) of acrylonitrile butadiene styrene plastic, the construction material for the robot. Finite element analysis was used for design optimization relevant to fatigue life, damage, safety, and fatigue sensitivity, and the weak areas in the components were identified. The approach described herein provides a theoretical basis for robotics design optimization.