We present a robot designed for children with developmental disorders. These disorders are categorized into autism spectrum disorder (ASD), attention deficit hyperactivity disorder (ADHD), and learning disability (LD). While growing, children generally learn through play activities. However, those with developmental disorders require external supports during play because they have difficulties in some aspects. For instance, children with ASD tend not to communicate, those with ADHD find it difficult to concentrate, and those with LD have difficulties in talking, reading, writing, and performing calculations. Thus, some researchers propose robots as solutions to enhance the effects of children's play. In this paper, we present a new type of spherical robot that can jump and roll on the floor. The purpose of this research was to develop a spherical robot that engages with children using its motion capabilities. Specifically, here we present the mechanical design and performance of the robot. The robot has two types of outer spheres with a diameter of 170 mm and made from varied materials. One is a soft sphere made of paper, and the other is a plastic hard sphere. As a result, the jumping height of the internal mechanism reaches 110 mm, that of the soft sphere reaches 65 mm, and that of the hard sphere goes up to 10 mm. The robot speed using the hard sphere is 0.65 m/s. In contrast, the robot with the soft sphere exhibits an unstable rolling motion, a seemingly dancing pace, which is difficult to control. Overall, we consider that the proposed jumping and rolling spherical robot can be a suitable tool to aid children with developmental disorders.