Social robots have shown some efficacy in assisting children with autism and are now being considered as assistive tools for therapy. The physical proximity of a small companion social robot could become a source of harm to children with autism during aggressive physical interactions. A child exhibiting challenging behaviors could throw a small robot that could harm another child’s head upon impact. In this paper, we investigate the effects of the mass and shape of objects thrown on impact at different velocities on the linear acceleration of a developed dummy head. This dummy head could be the head of another child or a caregiver in the room. A total of 27 main experiments were conducted based on Taguchi’s orthogonal array design. The data were then analyzed using ANOVA and then optimized based on the signal-to-noise ratio. Our results revealed that the two design factors considered (i.e. mass and shape) and the noise factor (i.e. impact velocities) affected the response. Finally, confirmation runs at the optimal identified shape and mass (i.e. mass of 0.3 kg and shape of either cube or wedge) showed an overall reduction in the resultant peak linear acceleration of the dummy head as compared to the other conditions. These results have implications on the design and manufacturing of small social robots whereby minimizing the mass of the robots can aid in mitigating the potential harm to the head due to impacts.