Abstract: This paper presents an analysis of forward and inverse kinematics for a humanoid robotic head. The robotic head is used for the study of social human-robot interaction, such as a support tool to maintain the attention of patients with Autism Spectrum Disorder. The design of a parallel robot that emulates human head movements through a closed structure is presented. The position and orientation in this space is controlled by three servomotors. For this, the solutions made for the kinematic problem are encompassed by a geometric analysis of a mobile base. This article describes a non-systematic method,
called the geometric method, and compares some of the most popular existing methods considering reliability and computational cost. The geometric method avoids the use of changing reference systems, and instead uses geometric
relationships to directly obtain the position based on joint variables; and the other way around. Therefore, it converges in a few iterations and has a low computational cost.