Robotic design involves modeling the behavior of a robot mechanism when it moves along potential paths set by the users. In this lecture, we will first give an overview of different approaches to design a set of kinematic equations associated with a robot mechanism. In particular, these equations can be used to solve the forward and the backward kinematics problems associated with a robot mechanism or to model its singularity locus. Then we will review methods to solve those equations, and notably methods to draw with guarantees the real solutions of an under-constrained system of equations modeling the singularities of a robot.