The dental apparatus or Aristotle's lantern of sea-urchins is a complex system of interacting skeletal ossicles, joints, muscles and ligaments arranged in a rigorous geometry and involved in a variety of activities. In this paper we study the movement of the whole lantern system modelled as a rigid body. The model lantern is constrained at its apex by the peristomial membrane and its movement is controlled by five pairs of antagonistic forces (retractor and protractor muscles). The other main forces applied to the lantern are the elastic reactions of both muscles and ligamental structures (compass depressors and peristomial membrane). The lantern is allowed to perform vertical movements and lateral inclinations but cannot rotate around its main axis. The equilibrium conditions of the system have been found by means of a numerical iterative procedure for solving non-linear equations. The results of the present analysis allow simulation of the overall mechanical activity of the lantern taking into account the experimental data regarding active and passive muscular forces and the tensile constraints due to ligaments.