The aim of this work is to develop and test the formulation of an inverse dynamic model for a 3-DOF parallel mechanism that belongs to the family of the Tripteron robots. The variant analyzed here is the so-called ‘single-rail’ Tripteron, whose main feature is having all actuated prismatic joints with coincident axes. This variant is particularly interesting since it allows to actuate the robot, which can provide translations in the three dimension Cartesian space, by a single Permanent Magnet Linear Synchronous motor with three shuttles. The analytic development of the inverse dynamic model is based on Kane’s method, resulting in a simple but very effective implementation. The model simulation, performed using Matlab, has been compared with the results from a multibody simulation performed in Simscape Multibody. The match between them provides a verification of the correctness of the proposed modeling method.