This paper analyses a hybrid optic fibre alignment positioning stage with six degrees of freedom (6-DOF) based on a 3-DOF parallel kinematic mechanism and a 3-DOF serial mechanism. The parallel kinematic mechanism uses three different types of ball joint to provide rotation and sliding movement. The advantages of the parallel kinematic mechanism include a simple structure, simplified kinematic analysis, zero accumulation of link errors, and high positioning accuracy. This study commences by introducing the parallel kinematic mechanism of the positioning stage and then proceeds to discuss its degrees of freedom. The Denavit-Hartenberg notation method is employed to analyse the kinematics of the positioning stage. Some simulation results are given to verify the correctness of this study and to show some potential for the optical fibre alignment applications. In the sequel, the effects of the dimensions of the mechanical components of the positioning stage on the workspace are also investigated and discussed.