This paper presents at first a static and kinematic analysis of closed chains mechanisms which permits to deduce different possible fully parallel architectures. Then we focus on a particular parallel architecture with C5 links designed to perform precise assembly tasks. A general modeling of this C5 parallel robot is presented. Two typical assembly tasks in the automotive industry are also proposed; the first one uses the C5 links parallel robot as a left-hand device, while the second one uses it as the terminal tool of a sequential manipulator.