Abstract: A probabilistic finite element method (PFEM) is developed for accurate reliability analysis of complex cyclic symmetric structures．On the basis of the three-parameter reliability analytical method，the basic theory and calculation procedures of PFEM for cyclic symmetric structural dynamic problem are presented．The formulas for solving structural dynamic problems on three-dimensional PFEM are derived in the case that the randomness occurs either in the material properties，geometric shapes，or a combination of these．The reliabilities of a cylindrical structure and a gear structure are evaluated by the approaches presented and compared with those obtained by Monte-Carlo method．

Key words: Cyclic symmetric structures, Finite element method, Reliability, Structural dynamics, Human-machine closed chain, Human-machine compatibility, Kinematic dexterity, Position inverse solution, Shoulder joint rehabilitation exoskeleton