Abstract: To develop deployable structures with novel geometric configuration,strong vitality,and convenient transportation and storage,mobility and folding analysis on deployable structures is important.As the involved configurations could be effectively deployed or folded,these structures would satisfy the hard conditions of time or space,and meet the needs of some specific tasks.In fact,most existing deployable structures show certain symmetries.From the point of view of symmetry,group theory was introduced to explain the essence of kinematic mobility in-depth.Afterwards,the sufficient condition for evaluating the mobility of symmetric systems was proposed.According to the property of geometric constraints and the variational principle,the compatibility matrix of a typical member in assembling deployable structures was derived.Based on the symmetry subspaces,the symmetry representations of internal mechanisms and self-stress states were deduced.Then,symmetry-adapted mobility analysis on a few closed-loop deployable structures was presented.The study is devoted to promote the design and development of novel symmetric deployable structures,providing a basis for further studies and potential applications on novel deployable structures and kinematically indeterminate structures.

Key words: deployable structures, symmetry, closed-loop, internal mechanism modes, folding behavior