Design Of One-DOF Triangular Ron Resch Pattern With Thick-panel Origami

Six-crease triangular Ron Resch pattern,with simple geometry and good mechanical properties,has a great potential to be utilized in many engineering applications and researches,as they can be folded into various curved profiles from planar sheets.The six-crease pattern has a large number of degrees of freedom(DOF),hence,how to control the multiple DOF to achieve the desired profile is a major difficulty in applications.Most of the existing researches only focus on the theoretical design of folded configurations or the mechanical properties of some specific configurations,but few on the kinematic analysis of folding.Therefore,this paper will analyze the kinematics of the six-crease triangular Ron Resch pattern and design its mechanisms with the theory of rigid origami in thick panels,to realize the single degree of freedom of the folding.In this paper,in order to achieve single mobility for the unit,which represented the kinematics of the triangular Ron Resch pattern,two methods are proposed.Firstly,by introducing symmetrical motion constraint method,each feature vertex is equivalent to a spherical six-bar(6R)linkage with symmetrical constraint,and the kinematic equations of the unit are constructed.The first method effectively reduces the mobility of the unit,but does not construct a one-DOF unit.Thus,the thick-panel technique,as the second method,is employed to construct the kinematically equivalent thick-panel models of the unit.Each spherical 6R linkage in the unit is transformed into an overconstrained spatial 6R linkage,and the compatible conditions between vertices of the unit are explored.Three construction schemes are proposed and two types of the one-DOF thick-panel units are constructed by the kinematic analysis and the compatible conditions.The kinematic performances of the two thick-panel units with different values of design variables are also analyzed.The physical models are manufactured to validate the analysis,which shows a good agreement.Finally,the two kinds of one-DOF thick-panel units are used to tessellate separately to get large structures with lower-mobility.By constructing linkage of the joint vertex between the two units,which are with the same design variables,the corresponding one-DOF multi-unit thick-panel structures will be obtained.Two kinds of splicing methods are proposed.A series of one-DOF multi-unit thick-panel structures are constructed by repeated or combined the methods.The folding configurations of thick-panel structures are analyzed briefly,and the method of eliminating interference in folding is also proposed.In this paper,the kinematic characteristics of triangular Ron Resch pattern are analyzed,and its one-DOF thick-panel structures are constructed by using the thick-panel technique.The results are suitable for variable rigid materials with different thicknesses,and could realize the transformation and the control of folding configurations,which could be widely used in the construction of large-scale continuous three-dimensional(3D)configurations in engineering.