Study On The Relationship Between Mobile Assemblies Of Spatial Linkages And Rigid Origami

Mobile assemblies of spatial linkages and rigid origami are of superiorly foldable properties.Therefore,they have great potential in various engineering fields,such as aerospace and robotics.Due to the motion complexity of them,it is a challenge to seek for novel designs.In this dissertation,the relationships between mobile assemblies of spatial linkages,thick-panel origami and rigid origami are studied.Transition technique based on thick-panel origami and vertex-splitting technique are proposed to design new mobile assemblies of spatial linkages,one-DOF(degree of freedom)origami and thickpanel origami with flat-surface unfolded profiles.The major findings of this dissertation are as follows.Firstly,the transition technique from four-crease origami patterns to mobile assemblies of Bennett linkages is developed by taking the thick-panel form of an origami pattern as an intermediate bridge.Applying this transition technique to the Miura-ori and graded Miura-ori patterns,assemblies of Bennett linkages with identical link lengths are obtain.Three cases of mountain-valley crease assignments of supplementary-type origami patterns correspond to different types of Bennett linkage assemblies with negative link lengths.And a new assembly of Bennett linkages is derived from the identical linkage-type origami pattern with the application of the transition technique.Secondly,the kinematic equivalence between the diamond thick-panel origami and mobile assembly of plane-symmetric Bricard linkages is set up based on the transition technique.Two general cases of mobile assemblies of plane-symmetric Bricard linkages are discovered by analysing the compatibility of diamond assembly which is derived from a diamond thick-panel origami pattern.One of the newly-found mobile assemblies inspires the variation of the sector angle and thickness of diamond thick-panel origami pattern.Thus,new diamond thick-panel origami patterns with flat unfolded profiles and/or spirally folded configuration are invented,and the graded one can be extended infinitely without physical interference.Finally,to reduce the number of DOF in the multi-DOF rigid origami pattern,a vertex-splitting technique including two splitting schemes on the diamond vertex are proposed to generate three types of unit patterns.Then,the technique is applied to the multi-vertex diamond origami pattern to produce several one-DOF basic assemblies and a number of one-DOF origami patterns.Two of the one-DOF origami patterns are discussed.One is flat-foldable origami pattern mixed with four-crease and six-crease vertices,and the other is non-flat-foldable origami pattern mixed with four-crease,fivecrease,and six-crease origami vertices.Hinge-removing is proposed by analysing the relationship between the construction of Waldron's hybrid 6R linkage from Bennett linkages and the variation of their corresponding thick-panel origami pattern.This indicates the thick-panel origami pattern with two four-crease vertices can be transformed into a kinematically equivalent pattern with six creases by removing the shared hinges to construct thick-panel origami patterns with flat-surface unfolded profiles.Therefore,the research in this dissertation is based on the transition technique and vertex-splitting technique.It reveals the close relationships among mobile assemblies of spatial linkages,rigid origami and thick-panel origami,which offers approaches to propose the new designs,and facilitates their applications.