Kinematics Of Spatial Linkages And Its Applications To Rigid Origami

This dissertation systematically explores the applications of spatial linkages into rigid origami.This is achieved by utilizing the kinematics of linkages to folding motion of rigid origami,where links and revolute joints are corresponded to paper facets and crease lines,respectively.Major findings of this dissertation are in three areas,and listed as follows.First,rigid foldability and motion behaviour of simple origami geometry are investigated.A well-known triangle twist origami is used,and converted into a network of spherical 4R linkages based on their kinematic equivalence.The compatibility of this network is combined to discuss the rigid foldability and motion behaviour of the pattern.It is found that diverse mountain-valley crease assignments of the pattern exist,based on the flat-foldable conditions of four-crease vertex.The pattern is then altered into a new overconstrained 6R linkage by using the kirigami technique,and shows a good agreement to our proposed kinematic analysis method.Secondly,kinematic bifurcation conditions for spatial overconstrained 6R linkages are considered by using a traditional D-H matrix method.A set of closure equations of plane-symmetric Bricard linkage are derived in explicit forms.This has allowed us to characterize various bifurcation behaviours and their corresponding geometric conditions,build up a connection between plane-symmetric Bricard and Bennett linkage families,and is ready to be applied in rigid origami geometries.Thirdly,the analysis method is extended from zero-thickness to thick-panel origami forms.A multi-degree of freedom(DOF)pattern consisted with six-crease vertices is used,namely waterbomb origami.Its zero-thickness and thick-panel forms under symmetric folding are converted into networks of plane-symmetric spherical 6R linkages and plane-symmetric Bricard linkages,respectively,resulting in one-DOF systems with kinematic equivalence.The zero-thickness form is shown to have a bifurcation behaviour with two different folding paths.However,this behaviour can be eliminated in thick-panel form,as the thickness has provided additional geometric constraints.Finally,an investigation of closed cylindrical form of waterbomb origami is conducted through a parametric study.It is seen that the folded tube may undergo different behaviours,including uniform radius configuration,mechanism-structuremechanism transition,wave-like configuration,and rigid twist motion.Nevertheless,the trigger condition of those behaviours can be determined by using the proposed kinematic analysis method of rigid origami with specified geometric conditions.The twist angle per axial strain and its relationship with geometrical parameters of the tube during the rigid twist motion are revealed.Experimental results show the enhancement in stiffness of the tube with occurrence of the continuous twist motion.