| Compared with other materials,Origami model has the advantages of simple and easy to understand,easy to bend,convenient to use and so on.The origami model of curve and surface is different from the traditional straight line crease,so it is very important to study the geometric transformation and motion of curve crease.Firstly,a paper origami model with single crease plane and curve combination is designed on the basis of straight line crease.The new combination model not only preserves the integrity of the structure,but also enhances the stability.In addition,the mechanism is extended to the spatial folding model of multiple planar and curved combinations,which is equivalent to a spatial spherical mechanism for geometric parameters analysis and motion analysis based on constrained helix theory.At the same time,considering the thickness factor can not be ignored in practical application,a combination of plane and curve models with thickness model is designed.After it is equivalent to the mechanism model,the geometric parameters are analyzed and the sector angle and dihedral angle with or without thickness are compared,and the relationship between sector angle and dihedral angle with or without thickness is compared.Draw the MATLAB parameter relation graph.Then a simple motion analysis of the thick plate equivalent mechanism is carried out by using the constrained helix theory.Secondly,the crease curve of the origami model with developable surface and curve combination changes constantly during the folding process from 2D to 3D space.When the crease curve is parabola,hyperbolic and elliptical,the deflection of the crease curve is zero.These crease curves can be used to simulate the creases at this time by cutting off the families of quadratic curves obtained from different cones in any plane.The parabola with the same curve property is used to simulate the actual different combination elements,and the relationship between crease curves under different curved surface folding combinations is studied.For the sake of simplicity of calculation,the curve family is then simplified in the same way by rotating translation.The mathematical relationship between space and plane crease curve is obtained,and then an example is designed.For the known crease curve and one side surface,the other side surface can be obtained by calculating the geometric relation of folding angle.Thus,a complete folding element of developable surface is obtained.Finally,the relationship between the simplified crease curve and the spatial curve is given.The discretization of the spatial surface is obtained by discretizing the crease curve with equal arc length,and the ruled line of the developable surface on both sides is drawn at the discrete point.Then according to the tangent and straight bus direction vector of the space crease,the normal vector of the developable surface on both sides is obtained,and the spherical face curve mapped by Gauss is drawn.Assuming that two Gaussian spheres with a known combination of cone and cylinder are oriented to the curve,the conical sphere is discretized with the equal arc length of the curve,and a new normal vector is obtained.These normal vector vectors are translated to the conical surface and the straight bus of the conical surface is made.The discretization of Gauss mapping to the conical surface is completed,and the discrete points are obtained at the crease of the curve at the same time..According to the direction vector of cylindrical straight bus,the discrete model of Gauss mapping of developable surface element is obtained,and the mathematical discretization problem of developable surface and folding element is analyzed. |
