Origami Usa Convention 2008 Pdf ##HOT## Download

Origami Usa Convention 2008 Pdf Download

Contrary to the previous examples, here we will illustrate the presence of panel contact in an origami folding problem and the effects of panel contact in this example. We choose a 3×4 folding of a four-leg geometry. The structure is deployed from the base point and has no need to fold in three dimensions. We view the folding as one dimensional. Here, the two rigid panels are placed side by side (figure 2 a). The simulation begins by unfolding the structure. As the unfolding continues, the model considers the constraint to be satisfied as a spring K pulls apart the two panels. Although the two panels are moving in the opposite directions, no contact is detected. When the panels start to get close to each other, a large energy release is produced due to the large contact force, resulting in the panels folding back onto themselves, forming a half-folded state (figure 2 b). This process repeats itself for a series of intermediate states until the panels align themselves parallel to each other (figure 2 c). At that moment, both panels form a single panel in two-dimensional space (figure 2 d). The panels start to travel apart again, and continue to do so until they meet at a new base point, i.e. the structure is unfolded again (figure 2 e). As soon as the panels return to the starting position, the process is repeated and the structure folds again. This cycle continues until the structure fully folds once (figure 2 f).

Now we introduce a model with hinges that provide constraints in all three directions, and it is based on the idea that many important phenomena in origami can be captured using hinge-only origami models, as shown in [ 35 ]. Only one row of hinges is illustrated for a simplified case. Specifically, a bar axis is defined as the line connecting a and b in figure 8 a,b, and a bar is the shaded region in figure 8 a,b. By linking two nodes, the shaded region has stiffness about the bar axis, which is analogous to the rotational springs defined in the bar and hinge model with compliant creases [ 40 ]. Thus the upper hinge is defined as the bar with stiffness about the bar axis, and the lower hinge is defined as the bar with stiffness about the bar axis. By linking two nodes, two hinges are created. The diagonal hinge in figure 8 a,b is used as an example to illustrate how two hinges can provide out-of-plane stiffness and how different hinge orientations are selected. The diagonal hinge in the upper panel has a positive opening angle a_o about the bar axis as it is always oriented in the x direction. While a transverse hinge in the lower panel is always oriented in the y direction, and thus provides out-of-plane stiffness only about the bar axis. The angle of a_o is defined as the angle between the bar axis and the hinge bar. By creating the two hinges properly, the model may possess both extensional and shear stiffness as indicated in figure 8 a,b. A possible configuration for a transverse hinge is shown in figure 8 a,b, and the resulting out-of-plane stiffness is similar to that of the rectangular hinge h_o in the flexible hinge model with rectangularly curved creases c₁ and c₂ (see [ 35 ]).

With the prototype being established, we can develop our framework with the following features: (i) calculate the contact boundary forces when a single- or double-fold origami structure meets an external panel; (ii) incorporate the panel contact model into the bar and hinge model; (iii) design a model-based optimisation process to evaluate the robustness of the origami design in terms of producing a minimum panel loading area. Firstly, the system is set up to run a simulation with a specified origami structure and a panel. The panel is treated as an external and rigid boundary to the origami structure. All nodes, bars and rotational springs are initialised as INIT_DIST, which is an accumulative distance throughout the simulation. From the initial stage of the simulation, the in-plane force at the contact boundary and the out-of-plane component of the internal force are both computed. The initial force evaluation is aimed to select the strongest edge or crease edge that is responsible for increasing the support reaction forces. With the forces being calculated, we can track how the total load decreases as the folding path is traced.
It should be noted that the contact forces are not restricted to only the contact boundary as the external panel can also initiate contact reactions on nodes, bars and rotational springs. Thus the proposed panel contact model can be treated as a separate subsystem. Each subsystem is associated with a domain grid and as such has both the local stiffness and global stiffness. The global stiffness is a measure of the in-plane and out-of-plane stiffness of the origami model. Through the local stiffness, the model can trace the equilibrium folding path while the global stiffness is to measure the ability of the origami model to withstand an external load. Figure 3. (a) Comparison of the effective stiffness of a bar and hinge origami model, which consists of 10 bars and 10 rotational springs, with and without panel contact. (b) A series of support reactions are obtained by varying the panel length L and width W (denoted as L/W). Origami Usa Convention 2008 Pdf Download
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