High–load capacity origami transformable wheel
高负载能力折纸可变形轮

Origami has been a rich source of inspiration for art, education, and mathematics, and it has proven to be an efficient and effective method for realizing transformable structures in nature (1–3) and artificial systems (4–8). Composite membrane origami, the design technique based on the laminar composition of flexible membranes with rigid facet constraints, opens a new field for robotics by the transition from component assembly to lamination, which considerably simplifies design, fabrication, and assembly. This transition simplifies and speeds up fabrication and enables reaching size scales that were difficult to access before (9, 10). In addition, membrane origami provides a versatile shape-changing ability that has been exploited in various applications (11–15), and its applicability has been extended by additional design dimensions obtained from material characteristics such as softness and stretchability (16–19).
折纸一直是艺术、教育和数学的丰富灵感来源，它已被证明是实现自然 （1-3） 和人工系统 （4-8） 中可转换结构的一种高效方法。复合膜折纸是一种基于柔性膜的层流组成的设计技术，具有刚性小面约束，通过从组件组装到层压的过渡，为机器人技术开辟了一个新的领域，大大简化了设计、制造和组装。这种转变简化并加快了制造速度，并能够达到以前难以达到的尺寸尺度（9,10）。 此外，膜折纸还具有多种形状变化能力，已在各种应用中得到利用 （11-15），并且通过从材料特性（如柔软度和拉伸性）获得的额外设计维度扩展了其适用性 （16-19）。

Beyond the aforementioned benefits, origami has been an effective design tool for constructing a high payload-to-weight structure, such as a honeycomb panel, by markedly increasing the buckling strength using unique geometric configurations (20, 21). Combining this feature with reconfigurability, various stiffness transition mechanisms have also been introduced (22–24). The rigidity of components is another important factor to secure high load capacity and closely related to the thickness. Origami design is, traditionally, a matter of organizing fold lines under fundamental and ideal assumptions—zero facet thickness and zero fold line width (25–27). However, in response to growing interest in origami-inspired applications that require load-bearing capability, various thickness accommodation methods have been introduced (28–30).
除了上述优点之外，折纸还是一种有效的设计工具，用于构建高有效载荷重量比结构，例如蜂窝板，通过使用独特的几何配置显着增加屈曲强度（20,21）。 将这一特性与可重构性相结合，还引入了各种刚度转换机制 （22–24）。部件的刚度是确保高负载能力的另一个重要因素，与厚度密切相关。传统上，折纸设计是在基本和理想假设下组织折叠线的问题 - 零刻面厚度和零折叠线宽度 （25-27）。然而，为了响应对需要承重能力的折纸启发应用日益增长的兴趣，已经引入了各种厚度调节方法 （28-30）。

Here, we examine a special load-bearing problem that cannot be solved by the aforementioned load-bearing design techniques: a wheel that can be transformable and should withstand a high load all through, even in the shape-transition state. In a previous study, we reported an origami design method for a transformable wheel (31). By introducing flexible facets, it was possible to achieve a degree of freedom that enables shifting between different wheel shapes; however, there was a limitation in its load-bearing capacity. The difficulty of high load bearing in a transition state comes from the variation in the stress distribution. In general, the joint membrane is vulnerable compared with the rigid facet, but it is possible to make the facet bear most of the stress through the structural design (23, 24). However, an arbitrary configuration in the transition state places high stress on all components so that the tensile load capacity of the membrane determines the load capacity of the overall system.
在这里，我们研究了一个特殊的承重问题，该问题无法通过上述承重设计技术解决：一个可以变形的轮子，即使在形状过渡状态下，也应该能够承受高负载。在之前的一项研究中，我们报道了一种可变形轮子的折纸设计方法 （31）。通过引入灵活的刻面，可以实现一定程度的自由度，允许在不同的车轮形状之间切换;然而，它的承载能力存在局限性。过渡状态下高承载的困难来自于应力分布的变化。一般来说，与刚性小平面相比，接缝膜是脆弱的，但是通过结构设计可以使小平面承受大部分应力（23,24）。 然而，过渡态的任意配置会对所有组件施加高应力，因此膜的拉伸负载能力决定了整个系统的负载能力。

To solve this issue, we introduce a wireframe design rule for thick membrane accommodation. Unlike the facet, the membrane experiences a large deformation in shape transition so that the increase in membrane thickness can cause geometric conflict and excessive strain energy accumulation. Thus, the design rules for accommodating membrane thickness aim to address both geometric and physical characteristics, and these rules are applied to basic origami patterns to obtain the desired wheel shapes and transformation. As a result, we demonstrate a transformable wheel with extreme load-bearing capability that can be applied to a passenger vehicle. With the high load capacity, the developed composite membrane origami provides softness and flexibility to the wheels in the kinematic mechanism, thus neutralizing distortions and absorbing shocks from the ground. Other benefits of the origami method—including fabrication efficiency (420 joint structures assembled within 4 hours), payload-to-weight ratio (>50), and shape variation ratio (~1.7)—are also demonstrated with the target scale.
为了解决这个问题，我们引入了厚膜容纳的线框设计规则。与小平面不同，膜在形状转变中会经历较大的变形，因此膜厚度的增加会导致几何冲突和过度的应变能积累。因此，适应膜厚度的设计规则旨在解决几何和物理特性，并将这些规则应用于基本的折纸图案，以获得所需的轮子形状和变换。因此，我们展示了一种具有极高承重能力的可变形车轮，可应用于乘用车。凭借高负载能力，开发的复合膜折纸为运动机构中的车轮提供了柔软性和灵活性，从而中和了变形并吸收了来自地面的冲击。折纸方法的其他优点——包括制造效率（在 4 小时内组装 420 个关节结构）、有效载荷重量比 （>50） 和形状变化比 （~1.7）——也通过目标秤得到了证明。

The wheel can transform into two shapes—a large protruding wheel and a small smooth wheel—by folding and unfolding the spokes through adjustments in the distance between the wheel hub plates (Fig. 1A). Therefore, the wheel width and diameter vary depending on the configuration, as illustrated in Fig. 1B, with the diameter varying from 0.46 to 0.8 m. We verified the load-bearing capacity of one wheel through experiments with cyclic loads of 5 ± 2, 7 ± 2, and 9 ± 2 kN in the shape-transition state. The wheel performance is maintained for loads below 11 kN, as shown in Fig. 1C. The detailed conditions and results of these experiments are available in the Supplementary Materials. We installed the developed transformable wheels on a single-passenger vehicle that was specially designed for independently transmitting torque for wheel rotation and force for wheel transformation (Fig. 1D).
通过调整轮毂板之间的距离来折叠和展开辐条，轮子可以变成两种形状——一个大的突出的轮子和一个小的光滑轮子（图 1A）。因此，车轮的宽度和直径根据配置而变化，如图 1B 所示，直径从 0.46 到 0.8 m 不等。通过在形状-过渡状态下，通过循环载荷为5 ± 2、7 ± 2和9 ± 2 kN的试验，验证了车轮的承载能力。如图 1C 所示，在低于 11 kN 的负载下，车轮性能保持不变。这些实验的详细条件和结果可在补充材料中找到。我们在单人车辆上安装了开发的可变形车轮，该车辆专门设计用于独立传递车轮旋转的扭矩和车轮变形的力（图1D）。

The shape-shifting wheel concept has been implemented by various origami patterns (32–34). We chose the waterbomb tessellation origami pattern, whose characteristics have been analyzed in (35–38), as a springboard for the wheel design due to the following reasons: The waterbomb-based wheel structure can have perpendicularity in directions of driving transformation (horizontal) and supporting payload (vertical). This configuration makes it possible to maintain the two different shapes with minimum energy input. The L beam–shaped spoke is another advantage of the waterbomb pattern that can increase the buckling resistance of the structure. To transfer the paper model into a heavy-duty wheel prototype, we applied the stepwise design approach, and the overall procedure is illustrated in Fig. 2. The paper model of the wheel is made of 3 × 12 repetitions of a basic pattern (Fig. 2, A to C). The transition from the paper model into a composite membrane is achieved by anchoring rigid facets to a flexible membrane (Fig. 2, D and E), with the default length of the membrane gap, l, being the main design parameter at this stage. Given the simple folding with two facets, the minimum l would be twice the thickness of the facet for flat foldability. However, a thick membrane with high curvature induces considerable resistance force and energy accumulation. On the other hand, increasing l makes the entire structure deviate from the desired shape. To select an appropriate interval for this parameter, we use the Euler-Bernoulli beam theory to estimate the accumulated energy according to l (Fig. 2, F and G) (39). The details about the corresponding parameter selection are available in Supplementary Text.
变形轮概念已通过各种折纸图案 （32-34） 实现。我们选择了水弹镶嵌折纸图案作为轮子设计的跳板，其特性在（35–38）中已经进行了分析，原因如下：基于水弹的轮子结构在驱动变换（水平）和支撑有效载荷（垂直）方向上可以具有垂直性。这种配置使得以最小的能量输入保持两种不同的形状成为可能。L型梁形辐条是水弹图案的另一个优点，可以增加结构的抗屈曲性。为了将纸质模型转换为重型车轮原型，我们采用了逐步设计方法，整个过程如图 2 所示。轮子的纸质模型由基本图案的 3 × 12 次重复制成（图 2，A 至 C）。从纸质模型到复合膜的过渡是通过将刚性面锚定到柔性膜来实现的（图2，D和E），膜间隙的默认长度l是该阶段的主要设计参数。鉴于具有两个刻面的简单折叠，为了实现平面折叠性，最小 l 将是刻面厚度的两倍。然而，具有高曲率的厚膜会引起相当大的阻力和能量积累。另一方面，增加 l 会使整个结构偏离所需的形状。 为了为该参数选择合适的区间，我们使用欧拉-伯努利束理论根据 l 估计累积能量（图 2，F 和 G）（39）。有关相应参数选择的详细信息，请参阅补充文本。

Securing the kinematical degrees of freedom is the next stage of the pattern design. The waterbomb tessellation pattern creates a dependency between the wheel diameter and spoke angle ψ, which is depicted as the red curve in Fig. 2J. Moreover, the connection between the wheel hub and spoke facet creates an additional dependency, depicted as the blue curve. This conflict causes an overconstraint, but it can be solved by expanding the flexible area as reported in the previous study (31). The expanded flexible area (Fig. 2H) produces an additional degree of freedom with the angle range of α_R and α_S (Fig. 2I), corresponding to the light yellow region in Fig. 2J. This relationship can be derived from the kinematical analysis of the wheel structure. The wheel structure consists of a rim part that makes the outer edge of the wheel and a spoke part that connects a wheel hub and the rim part (Fig. 3A). From the geometrical conditions shown in Fig. 3 (B and C), the position vector of the vertices according to the wheel center frame, O-xyz, can be calculated as
确保运动学自由度是图案设计的下一阶段。水弹镶嵌图案在车轮直径和辐条角ψ之间产生了依赖性，如图 2J 中的红色曲线所示。此外，轮毂和辐条面之间的连接会产生额外的依赖关系，如蓝色曲线所示。这种冲突会导致过度约束，但可以通过扩大弹性区域来解决，如上一份研究所述（31）。扩展的柔性区域（图2H）产生一个额外的自由度，角度范围为α_R和α_S（图2I），对应于图2J中的浅黄色区域。这种关系可以从车轮结构的运动学分析中得出。车轮结构由构成车轮外边缘的轮辋部分和连接轮毂和轮辋部分的辐条部分组成（图 3A）。根据图 3 所示的几何条件（B 和 C），根据车轮中心框架 O-xyz 的顶点位置矢量可以计算为 where 哪里and the z position of $\overrightarrow{p_C}$ can be defined as a radius of the wheel
而 Z 位置可以定义为车轮的半径

The vertex E should be on the symmetry plane, which reduces the dimension of the vector to two so that it can be described as
顶点 E 应位于对称平面上，这会将向量的维度减少到两个，以便可以将其描述为

These two variables can be specified using the following constraints on the distance between the vertices
可以使用以下对顶点之间距离的约束来指定这两个变量

Similar to $\overrightarrow{p_E}$, the position vector of G can be derived as
与 类似，G 的位置向量可以导出为whereas 而

The spoke angle, ψ, can be calculated from the result
ψ辐条角度可以根据结果计算出来

Separately, the vertex G should be connected with the wheel hub (Fig. 3C), and the radius of the wheel can be calculated as
另外，顶点G应与轮毂连接（图3C），车轮的半径可计算为：and the difference between r_R and r_S causes kinematic conflict represented by the errors, e
rR 和 rS 之间的差异会导致由误差表示的运动学冲突，e

This error can be compensated by expanding the flexible area with the design parameters f_R and f_S in Fig. 3D. The position vector of $B_R^{\prime }$ and $B_S^{\prime }$ can be calculated by the internal division of the line segment as follows
该误差可以通过扩大设计参数 f_R 和 f_S 的柔性区域来补偿Fig. 3D。和的位置向量可以通过线段的内部划分来计算，如下所示

By projecting $B_R^{\prime }$ and $B_S^{\prime }$ to yz plane, angle boundaries of additional degrees of freedom, α_R and α_S, can be derived (Fig. 3, E and F). Figure 2J shows how an extended flexible area handles kinematic errors. The flexibility on the value of r_R achieved by α_R and α_S allows full containment of the profile of r_S. The simulation uses the following conditions
通过向 yz 平面投影，可以导出附加自由度的角度边界，α_R 和 α_S（图 3、E 和 F）。图 2J 显示了扩展的柔性区域如何处理运动学误差。α_R 和 α_S 实现的 r_R 值的灵活性允许完全包含 r_S 的轮廓。模拟使用以下条件

The design rule for accommodating the thickness of facet and membrane is applied to the pattern. The waterbomb tessellation is composed of two types of vertices with six folds (Fig. 2L). Although both geometries satisfy the Kawasaki-Justin theorem for flat foldability, the theorem is based on a zero-thickness idealization, and the physical model with its thick components cannot achieve flat foldability. Similar to the single-fold problem, we expand the membrane area to accommodate its thickness considering both the geometrical conflict and strain energy accumulation on the membrane. Given the complex geometrical deformation of the membrane, obtaining an analytical model is difficult, whereas finite element analysis implies a high computational cost. Because design rules should allow preventing excessive energy accumulation, we establish a design rule by simplifying the membrane as a wireframe and predicting its overstretching without predicting the membrane behavior precisely. The wire-length ratio between the unfolded and folded states can be expressed graphically to obtain a design guideline representing the ratio by colors, as shown in Fig. 2M.
适应刻面和膜厚度的设计规则应用于图案。水弹曲面细分由两种类型的顶点组成，有六个折叠（图 2L）。尽管两种几何都满足川崎-贾斯汀定理的平面折叠性，但该定理基于零厚度理想化，并且具有厚分量的物理模型无法实现平面可折叠性。与单折问题类似，我们扩大了膜面积以适应其厚度，同时考虑了膜上的几何冲突和应变能积累。鉴于膜的几何变形复杂，获得解析模型很困难，而有限元分析意味着计算成本高。由于设计规则应允许防止过多的能量积累，因此我们将膜简化为线框并预测其过度拉伸，而无需精确预测膜的行为，从而建立了设计规则。展开状态和折叠状态之间的线长比可以用图形表示，以获得用颜色表示该比率的设计指南，如图2M所示。

Figure 4 shows a graphical illustration of a wireframe-based design rule for accommodating thickness in consideration of both geometrical and physical characteristics. In a folded configuration of the type A vertex, F1 and F4 overlap F2, F3, F5, and F6, which incur an offset in out-of-plane direction between F1 and F4 (Fig. 4A). This discrepancy can be accommodated by expanding a membrane area, and the expanded geometry and dimension of the area can be determined by the following steps. The first step is to draw lines on F1 and F4 that are parallel to the virtual fold line, the direction of the rotation vector between F1 and F4. By partially removing the facets based on these lines as described in Fig. 4B, the expanded membrane can reach both facets without stretching. However, in the folded state, F2, F3, F5, and F6 obstruct this connection, and these parts should be cleared as in Fig. 4C. As a result of expanding the membrane area, the single vertex in the original pattern was divided into 12 subvertexes.
图 4 显示了基于线框的设计规则的图形说明，该规则在考虑几何和物理特性的情况下调整厚度。在 A 型顶点的折叠配置中，F1 和 F4 与 F2、F3、F5 和 F6 重叠，这在 F1 和 F4 之间的平面外方向上产生偏移（图 4A）。这种差异可以通过扩大膜面积来适应，并且可以通过以下步骤确定该区域的扩展几何形状和尺寸。第一步是在 F1 和 F4 上绘制平行于虚拟折叠线的线，即 F1 和 F4 之间的旋转矢量方向。如图 4B 中所述，通过部分去除基于这些线的刻面，膨胀膜可以到达两个刻面而不会拉伸。然而，在折叠状态下，F2、F3、F5 和 F6 会阻碍这种连接，应如图 4C 所示清除这些部分。由于扩大了膜面积，原始模式中的单个顶点被划分为 12 个子顶点。

The design parameter for the expanded membrane region, f_e, was determined using a wireframe model. We can imagine virtual wires that connect each vertex, and the length of these wires will change as the model folds. The length of the wire between ith subvertex and jth subvertex can be presented as n_ij in the unfolded state, which is a function of the design variables l and e. Similarly, the wire length in the folded state can be represented as c_ij, and this is a function of t_m, t_f, and f_e. The supplementary length, w_S, is introduced to prevent the high curvature of the membrane. From these variables, the design criteria value, γ, and the condition can be defined as follows
扩展膜区域的设计参数 f_e 是使用线框模型确定的。我们可以想象连接每个顶点的虚拟线，这些线的长度会随着模型的折叠而变化。第 i个子顶点和第 j个子顶点之间的导线长度在展开状态下可以表示为 n_ij，它是设计变量 l 和 e 的函数。同样，折叠状态下的导线长度可以表示为 c_ij，这是 t_m、t_f 和 f_e 的函数。引入补充长度 w_S 是为了防止膜的高曲率。根据这些变量，可以按如下方式定义设计准则值、γ和条件

From this condition, f_e can be determined on the basis of t_m, t_f, l, and w_S, and the result is presented in a graphical map as in Fig. 4D with the following simulation parameters
根据该条件，可以根据 t_m、t_f、l 和 w_S 确定 f_e，并将结果以图形图的形式呈现，如图 4D 所示，具有以下模拟参数

The identical design rule can be used for the vertex type B in Fig. 4E. F1 and F6 enclose F2 to F5 with a different configuration. Similar to the type A vertex, the two parallel lines can be drawn with the desirable distance for covering inner facets as shown in Fig. 4F, and interference of F2 to F5 can be solved by removing the part of these facets (Fig. 4G). The result is presented in a graphical map as in Fig. 4H with the following simulation parameters
相同的设计规则可用于图 4E 中的顶点类型 B。F1 和 F6 以不同的配置将 F2 和 F5 括起来。与A型顶点类似，两条平行线可以绘制出覆盖内面所需的距离，如图4F所示，并且可以通过去除这些面的部分来解决F 2到F5的干涉（图4G）。结果以图形图的形式呈现，如图 4H 所示，具有以下仿真参数

We applied an additional pattern variation to reinforce the structure and adjusted the wheel transformation ratio, which is determined by design parameter w, as shown in Fig. 2O. A larger w is preferable to obtain a higher payload, but it reduces the transformation ratio, as described in Fig. 2 (O and P). w should be determined on the basis of a target payload, but analyzing the failure mode of the wheel is a challenging problem owing to its complex composition; the structure is built by assembling various materials and could fail for a variety of reasons, such as exceeding the tensile strength of materials, structural buckling, or disassembly of parts. In this study, a simplified static model was used to estimate the applied load to the components (fig. S2 and Supplementary Text). When the target payload is 10 kN, the required load capacity for components is 28.8 kN, and the dimension of components was determined on the basis of this criterion. Figure 2Q illustrates the final pattern of the wheel. The top and bottom edges of the wheel pattern are connected to the wheel hub. To reinforce the connection between the wheel pattern and wheel hub, we removed the patterns in the edge lines except the main spokes so that the edge line of the wheel pattern can maintain a dodecagonal shape in any state of the wheel transformation. The remaining flexible regions near the main spokes were clamped in the fabrication process. The final wheel prototype is presented in Fig. 2 (R and S), and the details of the fabrication procedures and materials are explained in figs. S3 to S5 and Materials and Methods.
我们应用了额外的花纹变化来加固结构，并调整了车轮变换率，该比例由设计参数 w 确定，如图 2O 所示。较大的 w 更可取以获得更高的有效载荷，但它会降低变换比，如图 2 （O 和 P） 所述。W应根据目标有效载荷确定，但由于其成分复杂，分析车轮的失效模式是一个具有挑战性的问题;该结构是通过组装各种材料构建的，并且可能由于各种原因而失效，例如超过材料的抗拉强度、结构屈曲或零件拆卸。在这项研究中，使用简化的静态模型来估计施加在组件上的负载（图 S2 和补充文本）。当目标有效载荷为10 kN时，部件所需的负载能力为28.8 kN，部件的尺寸是根据该准则确定的。图 2Q 显示了轮子的最终图案。车轮花纹的顶部和底部边缘连接到轮毂。为了加强车轮花纹和轮毂之间的连接，我们去除了除主辐条以外的边缘线中的花纹，以便车轮花纹的边缘线在车轮变换的任何状态下都可以保持十二边形。在制造过程中，靠近主辐条的其余柔性区域被夹紧。最终的车轮原型如图 2（R 和 S）所示，制造程序和材料的详细信息如图 2 所示。S3 至 S5 以及材料和方法。

Internal locking skeletons and tread pads are additional essential components to achieve full functionality of the wheel; internal locking structures keep the shape under lateral traction force, and tread pads absorb external impact and configure a ground contact shape (Fig. 5A). The internal locking structure made of elastic material prevents collapse by impact (Fig. 5B). The tread pad is made of urethane and has an internal plastic structure for assembly (Fig. 5C). The wheel can be transformed by linear actuation that changes the distance between the wheel hub plates (Fig. 5, D to F).
内部锁定骨架和胎面垫是实现车轮全部功能的额外重要组件;内部锁定结构在横向牵引力下保持形状，胎面垫吸收外部冲击并配置与地面接触的形状（图 5A）。由弹性材料制成的内部锁定结构可防止因冲击而倒塌（图 5B）。胎面垫由聚氨酯制成，内部具有用于组装的塑料结构（图 5C）。车轮可以通过线性驱动来改变，该驱动会改变轮毂板之间的距离（图 5，D 到 F）。

An electric motor vehicle with hydraulic linear actuators for wheel transformation was constructed to evaluate on-site wheel performance (Fig. 6). The required force of the linear actuator can be approximated by a simplified model of the wheel as described in fig. S2 and Supplementary Text. From a field test, we verified the wheel transformation in about 5 s, whereas the vehicle moved at 1 m/s (Movie 1). The vehicle was controlled manually, and the test lasted for about 30 min. We could not confirm the lifetime and maximum speed because of safety concerns. A video record of the development process and pre–field test is also included in Movie 1.
构建了一辆带有液压线性执行器的电动车辆，用于车轮变换，以评估现场车轮性能（图6）。线性致动器所需的力可以通过轮子的简化模型来近似，如图所示。S2和补充文本。通过现场测试，我们验证了车轮在大约 5 秒内的变化，而车辆以 1 m/s 的速度移动（视频 1）。车辆采用人工控制，测试持续约30分钟。由于安全问题，我们无法确认使用寿命和最大速度。电影 1 中还包含开发过程和现场测试前的视频记录。

Here, we present the transition of an origami paper model into a transformable wheel prototype. We demonstrate the feasibility of applying the origami technique in a passenger vehicle. Although the wheel performances regarding speed, lifetime, vibration, and noise were not evaluated in this study, we expect that our wheel prototype cannot compete with commercially available wheels and tires at this stage of development. However, because these performance factors are closely related to material and fabrication techniques, they can be improved by further optimizing the composite membrane origami processes. For instance, we can focus on the compatibility of the origami technique with industrial rubber or tire manufacturing processes. Moreover, the lamination process is ready for integration with rubber or tire composite manufacturing, and the recently introduced airless tire technology can provide high load capacity with reinforced rubber composites. We believe that the unique characteristics of the origami technique compared with traditional structure construction will foster its development and adoption.
在这里，我们展示了折纸模型到可变形轮子原型的过渡。我们证明了在乘用车中应用折纸技术的可行性。尽管本研究未评估车轮在速度、寿命、振动和噪音方面的性能，但我们预计，在目前的开发阶段，我们的车轮原型无法与商用车轮和轮胎竞争。然而，由于这些性能因素与材料和制造技术密切相关，因此可以通过进一步优化复合膜折纸工艺来改进它们。例如，我们可以关注折纸技术与工业橡胶或轮胎制造过程的兼容性。此外，层压工艺已准备好与橡胶或轮胎复合材料制造集成，最近推出的无气轮胎技术可以为增强橡胶复合材料提供高负载能力。我们认为，与传统结构施工相比，折纸技术的独特特性将促进其发展和采用。

The main components of the wheel include an origami body, tread pads, internal locking skeletons, and hub plates. Materials and processing methods for all components are presented in table S1, and the stepwise assembly procedure is illustrated in figs. S3 to S5. This section describes the details of fabrication procedures for the origami composite and tread pad.
车轮的主要部件包括折纸体、踏步垫、内部锁定骨架和轮毂板。表S1列出了所有组件的材料和加工方法，图中说明了逐步组装过程。S3 到 S5。本节介绍折纸复合材料和踏面垫的制作步骤的详细信息。

We thank N. Chang (EMVcon, KAIST) and H. Kim (OXK) for designing and implementing the vehicle for the transformable wheel and H. Jang (Hankook Tire) for designing the appearance of the transformable wheel. Funding: This work was supported by Innocean Worldwide Inc. and the National Research Foundation of Korea (NRF) (NRF-2016R1A5A1938472). Author contributions: D.-Y.L. designed and built the wheel, developed a fabrication method, and wrote the manuscript. J.-K.K. assisted in building the wheel and experimental works. C.-Y.S. assisted in developing a fabrication method, organized fabrication facilities, and conducted experimental works. J.-M.H. assisted in developing a fabrication method and building the wheel. K.-J.C. directed the project and edited the manuscript. Competing interests: D.-Y.L., J.-K.K., C.-Y.S., J.-M.H., and K.-J.C. are inventors on patent (KR. 10-2136158) submitted by Hankook Tire and Technology Co. Ltd. and Seoul National University. The concept art of the result was used for a commercial film (The next driving lab project, Hankook Tire). Data and materials availability: All data needed to support the conclusions of this manuscript are included in the main text or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
我们感谢 N. Chang （EMVcon， KAIST） 和 H. Kim （OXK） 设计和实施了可变形车轮的车辆，感谢 H. Jang（韩泰轮胎）设计了可变形车轮的外观。资金：这项工作得到了Innocean Worldwide Inc.和韩国国家研究基金会（NRF）（NRF-2016R1A5A1938472）的支持。作者贡献：D.-Y.L. 设计并制造了轮子，开发了一种制造方法，并撰写了手稿。J.-K.K. 协助建造了轮子和实验工作。C.-Y.S.协助开发了一种制造方法，组织了制造设施，并进行了实验工作。J.-M.H. 协助开发了一种制造方法并制造了轮子。K.-J.C. 指导了这个项目并编辑了手稿。利益争夺：D.-Y.L.、J.-K.K.、C.-Y.S.、J.-M.H. 和 K.-J.C.是韩泰轮胎科技株式会社和首尔国立大学提交的专利（KR.10-2136158）的发明人。结果的概念艺术被用于一部商业电影（下一个驾驶实验室项目，韩泰轮胎）。数据和材料可用性：支持本手稿结论所需的所有数据均包含在正文或补充材料中。可向作者索取与本文相关的其他数据。