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Layer by Layer, Patterned Valves Enable Programmable Soft Surfaces
逐层图案化阀门实现可编程软表面

JESSE T. GONZALEZ and SCOTT E. HUDSON, Carnegie Mellon University, USA
美国卡内基梅隆大学 JESSE T. GONZALEZ 和 SCOTT E. HUDSON

Fig. 1. Through a combination of bulk fabrication processes and layered assembly, we arrive at a composite material that contains both computational elements (a) and embedded, mechanical mesostructures. One such mesostructure is an electrostatic valve (b), which enables pneumatic control of soft surfaces (c). We refer to this particular composite (the electrostatic valve array) as Stoma-Board, an allusion to the pores in plant leaves (stomata) that regulate air exchange.
图 1.通过结合批量制造工艺和分层组装，我们得到了一种复合材料，其中既包含计算元件（a），也包含嵌入式机械中间结构。其中一个中间结构是静电阀门（b），它能对软表面进行气动控制（c）。我们将这种特殊的复合材料（静电阀门阵列）称为 "气孔板"（Stoma-Board），暗指植物叶片上调节空气交换的气孔（气孔）。

Programmable surfaces, which can be instructed to alter their shape or texture, may one day serve as a platform for tangible interfaces and adaptive environments. But so far, these structures have been constrained in scale by a challenging fabrication process, as the numerous constituent actuators must be built and assembled individually. We look towards emerging trends in mechanical engineering and consider an alternate framework - layer-driven design, which enables the production of dynamic, discretely-actuated surfaces at multiple scales. By centering the construction around patterning and stacking, forgoing individual assembly in favor of bulk processes such as photo-etching and laser cutting, we avoid the need for multiple manufacturing steps that are repeated for each of the many actuators that compose the surface. As an instance of this layer-driven model, we build an array of electrostatic valves, and use this composite material (which we refer to as Stoma-Board) to drive four types of pneumatic transducers. We also show how this technique may be readily industrialized, through integration with the highly mature and automated manufacturing processes of modern electronics.
可编程表面可以根据指令改变形状或纹理，有朝一日可能会成为有形界面和自适应环境的平台。但迄今为止，这些结构的规模一直受制于具有挑战性的制造工艺，因为众多组成致动器必须单独制造和组装。我们将目光投向机械工程领域的新兴趋势，并考虑另一种框架--层驱动设计，它能在多个尺度上制造出动态、离散的致动表面。通过以图案化和堆叠为中心的构造，放弃单个组装，转而采用批量工艺（如光蚀刻和激光切割），我们避免了为组成表面的众多致动器中的每个致动器重复多个制造步骤的需要。作为这种层驱动模型的一个实例，我们构建了一个静电阀门阵列，并使用这种复合材料（我们称之为 Stoma-Board）来驱动四种类型的气动传感器。我们还展示了如何通过与现代电子技术高度成熟和自动化的制造工艺相结合，将这种技术随时实现工业化。

CCS Concepts: - Hardware $→$ PCB design and layout; - Human-centered computing $→$ Haptic devices; Interface design prototyping; $⋅$ Computer systems organization $→$ Robotics.
CCS 概念：- 硬件 $→$ PCB 设计和布局；- 以人为本的计算 $→$ 触觉设备；界面设计原型； $⋅$ 计算机系统组织 $→$ 机器人技术。

Additional Key Words and Phrases: programmable materials, metamaterials, tangible interfaces, soft robotics
其他关键词和短语：可编程材料、超材料、有形界面、软机器人技术

ACM Reference Format:
ACM 参考格式：

Jesse T. Gonzalez and Scott E. Hudson. 2022. Layer by Layer, Patterned Valves Enable Programmable Soft Surfaces. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol. 6, 1, Article 12 (March 2022), 25 pages. https://doi.org/10.1145/3517251
Jesse T. Gonzalez and Scott E. Hudson.2022.逐层图案化阀门实现可编程软表面。Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.6，1，第 12 条（2022 年 3 月），25 页。https://doi.org/10.1145/3517251

1 INTRODUCTION
1 引言

Every day, we interact with dozens of physical surfaces that are largely static. Forward-looking designers have perceived an opportunity in this space - anticipating a suite of tangible, shape-changing interfaces that are as mutable as their digital relatives [57]. But such surfaces, clearly, are far from commonplace today.
每天，我们都要与数十种基本静态的物理表面进行交互。高瞻远瞩的设计师们已经意识到了这一领域的商机--他们期待着一系列有形的、可改变形状的界面，这些界面就像它们的数字界面一样可变[57]。但显然，这样的表面在今天还远远没有普及。

Fig. 2. A module-driven design (a), in the form of a solenoid array, is contrasted with a layer-driven design (b), in the form of an electrostatic valve array. Actuators in (a) are distinct mechanisms; actuators in (b) are cells in a common substrate. Communication in (a) is centralized (one-to-many); communication in (b) is distributed (neighbor-to-neighbor). Energy in (a) is transmitted via independent branches; energy in (b) is accessible through a global, unified reservoir.
图 2.模块驱动设计（a）（电磁阀阵列）与层驱动设计（b）（静电阀阵列）的对比。(a) 中的执行器是不同的机构；(b) 中的执行器是共同基底中的单元。(a) 中的通信是集中式的（一对多）；(b) 中的通信是分布式的（邻居对邻居）。(a) 中的能量通过独立的分支机构传输；(b) 中的能量可通过一个全球统一的储存库获取。

The few existing objects that do adapt to our inputs (tactile displays¹, for instance) are specialized devices, only able to achieve a physical state change through the complex manipulation of multiple independent elements $[13, 21]$ . This modular design, while workable in cost-agnostic settings, is limited in practice by a labor-intensive construction process [1]. If we are interested in making shape-shifting surfaces pervasive within our world, then this discretely-assembled machinery must be replaced with a more fabrication-friendly alternative.
少数能够适应我们输入的现有对象（例如触觉显示器¹ ）都是专用设备、 $[13, 21]$ 只能够通过对多个独立元素的复杂操作来实现物理状态的改变。这种模块化设计虽然在成本不变的情况下可行，但在实践中却受到劳动密集型建造过程的限制 [1]。如果我们有兴趣在我们的世界中普及可变形表面，那么就必须用一种更便于制造的替代方案来取代这种独立组装的机械。

Layered construction provides a solution. Among some mechanical engineers, there is an emerging migration from multi-piece mechanisms to cleverly-designed composites - soft and flexible structures that arise from the stacking of patterned films [40, 47]. In this paper, we adopt layer-driven design as a method for building programmable pneumatic surfaces that are inherently scalable. We introduce an electrostatic valve array (Figure 1), which we refer to as Stoma-Board - an allusion to the micro-scale pores (stomata) that regulate air intake from the surface of plant leaves.
分层结构提供了一种解决方案。在一些机械工程师中，出现了从多件机械装置向巧妙设计的复合材料迁移的趋势--复合材料是由图案化薄膜堆叠而成的柔软而灵活的结构[40, 47]。在本文中，我们采用层驱动设计作为构建可编程气动表面的方法，这种气动表面本身具有可扩展性。我们引入了一个静电阀门阵列（图 1），并将其称为 "气孔板"（Stoma-Board）--暗指调节植物叶片表面进气量的微尺度气孔（气孔）。

By orienting our fabrication process around bulk procedures - actions that can be performed in one or more "sweeps", such as casting, photo-etching, and laser cutting - we eliminate the many individual manufacturing steps that are common in more module-driven designs. These modular pneumatic surfaces consist of separate cells that are each tied to independent solenoid valves $[11, 35]$ ; in contrast, our approach allows for the creation of variable-sized arrays within a fixed number of fabrication steps.
通过将我们的制造流程定位在批量程序（可在一次或多次 "扫描 "中执行的操作，如铸造、光蚀刻和激光切割）上，我们省去了模块驱动设计中常见的许多单独制造步骤。这些模块化气动表面由独立的单元组成，每个单元都与独立的电磁阀相连 $[11 、 35]$ ；相比之下，我们的方法允许在固定数量的制造步骤内创建大小可变的阵列。

This layer-driven design integrates well with the type of composite transducers that have taken hold within the soft robotics community [2], providing a scalable bed of actuators that can replace networks of individually connected tubes. Such a system may be well-suited for the production of room-scale pneumatic surfaces [59, 61], which, like current toolkits [22, 37, 53], have so far relied on a modular approach. Composite arrays such as Stoma-Board, which simplify manufacturing through the use of bulk-fabricated layers, may bring large-scale structures and high-resolution surfaces within reach.
这种分层驱动的设计与软体机器人界[2]流行的复合传感器类型结合得很好，提供了一个可扩展的执行器床，可以取代单独连接的管道网络。这样的系统可能非常适合生产房间规模的气动表面[59, 61]，就像目前的工具包[22, 37, 53]一样，迄今为止一直依赖于模块化方法。复合阵列（如 Stoma-Board）通过使用散装制造层简化了制造过程，可实现大规模结构和高分辨率表面。

2 LAYER-DRIVEN DESIGN
2 层驱动设计

In Figure 2, we illustrate the driving principle of our design process: functionality arises from a stacked configuration of bulk-fabricated layers, rather than the assembly of many individual parts. (We observe that sufficiently mature robotic processes, such as "pick-and-place" or 3D-printing, may also be considered bulk procedures.) Though this imposes an additional engineering challenge during the development of the primary actuation mechanism, the resulting material cell will necessarily be scalable under this framework. Such designs are distinguished by four characteristics:
在图 2 中，我们说明了我们设计流程的驱动原则：功能来自于批量制造层的堆叠配置，而不是许多单独部件的组装。(我们注意到，足够成熟的机器人工艺，如 "拾放 "或三维打印，也可被视为批量工艺）。虽然这给主要驱动机制的开发带来了额外的工程挑战，但在此框架下，由此产生的材料单元必然是可扩展的。这种设计有四个特点：

(1) Constituent actuators are not distinct components, but instead cells within a common substrate. In our implementation, this substrate is a patterned electrode array, with each node able to exert an attractive force on one section of a shared diaphragm.
(1) 组成致动器的不是不同的组件，而是一个共同基板中的单元。在我们的设计中，这个基底是一个图案化的电极阵列，每个节点都能对共享膜片的一个部分施加吸引力。

(2) Communication, and in some cases computation, is not centralized, but instead distributed throughout the surface. Neighboring cells exchange messages with each other, which our system exhibits by means of a daisy-chained control scheme.
(2) 通信和某些情况下的计算不是集中进行的，而是分布在整个表面。相邻的细胞会相互交换信息，我们的系统通过菊花链控制方案实现了这一点。

(3) Energy is not delivered through individual connections, but instead made available through a globally accessible reservoir. Analogous to the power and ground planes that have long been a staple of multi-layer circuit boards, the base layer of our system is a vacuum-connected cavity that acts as a global pneumatic sink.
(3) 能量不是通过单独的连接输送，而是通过一个全球可访问的储能器提供。与长期以来多层电路板上的电源层和接地层类似，我们系统的底层是一个真空连接的空腔，充当全球气动汇。

(4) Pattern generation precedes fabrication and assembly. In a module-driven design, actuators may be built independently, and then placed in positions across a surface. In our system, patterning must take place earlier in the design process, as all actuators are built concurrently during the layer-stacking assembly procedure. We implement a simple computational tool to generate these layouts.
(4) 在制造和组装之前生成图案。在模块驱动的设计中，致动器可能是独立制造的，然后放置在表面的各个位置。在我们的系统中，由于所有致动器都是在层堆叠组装过程中同时制造的，因此必须在设计流程的早期进行图案生成。我们采用了一种简单的计算工具来生成这些布局。

We demonstrate the validity of this approach through the fabrication of a programmable surface, which serves as a "raw" base layer for mounting multiple types of pneumatic transducers.
我们通过制作一个可编程表面来证明这种方法的有效性，该表面可作为安装多种类型气动传感器的 "原始 "底层。

3 BACKGROUND AND RELATED WORK
3 背景和相关工作

3.1 Shape-Changing Surfaces and Tactile Displays
3.1 可改变形状的表面和触觉显示器

Programmable surfaces can be broadly separated into two categories - dynamic matter (collections of actuators) that can be arbitrarily reconfigured $[25, 32, 50, 69]$ , and "morphing" materials, for which certain shape-changing capabilities are encoded as part of the fabrication process $[12, 43, 64]$ . Our system is an instance of the former, but we leverage the composite material fabrication techniques that are common in the latter.
$[25 可编程表面可大致分为两类--可任意重新配置的动态物质（执行器集合）[25 、 32, 50 、 69]和 "变形 "材料、[12 具有某些形状变化能力的材料，其编码是制造过程的一部分、 43, 64]。我们的系统是前者的一个实例，但我们利用了后者常用的复合材料制造技术。$

A popular instance of the first type of material is the "pin display" [27]. This is a two-dimensional surface, composed of linear actuators (pins) that can independently extend out-of-plane. Pins can be rigid, driven by miniature lead screw assemblies [54, 68], as well as soft, driven pneumatically [44]. This type of modular construction trades scalability for precise actuation - pins move independently, but the discrete assembly process imposes a practical limit on the number that can be fabricated.
第一种材料的常用实例是 "针脚显示器"[27]。这是一个二维表面，由可独立伸出平面外的线性致动器（引脚）组成。引脚可以是刚性的，由微型导螺杆组件驱动 [54, 68]，也可以是软性的，由气动驱动 [44]。这种模块化结构以可扩展性换取精确致动--销钉可独立移动，但离散装配工艺对可制造的数量造成了实际限制。

Work by Zárate et al. [69, 70] hints at a solution. Their variant of a tactile display, while still consisting of individual (magnetic) pins, is driven by coils that are patterned on a printed circuit board. Since these multiple coils are all formed as part of a single fabrication step (photo-etching, during the printed circuit board manufacturing process), this act of patterning reduces the ultimate assembly time for the device. These copper traces can similarly be used for within-plane steering of magnetic markers [39, 58], and stand in contrast to prior approaches that employed beds of individually packaged solenoids [38, 65]. Notably, there is a trade-off here - while these layered coils can be replicated across large surfaces with relative ease, they are generally less powerful than their discrete counterparts (owing to the reduced number of turns).
扎拉特等人的研究[69, 70]暗示了一种解决方案。他们的触觉显示器变体虽然仍由单个（磁性）引脚组成，但由印刷电路板上的线圈驱动。由于这些多线圈都是在单一制造步骤（印刷电路板制造过程中的光蚀刻）中形成的，因此这种图案化行为缩短了设备的最终组装时间。这些铜线同样可用于磁性标记的平面内转向 [39, 58]，与之前采用独立封装螺线管的方法形成鲜明对比 [38, 65]。值得注意的是，这里有一个权衡问题--虽然这些分层线圈可以相对容易地在大表面上复制，但它们的功率通常不如分立线圈（因为匝数减少了）。

One way to circumvent this dilemma is by using patterned elements as a means of "tapping in" to a larger energy source. Under this paradigm, power and control are fully decoupled, and the actuators serve as gateways to a global reservoir. Qiu et al. [42] employ this approach, spray-coating an array of resistive traces onto an electroactive polymer film, which is suspended above a pressurized pneumatic chamber. Through targeted Joule-heating of the film (via the resistive traces), they force heat-softened sections of the membrane to deflect outward and raise a layer of pins. Previously, Besse et al. $[6, 7]$ demonstrated a similar design, fabricating a shape-memory polymer membrane with integrated heating elements. This membrane was mounted over an alternating pressure source - positive pressure pushes the selected areas upward, and negative pressure pulls them back down.
规避这一困境的一种方法是使用图案元件作为 "接入 "更大能源的手段。在这种模式下，动力和控制完全解耦，执行器充当通向全球储能器的网关。Qiu 等人[42] 采用了这种方法，将电阻迹线阵列喷涂在电活性聚合物薄膜上，该薄膜悬挂在加压气动室上方。通过对薄膜进行有针对性的焦耳热（通过电阻迹线），他们迫使薄膜的热软化部分向外偏转，并升起一层引脚。在此之前，Besse 等人已经开发出了一种新的薄膜。 $[6 、 7]$ 展示了一种类似的设计，制造了一种带有集成加热元件的形状记忆聚合物膜。该膜安装在一个交变压力源上--正压将所选区域向上推，负压将其向下拉。

Our Stoma-Board system makes use of this "patterned gates" strategy as well, with an array of layered, miniature valves that connect an upper transducer layer to a pneumatic sink. In contrast to related approaches, which use an external bank of solenoid valves to inflate sections of a membrane [36, 49], our actuators are directly integrated into the surface, and do not need to be discretely assembled. Layered composites, then, may be key in creating programmable surfaces that can scale in size and density.
我们的造口护板系统也采用了这种 "模式化门 "策略，通过一系列分层的微型阀门将上部传感器层与气动汇连接起来。与使用外部电磁阀组为膜的各个部分充气的相关方法相比 [36, 49]，我们的致动器直接集成到表面，无需单独组装。因此，层状复合材料可能是创造可按尺寸和密度扩展的可编程表面的关键。

3.2 Soft and Foldable Robots
3.2 柔软和可折叠机器人

Roboticists, in recent years, have been drawn to composites as well - with some eschewing traditional linkages in favor of flat materials that fold or stretch [40, 47]. By stacking layers with dissimilar mechanical properties, or by cutting patterns into overlapping sheets [56], sections of the resultant material can be constrained to move along predefined paths when actuated. In a soft robot, for example, a bending motion might be achieved by depositing a compliant silicone layer on top of a more rigid, strain-resisting substrate. When subjected to an axial force, either via piezoelectric [66], electrostatic [5], or pneumatic actuation [29], the material curves in the direction of the less-stiff layer.
近年来，机器人专家也被复合材料所吸引--一些人放弃了传统的连接方式，转而使用可折叠或拉伸的平面材料 [40, 47]。通过堆叠具有不同机械特性的层，或在重叠的薄片上切割图案 [56]，可以在驱动时限制所产生材料的部分沿预定路径移动。例如，在软体机器人中，可以通过在刚性较强的抗应变基底上沉积顺应性硅胶层来实现弯曲运动。当通过压电[66]、静电[5]或气动致动[29]受到轴向力时，材料就会沿着刚度较低的层的方向弯曲。

By micro-machining these individual layers (selectively removing material), bending behaviors can be further restricted to specific regions of the composite. This enables "pop-up" mechanisms, such as the origami-inspired joystick by Mintchev et al. [33], or the millimeter-scale delta robot by McClintock et al. [31]. In each of these systems, the composites consist of a flexible layer (polyimide), sandwiched between two rigid layers (fiberglass, or carbon-fiber). Strategic cuts in these layers give rise to Sarrus linkages, which lift sections of the composite out-of-plane. (These particular mechanisms are both driven by external base-stations, though other researchers have begun to explore foldable composites with self-actuating inner layers [60].)
通过对这些单个层进行微加工（有选择性地去除材料），可进一步将弯曲行为限制在复合材料的特定区域内。这就实现了 "弹出式 "机械装置，例如 Mintchev 等人[33]受折纸启发设计的操纵杆，或 McClintock 等人[31]设计的毫米级三角洲机器人。在这些系统中，复合材料都由一个柔性层（聚酰亚胺）和两个刚性层（玻璃纤维或碳纤维）组成。在这两层中进行战略性切割可产生 Sarrus 连杆，从而将复合材料的不同部分提升到平面外。(这些特殊机制都是由外部基站驱动的，不过其他研究人员已经开始探索带有自驱动内层的可折叠复合材料[60]）。

Further embracing deformation, roboticists such as Kellaris et al. [20] achieve out-of-plane motion through the manipulation of flexible, fluid-filled membranes. These sandwich-style actuators are characterized by "zippering" motions - as portions of the outer membranes are squeezed together, an inner layer of fluid flows into a predefined pocket, causing the membranes to bulge outward. This squeezing is initiated by an applied electrostatic force, similar to the operation of dielectric elastomer actuators. Artificial muscles such as these can be fabricated from stacked thermoplastic sheets, which are then heat-sealed, filled with fluid, and patterned with compliant electrodes [34]. Other researchers have used similar constructions for the production of wearable haptic interfaces [28], indicating that this may be a viable technique for the creation of programmable surfaces.
Kellaris 等人[20]等机器人专家通过操纵充满液体的柔性薄膜，实现了平面外运动。这些夹层式致动器的特点是 "拉链 "运动--当外层膜的一部分被挤压在一起时，内层流体流入一个预定的口袋，导致膜向外鼓起。这种挤压是由外加的静电力引发的，与介电弹性体致动器的工作原理类似。类似的人造肌肉可以用堆叠的热塑性塑料板制造，然后进行热封、填充流体并用顺应电极进行图案化[34]。其他研究人员也利用类似结构制作了可穿戴触觉界面[28]，这表明这可能是制作可编程表面的一种可行技术。

For these devices, electrostatic actuation is a reasonable choice. It is a low-power method, only drawing current during transient periods; and at small distances, these actuators can provide a significant amount of force. We discuss this further in the next section.
对于这些设备，静电致动器是一个合理的选择。它是一种低功耗方法，只在瞬态期间消耗电流；而且在较小的距离内，这些致动器可以提供很大的力。我们将在下一节对此进行进一步讨论。

3.3 Electrostatic Actuators
3.3 静电致动器

Two charged objects of opposite polarity, when placed in close enough proximity, will begin to move towards each other as they experience an attractive electrostatic force. This seemingly straightforward transformation of electrical energy into mechanical work has seeded a significant body of research relating to electrostatic actuators - perhaps most widely in the MEMS community. Here, investigators have leveraged this principle to develop micro-scale (sub-millimeter) sensors, switches, pumps, and valves [72]. Many of these devices incorporate some displacement mechanism, consisting of an anchored electrode that pushes or pulls a moveable plate.
两个极性相反的带电物体，当被放置在足够近的距离时，会因为受到静电力的吸引而开始相互移动。这种看似简单的将电能转化为机械功的过程，为有关静电致动器的大量研究提供了契机，其中以 MEMS 界的研究最为广泛。在这里，研究人员利用这一原理开发出了微米级（亚毫米级）传感器、开关、泵和阀门 [72]。其中许多设备都采用了某种位移机制，包括一个锚定电极来推动或拉动一个可移动的板。

At the meso-scale (centimeter) and larger, this attractive electrostatic force has been harnessed for braking and locking - modulating the frictional force between two electrodes that slide against one another. Diller et al. explored this through the construction of an electrostatic clutch, engaging and disengaging spring elements in a leg exoskeleton [9]. Hinchet et al. developed a similar concept, for grasping in virtual reality [14]. Their slimmer strips were worn on the fingers, constraining hand movement when a voltage was applied. Recent work by Zhang et al. [71] has adapted this technique for use in for shape-changing pin displays - individual braking mechanisms will lock brass pins in place as a global upward force is applied, resulting in a reconfigurable height field.
在中尺度（厘米）或更大尺度上，这种有吸引力的静电力已被用于制动和锁定--调节两个相互滑动的电极之间的摩擦力。Diller 等人通过建造一个静电离合器，使腿部外骨骼中的弹簧元件啮合和脱离，探索了这一方法[9]。Hinchet 等人提出了一个类似的概念，用于虚拟现实中的抓取[14]。他们在手指上佩戴了更薄的条带，在施加电压时限制手的运动。Zhang 等人最近的研究[71]将这一技术应用于形状可变的针脚显示器--当施加整体向上的力时，单个制动机制将锁定黄铜针脚，从而形成一个可重新配置的高度场。

An advantage of this friction-based mechanism is that during operation, the components are always in close proximity, where electrostatic forces are strongest. (Theses forces fall off with the square of the distance between charged elements.) Consequently, such systems have been able to bear human-scale forces (up to $100 N$ for the 10 $cm$ wide electrode pairs in [9]). A key consideration is that the direction of actuation is normal to the applied electrostatic force (i.e. attraction up and down prevents sliding from left to right).
这种以摩擦为基础的机制的一个优点是，在运行过程中，元件始终紧靠在一起，静电力最强。(静电力随带电元件之间距离的平方而减小）。因此因此，此类系统能够承受人体规模的力量（高达 $100 N$ 为 10 $cm$ 宽电极对（见 [9]）。一个关键的考虑因素是致动方向与所施加的静电力成法线关系（即上下吸引可防止从左到右滑动）。

This has not typically been the case with regard to valves, for which electrostatic forces must resist an applied pressure directly. In the most basic construction [41], a flexible conductive diaphragm sits on top of an insulated electrode, covering a hole in the center of that electrode. When a voltage is applied, the attractive electrostatic force creates a seal over the hole, restricting air flow (Figure 6).
阀门通常不属于这种情况，因为静电力必须直接抵抗外加压力。在最基本的结构中 [41]，柔性导电膜片位于绝缘电极之上，覆盖着电极中心的一个孔。当施加电压时，有吸引力的静电力会在孔上形成密封，从而限制空气流动（图 6）。

The difficulty here is that as soon as a small gap emerges, a peeling effect rapidly dislodges the diaphragm. As a result, valves with this construction are often constrained to operate within low pressure conditions $(1 kPa) [8]$ , or to be driven with high voltages $(> 600 V) [3]$ .
这里的困难在于，一旦出现一个小缝隙，剥离效应就会迅速使隔膜移位。因此、 $(1 kPa) [8]$ 、或以高电压 $(> 600 V) [3]$ .

To address this limitation, researchers have used additional pneumatic ports, which serve to balance the applied pressure and hold the diaphragm in place $[4, 62, 67]$ . This, however, requires a second pneumatic source (one that sits just below the input pressure), which increases the overall fabrication complexity. In the next section, we introduce a novel valve design that overcomes this problem without the addition of extra pneumatic channels. By inverting the diaphragm actuation mechanism, such that it acts as a check valve rather than a lid or a cap, we are able to regulate pressures 80 times larger than comparable implementations [8] - a necessary performance increase for working with human-scale forces.
$[4 、 62, 67]$ 。但是，这需要第二个气动源（一个位于输入压力下方的气动源），从而增加了整体制造的复杂性。在下一节中，我们将介绍一种新型阀门设计，无需增加额外的气动通道即可克服这一问题。通过将膜片驱动机制倒置，使其充当单向阀而不是盖子或帽，我们能够调节比同类实施方案大 80 倍的压力[8]--这对于处理人体尺度的力量来说是必要的性能提升。

4 PATTERNED VALVES FOR PROGRAMMABLE SURFACES
4 个图案阀门，用于可编程表面

In the remainder of this paper, we describe the design and fabrication of a material that emerges from our layer-driven framework: Stoma-Board. This is an array of patterned, electrostatic valves, situated on top of a global cavity (Figure 3a, 3b). By switching individual valves on and off, we are able to control the flow of air into a transducer layer on top of the board. For instance, as shown in Figure 3d, we can regulate airflow into discrete pockets of an elastic substrate (causing these cells to inflate, buckle, or bend, depending on the geometry).
在本文的其余部分，我们将介绍一种材料的设计和制造过程，这种材料就产生于我们的层驱动框架：造口板。这是位于一个整体空腔顶部的图案化静电阀门阵列（图 3a、3b）。通过开关各个阀门，我们可以控制进入造口板顶部传感器层的气流。例如，如图 3d 所示，我们可以调节气流进入弹性基板的离散袋（根据几何形状，使这些单元膨胀、弯曲或折叠）。

Many programmable surfaces, if they are discretely actuated, more often resemble collections of machines than they do continuous matter. This is due in part to the limitations of a module-driven design - if actuators are assembled as independent components, increased resolution comes at a high manufacturing cost. Our aim at the outset of this work was to solve this by identifying a fabrication process for which assembly time is proportional to the number of layers, rather than the number of actuators. This decoupling allows us to pack more actuators into the same area with little or no additional time loss.
许多可编程表面，如果是离散驱动的，往往更像机器的集合，而不是连续的物质。这部分是由于模块驱动设计的局限性造成的--如果将致动器作为独立组件进行组装，分辨率的提高需要付出高昂的制造成本。我们在这项工作之初的目标就是通过确定一种制造工艺来解决这个问题，这种工艺的装配时间与层数而不是致动器的数量成正比。这种解耦使我们能够在相同的区域内安装更多的致动器，而几乎不会造成额外的时间损失。

Researchers in MEMS have long embraced lithography as a means of achieving this type of feature density [63]. However, industrial processes in the this area are usually optimized for the production of singular devices at the micro-scale (accelerometers, gyroscopes, etc.), as opposed to networks of actuators that extend over a centimeter-scale surface area or larger. For this more expansive application, we looked towards the already-mature process of printed circuit board (PCB) manufacturing, and focused on integration into that pipeline.
长期以来，微机电系统（MEMS）领域的研究人员一直将光刻技术作为实现这种特征密度的手段[63]。然而，该领域的工业流程通常是针对生产微米尺度的单个设备（加速计、陀螺仪等）而优化的，而不是在厘米尺度或更大表面积上延伸的致动器网络。为了实现这一更广泛的应用，我们将目光投向了已经成熟的印刷电路板（PCB）制造工艺，并将重点放在了与该流水线的集成上。

PCB manufacturing is characterized by patterning, etching, and layup (stacking and bonding layers) [16]. Most fabricators start with a copper-clad fiberglass sheet, and begin production by applying a photosensitive coating and printed mask. They follow these steps with a chemical procedure that selectively removes exposed copper from the substrate. For boards with more than two layers, additional material is then stacked around the core and laminated together - usually with an insulating dielectric on both sides of the sheet, and copper foil on the outer layers. This new material can be etched again, and the process may be repeated as more layers are added (such that a multi-layer board is effectively a sandwich of smaller sub-boards). Some complex PCBs, particularly those with embedded electronic components, are actually composites of other fully drilled, plated, and soldered circuit boards [55].
印刷电路板制造的特点是图案化、蚀刻和层叠（堆叠和粘合层）[16]。大多数制造者从覆铜的玻璃纤维板开始，通过涂敷感光涂层和印刷掩模开始生产。在这些步骤之后，他们会使用化学程序选择性地去除基板上裸露的铜。对于两层以上的电路板，则在板芯周围堆叠其他材料并层压在一起--通常在板材两侧使用绝缘介质，外层使用铜箔。这种新材料可以再次蚀刻，随着层数的增加，这个过程也可以重复进行（这样，多层电路板实际上就是由较小的子板组成的三明治）。一些复杂的印刷电路板，尤其是内嵌电子元件的印刷电路板，实际上是其他完全钻孔、电镀和焊接电路板的复合体[55]。

Fig. 3. One of our 19-cell Stoma-Boards (a). Directly below the top circuit board is a conductive diaphragm (b), which regulates air flow into a global reservoir. Cells are individually addressable. We treat Stoma-Board as a "raw material", using it with different transducer layers to build a variety of devices. Example transducers include: (c, d) Bistable dome, part of a larger cast membrane. (e, f) 3D-printed bellows-style transducer, which contracts under negative pressure. (g, h) Rigid Luer-lock attachment, connected to a syringe for linear actuation.
图 3.我们的 19 芯造口袋之一（a）。顶部电路板正下方是一个导电膜片（b），用于调节进入总储气室的气流。各单元可单独寻址。我们将造口板视为一种 "原材料"，将其与不同的传感器层配合使用，制造出各种设备。传感器示例包括(c、d）双稳态穹顶，较大型铸膜的一部分。(e、f）3D 打印的波纹管式换能器，在负压作用下会收缩。(g、h）刚性鲁尔锁附件，与注射器相连，用于线性驱动。

From this standpoint, the Stoma-Board layers that we introduce can be seen as an extension of this manufacturing process - a few extra steps during the layup and bonding stage. The result of our procedure is a composite material with integrated electronic and pneumatic components (Figure 4). From top to bottom, these layers are:
从这个角度来看，我们引入的造口板层可以看作是这一制造工艺的延伸--在铺层和粘合阶段增加了几个步骤。我们的工艺结果是一种集成了电子和气动元件的复合材料（图 4）。从上到下依次为

(1) An application-dependent transducer. (For example, an elastic surface, with air-filled pockets that buckle or bend when actuated.)
(1) 与应用有关的传感器。(例如，一个弹性表面，上面有充满空气的口袋，启动时会扣动或弯曲）。

(2) A printed circuit board, with control circuitry on top, and patterned electrodes on the underside.
(2) 一块印刷电路板，上面是控制电路，下面是图案化电极。

(3) A metallized polyester diaphragm (Mylar, $25μ m$ ), which regulates air flow.
(3) 金属化聚酯隔膜（Mylar， $25μ m$ ），用于调节气流。

(4) A natural rubber spacer $(150μ m)$ , through which the diaphragm travels.
(4) 天然橡胶隔膜 $(150μ m)$ ，膜片穿过该隔膜。

(5) A second printed circuit board, with patterned electrodes on top.
(5) 第二块印刷电路板，上面有图案化的电极。

(6) An SLA 3D-printed cavity, which serves as a global pneumatic sink.
(6) SLA 3D 打印的空腔，可用作全局气动水槽。

Note that although each layer is manufactured by a bulk process (casting, etching, laser-cutting, or machine placement), we still retain the ability to dynamically actuate discrete subsections of the finished surface.
请注意，虽然每一层都是通过批量工艺（铸造、蚀刻、激光切割或机器贴装）制造的，但我们仍保留了动态驱动成品表面离散部分的能力。

4.1 Working Principle
4.1 工作原理

Air flow through each valve is regulated by a metallized polyester diaphragm, which rests underneath an insulated copper electrode (Figure 4). This diaphragm cell is connected to the greater membrane layer by three hinges (Figure 4i), which allow it to flex out of plane.
通过每个阀门的气流由金属化聚酯膜片调节，膜片位于绝缘铜电极下方（图 4）。隔膜单元通过三个铰链（图 4i）与大膜层相连，使其可以在平面外弯曲。

Fig. 4. Exploded view of the Stoma-Board structure. The transducer layer (a), in this case, is an elastic surface, composed of multiple pockets that can inflate, buckle, or bend independently. Air flow into this layer is regulated by a flexible, conductive diaphragm (c, i). When a vacuum is applied, this diaphragm deflects downward though a rubber spacer layer (d, j), and is pulled flat against an outlet(e, k). This closes the valve and (in this example) traps air inside the pockets of(a). To open the valve and allow air to flow, a electric charge is applied to an electrode (h) on the underside of a printed circuit board (b). Electrostatic forces retract the diaphragm from the valve outlet, allowing air to move from the transducer layer (a) to a global sink (f). Cells are hexagonally packed, with an $18 mm$ pitch.
图 4.造口护板结构剖视图。在这种情况下，传感器层（a）是一个弹性表面，由多个可独立充气、扣合或弯曲的口袋组成。进入该层的气流由柔性导电膜片（c，i）调节。当施加真空时，隔膜通过橡胶隔层（d，j）向下偏转，并被拉平抵住出气口（e，k）。这就关闭了阀门，并（在本例中）将空气阻隔在（a）的袋内。为了打开阀门，让空气流通，需要向印刷电路板（b）底部的电极（h）施加电荷。静电力使隔膜从阀门出口处缩回，从而使空气从传感器层（a）流向全局汇（f）。单元呈六边形排列，间距为 $18 mm$ 间距。

In the active state (when a voltage is applied), electrostatic forces hold the diaphragm in place, and air passes freely from inlet to outlet (Figure 5a). In the non-active state, negative pressure at the valve outlet instead pulls the diaphragm downstream, blocking the outlet and impeding further flow (Figure 5b). To mitigate leakage in the non-active state, an optional secondary electrode at the outlet can be activated and used to further seal the valve (Figure 5c). Throughout this paper, we will refer to the first electrode as the valve-opening electrode, and the second electrode as the valve-sealing electrode.
在激活状态下（施加电压时），静电力将膜片固定到位，空气从入口自由流向出口（图 5a）。在非激活状态下，阀门出口处的负压会将膜片拉向下游，从而堵住出口，阻碍空气进一步流动（图 5b）。为减少非激活状态下的泄漏，可激活出口处的可选辅助电极，用于进一步密封阀门（图 5c）。在本文中，我们将第一个电极称为阀门开启电极，第二个电极称为阀门密封电极。

The attractive force between (either) electrode and the valve diaphragm is expressed by the relationship:
任一）电极与阀门隔膜之间的吸引力用以下关系表示：

$F ∝ \frac{V^{} A}{d^{}}$
$F ∝ \frac{V^{} A}{d^{}}$

where $F$ is the electrostatic force, $A$ is the overlapping electrode area, $V$ is the applied voltage, and $d$ is the distance between the electrode and the diaphragm [3]. For an electrostatic valve, the parameter of greatest concern is the distance $d$ (the other two right-side variables can be readily controlled, but this distance will vary during operation). Since the attractive force decreases with the square of this value, small fluctuations in distance have large consequences for valve behavior.
ata-imersive-translate-walke $d$ ="c9d70191-c8eb-4b3e-b2e9-9ea4bec76614"> 其中 $F$ 为静电力、 $A$ 是重叠电极面积、 $V$ 是外加电压、和 $d$ 是电极与膜片之间的距离 [3]。对于静电阀门，最值得关注的参数是距离 $d$ （其他两个右侧变量可随时控制，但该距离在操作过程中会发生变化）。由于吸引力随该值的平方而减小，因此距离的微小波动会对阀门行为产生很大影响。

Fig. 5. The three states of operation. (a) Active state: A voltage is applied between the valve-opening electrode and the conductive diaphragm. The resulting electrostatic force causes the diaphragm to adhere to this electrode, allowing air to pass underneath. (b) Non-active state: If no voltage is applied, a pressure differential will pull the diaphragm flat against the valve outlet, restricting air flow. (c) Sealed state: A voltage is applied between the conductive diaphragm and the valve-sealing electrode. Electrostatic forces pull the diaphragm tight against the outlet, mitigating leakage. (d, e) Diaphragm and valve-opening electrode in active (open) and non-active (blocking flow) states. To show actuation in these photographs, a clear acrylic plate is used in place of the opaque valve-sealing electrode. (f) An image of the valve-sealing electrode, by itself.
图 5.三种运行状态(a) 激活状态：在阀门开启电极和导电膜片之间施加电压。由此产生的静电力使隔膜附着在电极上，使空气从下面通过。(b) 非激活状态：如果不施加电压，压差会将隔膜拉平，使其紧贴阀门出口，从而限制空气流通。(c) 密封状态：在导电膜片和阀门密封电极之间施加电压。静电力将隔膜拉紧出口，减少泄漏。(d、e）处于激活（打开）和非激活（阻止流动）状态的隔膜和阀门开启电极。为了在这些照片中显示驱动情况，用一块透明的丙烯酸板代替了不透明的阀门密封电极。(f) 阀门密封电极本身的图像。

In particular, electrostatic latching mechanisms such as these are often susceptible to "peeling" [18]; and some valve geometries are more vulnerable than others. One of these configurations is shown in Figure 6, in which the diaphragm is positioned to block incoming flow from below, as opposed to sealing outgoing leakage from above. As soon as a minor gap emerges under the diaphragm (due to pressure fluctuations, surface roughness, or other environmental factors), the electrostatic force at that interface is greatly diminished. This reduction in force means that a section of the diaphragm may begin to balloon or lift away, propagating until the seal is fully broken. Our earliest prototypes were built in this style, and (just as in similar implementations [8]), they were unable to regulate pressures above several kilopascals.
特别是，此类静电闩锁机制往往容易发生 "剥离"[18]；而且某些阀门的几何结构比其他结构更容易受到影响。图 6 显示了其中的一种结构，在这种结构中，隔膜的定位是阻挡从下方流入的水流，而不是密封从上方流出的泄漏水流。一旦隔膜下方出现微小缝隙（由于压力波动、表面粗糙度或其他环境因素），该界面上的静电力就会大大减弱。静电力的减弱意味着隔膜的一部分可能开始膨胀或脱落，直至密封完全破坏。我们最早的原型就是以这种方式制造的，而且（正如类似的实施方案 [8]），它们无法调节超过几千帕的压力。

It is possible to address this limitation by adding additional pneumatic sources and channels, in order to keep the pressure differential around the diaphragm within a small threshold $[4, 62, 67]$ . But seeking a simpler construction, we took an alternate approach - by inverting the diaphragm configuration as described earlier (Figure 5a-c), we were able to take advantage of a "zippering" effect [52] to actuate the valve.
$[4 、 62, 67]$ 。但为了寻求更简单的结构，我们采取了另一种方法--如前所述（图 5a-c），通过倒置膜片配置，我们能够利用 "拉链 "效应 [52] 来驱动阀门。

Fig. 6. Early Stoma-Board prototypes used an alternate valve configuration, inspired by common MEMS implementations [41]. The diaphragm rests above the valve inlet, and when actuated, blocks air flow from below (b). At pressures beyond 1 $kPa$ , small gaps begin to emerge at the valve inlet, which propagate across the surface and eventually dislodge the diaphragm [8]. When no voltage is applied, air passes through the valve unimpeded (a).
图 6。早期的造口护板原型采用了另一种阀门配置，其灵感来自常见的 MEMS 实现[41]。隔膜位于阀门入口上方，启动时可阻止气流从下方进入（b）。当压力超过 1 $kPa$ 时，阀门入口处开始出现小缝隙，这些缝隙在表面传播，最终使隔膜脱落 [8]。当没有施加电压时，空气会畅通无阻地通过阀门（a）。

"Zippering" motions, in our system, start at the hinges of the diaphragm and move inward. Consider the valve in the non-active state (Figure 5b): negative pressure has pulled the diaphragm flat against the outlet. This is $150μ m$ below the valve-opening electrode - small on a human scale, but large enough for electrostatic forces to be noticeably weakened. The diaphragm hinges, by contrast, are ten times closer - separated only by a thin dielectric layer, just $15μ m$ thick. When we switch to the active state, strong electrostatic forces near the hinges allow us to retract a diaphragm that would otherwise be out of reach at high negative pressures (> 80 kPa).
在我们的系统中，"拉链 "运动从隔膜的铰链处开始并向内移动。假设阀门处于非活动状态（图 5b）：负压将膜片拉平，使其紧贴出口。这是 $150μ m$ 阀门开启电极下方的位置--在人体尺度上很小，但足以使静电力明显减弱。相比之下，隔膜铰链的距离要近十倍--中间只隔着一层薄薄的介电层，厚度仅为 $15μ m$ 。当我们切换到活动状态时，铰链附近强大的静电力使我们能够缩回隔膜，否则在高负压（> 80 kPa）条件下隔膜将无法缩回。

4.2 Insulating Dielectric and Driving Voltage
4.2 绝缘介质和驱动电压

When we apply a voltage between an electrode and the valve diaphragm, an insulating layer is needed in the middle to prevent electrical shorts. In early prototypes, we used $25μ m$ polyimide sheets, hand-laminated onto bare copper electrodes. (This technique is similar to [14], though we did not use any adhesive.) Polyimide is a natural choice for this layer - with a breakdown voltage in excess of $250 V/ μ m$ , we can administer several kilovolts before the insulating layer fails and conducts.
当我们在电极和阀门隔膜之间施加电压时，中间需要一个绝缘层来防止电气短路。在早期的原型中，我们使用了 $25μ m$ 聚酰亚胺片，手工层压到裸铜电极上。(这种技术与 [14] 类似，但我们没有使用任何粘合剂）。聚酰亚胺是该层的自然选择--其击穿电压超过 $250 V/ μ m$ 、我们可以在绝缘层失效和导电之前施加数千伏电压。

Our system, however, operates between $150 V$ and $300 V$ (drawing a low and safe $50μ A$ ). At these levels, a thin layer of solder mask (breakdown voltage around $25 − 30 V/ μ m$ ) is sufficient insulation, with the additional benefit of a smaller minimum distance $d$ between conductors. Consequently, we use only solder mask to separate the valve-opening electrode from the metallized side of the diaphragm.
ata-imersive-translate-walked="c9d70191-c8eb-4b3e-b2e9-9ea4bec76614"> 然而，我们的系统、 $150 V$ 和 $300 V$ （绘制低且安全的 $50μ A$ ）。在这些层面上、一薄层阻焊（击穿电压约为 $25 - 30 V/ μ m$ ）就足够绝缘、此外，导体之间的最小距离 $d$ 也更小。因此，我们仅使用阻焊层将阀门开启电极与隔膜的金属化侧分开。

The valve-sealing electrode is left exposed (bare copper). It does not contact the metallized side of the diaphragm - the $25μ m$ Mylar sheet itself provides adequate insulation.
阀门密封电极裸露在外（裸铜）。它不与隔膜的金属化侧接触-- $25μ m$ Mylar 片本身提供了足够的绝缘。

4.3 Daisy-Chained Electronic Communication
4.3 菊花链式电子通信

Fully distributed computation is a target that arises from the layer-driven model (and is addressed briefly in Section 7). This is desirable not only from a fabrication perspective (eliminating multiple physical connections to a central hub), but also important for making robust programmable materials that scale without regard to the processing power of a master controller.
完全分布式计算是层驱动模型的一个目标（第 7 节将简要论述）。这不仅从制造的角度来看是可取的（消除了与中心枢纽的多个物理连接），而且对于制造不受主控制器处理能力影响的坚固可编程材料也很重要。

A first step towards this objective is casting each material subsection as a distinct computational node, capable of communication with its immediate neighbors. We implement this (somewhat simply) in our system by means of a daisy-chained control scheme.
实现这一目标的第一步是将每个材料分节作为一个独立的计算节点，能够与其近邻进行通信。在我们的系统中，我们通过菊花链控制方案实现了这一点（有点简单）。

Physically, this communication takes place in the layer above the valve diaphragm (Figure 4b). Each material cell contains several discrete electronic components, as well as the patterned copper circuitry that connects them, which includes the valve-opening electrode. A shared clock line and global power sources (high-voltage rails for actuation and low-voltage rails for signaling) run across the surface and are accessible by each cell.
从物理上讲，这种通信发生在气门隔膜的上层（图 4b）。每个材料单元都包含几个分立的电子元件，以及连接它们的图案化铜电路，其中包括阀门开启电极。一条共用时钟线和全局电源（用于驱动的高压导轨和用于信号传输的低压导轨）贯穿整个表面，每个单元都可以访问。

Fig. 7. Electronic components within a Stoma-Board cell. Cells are daisy-chained, and change state in response to a global clock signal.
图 7.Stoma-Board 单元内的电子元件。单元以菊花链方式连接，并根据全局时钟信号改变状态。

A simplified schematic is shown in Figure 7. An electrode may be connected to either of the high voltage rails through a pair of opto-isolated solid-state relays $^{}$ . A discrete flip-flop $^{}$ drives the LEDs of the opto-isolater, and also serves as the main communication element. On every clock pulse, the cell as a whole follows two rules:
简化示意图如图 7 所示。电极可通过一对光隔离固态继电器 $^{}$ 连接到任一高压轨。离散触发器 $^{}$ 驱动光隔离器的 LED，同时也是主要的通信元件。在每个时钟脉冲中，整个单元遵循两条规则：

(1) Pass the current cell state to the right-side neighbor.
(1) 将当前单元状态传递给右侧邻居。

(2) Receive a new cell state from the left-side neighbor.
(2) 从左侧邻居接收新的小区状态。

With this configuration, an external microcontroller upstream can quickly send data to all nodes in the chain. This operation is similar to that of the addressable LED strings (such as the APA102 or WS2812) that in recent years have served a material-like role in maker and DIY communities [30]. Our clock signal runs at $300 kHz$ , which allows us to set the state of 300 valves per millisecond. This rapid switching means that in practice, the overall refresh rate of the surface is generally independent from the number of valves, and instead a function of the pneumatic control scheme (see Section 4.4).
通过这种配置，上游的外部微控制器可以快速向链中的所有节点发送数据。这种操作类似于可寻址 LED 灯串（如 APA102 或 WS2812），近年来在创客和 DIY 社区中发挥了类似材料的作用 [30]。我们的时钟信号运行频率为 $300 kHz$ ，这使我们能够在每毫秒内设置 300 个阀门的状态。这种快速切换意味着，在实际应用中，表面的整体刷新率通常与阀门数量无关，而是气动控制方案的函数（见第 4.4 节）。

Opto-isolated relays are not the only driver option. In earlier prototypes, we used resistor-transistor logic to control the valve array - electrodes were either actively switched low or passively pulled high. Though smaller in footprint, which is desirable, this design wastes power on the actuation side, continuously sending current through the resistor when the electrode is held low. A more efficient half-bridge topology was also considered, but ultimately discarded due to the need for additional high-voltage bias supplies. While the package size of the solid-state relays did limit our electrode density, we decided that the reduced complexity, low-power actuation, and isolation benefits made them a reasonable choice for this implementation.
光隔离继电器并不是唯一的驱动选择。在早期的原型中，我们使用电阻晶体管逻辑来控制阀阵列--电极要么主动切换为低电平，要么被动拉高。这种设计虽然占地面积较小，是可取的，但却浪费了驱动侧的功率，当电极保持低电平时，电流会持续通过电阻器。我们还考虑过效率更高的半桥拓扑结构，但由于需要额外的高压偏置电源而最终放弃。虽然固态继电器的封装尺寸确实限制了我们的电极密度，但我们认为，降低复杂性、低功耗致动和隔离等优点使其成为本实施方案的合理选择。

Fig. 8. The "push-pull" actuation sequence for driving Stoma-Board prototypes using bi-stable silicone domes. (The alternating pressure source is represented by a moving piston, in gray.) Initially, the system is at rest (a). When positive pressure is created in the global reservoir, all diaphragm cells are pushed upward towards the top electrodes (b). At this stage, we may apply a voltage to latch one or more diaphragm cells in place (c, left). When negative pressure is created in the global reservoir, air exits the latched cells, and the elastic structures buckle (d, left). Note that in the unlatched cells, the elastic structures remains upright, as the diaphragm prevents air from escaping (d, right). If we remove the applied voltage, the valves may close, but the buckled cells remain unchanged (e, left). To restore these cells, we can again create a positive pressure (f), at which point we may choose to actuate another group of cells by the same process (f-h). The global pressure oscillations effectively determine the "refresh rate" of the Stoma-Board.
图 8.使用双稳态硅胶圆顶驱动造口护板原型的 "推拉 "驱动顺序。(最初，系统处于静止状态（a）。当总储液器中产生正压时，所有隔膜单元都会被向上推向顶部电极（b）。在此阶段，我们可以施加电压将一个或多个膜片细胞锁定在原位（c，左图）。当全球储气罐中产生负压时，空气会从锁定的细胞中流出，弹性结构会发生弯曲（d，左图）。请注意，在未锁定的单元中，弹性结构保持直立，因为隔膜阻止了空气的流出（d，右图）。如果我们移除施加的电压，瓣膜可能会关闭，但屈曲的细胞保持不变（e，左图）。为了恢复这些细胞，我们可以再次产生正压（f），此时我们可以选择通过相同的过程激活另一组细胞（f-h）。全局压力振荡有效地决定了造口护板的 "刷新率"。

4.4 Pneumatic Push-Pull Control Scheme
4.4 气动推拉控制方案

The bottom layer of our Stoma-Board (Figure 4f) is a global reservoir, which typically acts as a pneumatic sink (negative pressure, pulling air down through the material). The presence of this common driver has implications for the design of the transducer layer, as well as for the actuation control scheme.
造口护板的底层（图 4f）是一个整体储气罐，通常充当气动下沉器（负压，通过材料将空气向下拉）。这种共同驱动力的存在对传感器层的设计以及驱动控制方案都有影响。

Consider the following example, relating to the silicone domes in Figure 3c. An open valve allows air to flow from a pocket in the top layer to the global sink, deflating or depressurizing that top pocket in the process. Closing the valve will restrict that air flow, preventing further deflation - but this stoppage alone can not put the top pocket back in the inflated or neutral position.
请看下面与图 3c 中硅胶圆顶有关的例子。一个打开的阀门允许空气从顶层的一个口袋流向全局水槽，在此过程中顶层口袋被放气或减压。关闭阀门会限制气流，防止进一步瘪气，但仅靠这种阻断作用无法将顶层口袋恢复到充气或中性位置。

In order for this layer to "rebound", spring forces in the elastomer must overcome the negative air pressure within the cell. One way to address this is by strategically adding drain holes in the top layer, allowing outside air to leak into the cell so that the pressure can begin to equalize. However, for more predictable behavior, we can instead use the "push-pull" actuation scheme outlined in Figure 8. Under this scheme, a global reservoir is connected to an alternating pressure source (such as the syringe pump in Figure 9). During the "pull" stroke, air flows out of the Stoma-Board, and actuated cells buckle under the negative pressure. During the "push" stroke, positive pressure restores all cells to their upright positions.
为了让这一层 "回弹"，弹性体中的弹簧力必须克服电池内的负气压。解决这一问题的方法之一是在顶层战略性地增加排水孔，让外部空气渗入电池，从而开始平衡压力。不过，为了获得更可预测的行为，我们可以采用图 8 所示的 "推拉 "致动方案。在这种方案下，全局储气罐与交变压力源（如图 9 中的注射泵）相连。在 "拉 "冲程中，空气从造口护板中流出，致动细胞在负压作用下折叠。在 "推 "冲程中，正压使所有细胞恢复直立位置。

For this procedure, the global reservoir is connected to a variable source, which alternates between positive and negative pressure. To generate this behavior, we use a custom syringe pump (Figure 9). In the "push" stage, air is forced upward through the valves, into every cell of the top layer. In the "pull" stage, air is drawn out of the system - but only through valves that are in the active state.
在此过程中，全局贮存器与一个可变源相连，可在正压和负压之间交替变化。为了产生这种行为，我们使用了一个定制的注射泵（图 9）。在 "推 "阶段，空气通过阀门被向上推入顶层的每个单元。在 "拉 "阶段，空气被抽出系统--但只能通过处于激活状态的阀门。

Fig. 9. The linear-actuator syringe pump used to pneumatically drive our Stoma-Board surfaces.
图 9.用于气动驱动造口护板表面的线性注射泵。

Note that since every cell is affected by the "push" stroke, the transducer layer is fully inflated between refreshes. For some applications, such as refreshable Braille displays, this is sufficient [48]. However, if more dynamic control is desired, then a secondary valve layer is necessary to block the positive pressure from the "push" stroke. (We describe such a construction in Section 8.4.)
请注意，由于每个单元都受到 "推动 "行程的影响，换能器层在两次刷新之间是完全充气的。对于某些应用，例如可刷新盲文显示器，这就足够了[48]。但是，如果需要更多的动态控制，则需要一个辅助阀层来阻挡来自 "推动 "冲程的正压力。(我们将在第 8.4 节介绍这种结构）。

While we use a syringe pump in our applications, any alternating pneumatic source will suffice. Ultimately, it is the frequency of this source that determines the refresh rate of a Stoma-Board surface. If fast refreshes are necessary, then the flow rate of the pump must large enough to quickly pressurize and depressurize the global cavity.
虽然我们在应用中使用的是注射泵，但任何交替的气动源都可以。最终，决定造口护板表面刷新率的是气源的频率。如果需要快速刷新，那么泵的流速必须足够大，以便对整个腔体快速加压和减压。

5 FABRICATION PROCESS
5 制造工艺

5.1 Cutting: Diaphragm and Spacer
5.1 切割：隔膜和垫片

The Stoma-Board diaphragm is laser-cut from a 25 µm thick Mylar film, metallized on one side (CS Hyde 48-1F-1M). It is important that this film is held flat during the cutting process - if manufactured imprecisely, it may kink or buckle out-of-plane when aligned with the electrode array. We solve this by first laminating the uncut Mylar film onto a sacrificial acrylic sheet (using isopropyl alcohol and a rubber squeegee), which lies flat on the laser bed. After the cut, we peel the finished diaphragm off of the acrylic substrate in a single step, with no weeding or deburring necessary.
造口护板隔膜由 25 微米厚的 Mylar 薄膜激光切割而成，单面镀金属（CS Hyde 48-1F-1M）。在切割过程中，薄膜必须保持平整，这一点非常重要--如果制作不精确，在与电极阵列对齐时，薄膜可能会扭结或弯曲到平面外。为了解决这个问题，我们首先使用异丙醇和橡胶刮板将未切割的 Mylar 薄膜层压在牺牲的丙烯酸板上，使其平铺在激光床上。切割后，我们只需一步就能将完成的隔膜从丙烯酸基板上剥离，无需除杂或去毛刺。

Notice that our diaphragm is cut with a small tab near the bottom edge (Figure 10c). Later, in the layup process, we use silver epoxy (MG Chemicals 8331) to adhere this tab to an exposed copper pad on our circuit board.
请注意，我们的隔膜在靠近底部边缘的地方切割了一个小片（图 10c）。稍后，在铺层过程中，我们将使用环氧银（MG Chemicals 8331）把这个小片粘到电路板上的裸露铜垫上。

The spacer (Figure 4d) that separates the diaphragm from the valve outlet is cut from a sheet of natural gum rubber, $150μ m$ thick (McMaster-Carr 8611K11). The fabrication process is similar to the one described above-the rubber is laid flat on an acrylic sheet prior to the cut, and peeled away afterwards in a single motion. We first experimented with rigid spacers (polyester sheets ranging from 50 to $250μ m$ ), but ultimately found that a more compliant material led to better valve performance, perhaps due to a tighter pneumatic seal.
将隔膜与阀门出口隔开的隔片（图 4d）由天然胶橡胶板切割而成， $150μ m$ 厚（McMaster-Carr 8611K11）。制作过程与上述过程类似--切割前将橡胶平铺在丙烯酸板上，切割后一次性剥离。我们首先使用硬质垫片（聚酯薄膜，厚度从 50 到 $250μ m$ ）进行试验，但最终发现更顺滑的材料能带来更好的阀门性能，这可能是由于气动密封更紧密的缘故。

For some prototypes, we used this same rubber material as a bottom gasket layer, which sits between the valve-sealing electrodes (Figure 4e) and the common cavity or printed piping structure (Figure 4f). These gaskets were cut in the same manner as the spacer.
在一些原型中，我们使用了相同的橡胶材料作为底部垫层，它位于阀门密封电极（图 4e）和公共空腔或印刷管道结构（图 4f）之间。这些垫片的切割方式与隔板相同。

Fig. 10. To fabricate the diaphragm, we first use isopropyl alcohol and a rubber squeegee to laminate a metallized Mylar film onto an acrylic sheet (a). The diaphragm pattern is then laser cut (b), and the finished diaphragm is removed (c).
图 10.为了制作隔膜，我们首先使用异丙醇和橡胶刮板将金属化的 Mylar 薄膜层压到丙烯酸板上（a）。然后用激光切割膜片图案（b），最后取出成品膜片（c）。

5.2 Casting: Upper Gasket and Soft Transducers
5.2 铸造：上垫片和软传感器

For the top layer of our system, we tested a variety of custom-made transducers. Some of these were 3D-printed (Formlabs Elastic Resin 50A), and some of them were cast (Smooth-On Dragon Skin 30 and Mold Star 30). Additionally, some experiments required a rigid manifold, which sat on top of a cast gasket layer.
对于系统的顶层，我们测试了各种定制的传感器。其中有些是 3D 打印的（Formlabs 弹性树脂 50A），有些是铸造的（Smooth-On Dragon Skin 30 和 Mold Star 30）。此外，有些实验还需要使用刚性歧管，它位于铸造垫层之上。

To begin the casting process, we first spray a release agent (Mann Ease Release 200) onto a two-piece 3D-printed mold (Figure 11). This mold is left to sit for ten minutes. In that interval, the uncured silicone is mixed and degassed at-27in $Hg$ , in order to remove any large air pockets. The silicone is then poured into the mold, and left to cure at room temperature for 16 hours.
开始铸造过程时，我们首先在两件式 3D 打印模具上喷洒脱模剂（Mann Ease Release 200）（图 11）。该模具放置十分钟。在此期间，我们会混合未固化的硅胶，并在 27in $Hg$ 处进行脱气，以去除任何大的气穴。然后将硅胶倒入模具，在室温下固化 16 小时。

Fig. 11. A 3D-printed mold used to cast one of our soft transducer layers (the bistable dome array).
图 11.用于铸造我们的一个软传感器层（双稳态圆顶阵列）的 3D 打印模具。

5.3 Printing: Global Reservoir and Upper Manifold
5.3 印刷：全球储液器和上歧管

Our Stoma-Board valves rest on common reservoir, used as a global pneumatic sink (Figure 12). While this could be a single, open cavity (CNC-milled, for example), we chose to 3D-print a connected pipe structure, in order to minimize the reservoir volume and allow for quicker pressure changes.
我们的 Stoma-Board 阀门安装在共同的储气罐上，作为一个整体气动汇（图 12）。虽然这可以是一个单一的开放式空腔（例如 CNC 铣削），但我们选择 3D 打印一个连接的管道结构，以最大限度地减少储气罐的体积，并实现更快的压力变化。

We also printed rigid manifold layers (Figure 19a) for mounting some of our elastic transducers. While these transducers could be fixed to the upper PCB directly, we found that the manifold helped to ease prototyping, as transducers of different geometries could be more easily swapped and tested.
我们还打印了刚性歧管层（图 19a），用于安装一些弹性传感器。虽然这些传感器可以直接固定在上印刷电路板上，但我们发现分流板有助于简化原型制作，因为不同几何形状的传感器可以更容易地交换和测试。

Fig. 12. (a) 3D-printed reservoir that serves as a global pneumatic sink. (b) Cross section.
图 12.(a) 作为全球气动汇的 3D 打印储气罐。 (b) 截面图。

Fig. 13. Our command-line interface auto-generates KiCad-compatible design files, for hexagonal Stoma-Board patterns at multiple scales. (a) A single cell, with valve-opening electrode in green, pads for surface-mount components in red, valve inlets in yellow (small), and transducer mounting holes in yellow (large). (b, c) Patterns of 7 and 127 cells. (d, e) Fabricated circuit board, with electronic components on top (d) and patterned electrodes on bottom (e). Note that while our design software can produce Stoma-Board patterns at various scales, all actuation characteristics are measured from a 19-valve test rig, not the 127-valve board.
图 13.我们的命令行界面可自动生成与 KiCad 兼容的设计文件，用于制作多种比例的六边形造口板图案。(a）单个细胞，绿色为瓣膜打开电极，红色为表面贴装元件垫，黄色为瓣膜入口（小），黄色为传感器安装孔（大）。(b、c）7 个和 127 个电池的图案。(d、e）制作好的电路板，上面是电子元件（d），下面是图案化电极（e）。请注意，虽然我们的设计软件可以制作各种尺寸的造口板图案，但所有致动特性都是通过 19 个阀门的测试台测量的，而不是 127 个阀门的电路板。

6 ACTUATION CHARACTERISTICS
6 执行特性

There are two ways we might wish to actuate a cell of our Stoma-Board. We can either start with the global vacuum active and try to lift the valve diaphragm upwards; or we can first latch the valve diaphragm in the raised state, and apply a vacuum only after the valve is already open.
我们可以通过两种方式启动造口板的一个单元。我们可以先启动全局真空，然后尝试将阀膜片向上抬起；或者我们可以先在抬起状态下锁定阀膜片，然后在阀门已经打开的情况下才施加真空。

We make the distinction because Stoma-Board valves exhibit a degree of hysteresis (Figure 14). Once the diaphragm has been pulled close to the valve-opening electrode, the newly strengthened electrostatic forces tend to hold it in place, even if the voltage drops. (Recall that the electrostatic force between two objects is inversely proportional to the squared distance.)
我们之所以这样区分，是因为造口护板瓣膜表现出一定程度的滞后性（图 14）。一旦膜片被拉近阀门开启电极，即使电压下降，新增强的静电力也会将膜片固定在原位。(回想一下，两个物体之间的静电力与距离的平方成反比）。

Fig. 14. Average flow rate through a single Stoma-Board valve $(ΔP = 30 kPa,n= 3)$ over a range of applied voltages. The behavior differs in lifting (vacuum-first) and latching (voltage-first) modes. (a) Lifting: Below 200V, negative pressure dominates this interaction and keeps the valve diaphragm closed. Beyond this point, air flow grows linearly as electrostatic forces lift the diaphragm away from the valve outlet. (b) Latching: If a valve is latched open before negative pressure is applied, electrostatic forces are stronger due to the reduced diaphragm distance. Above 200V, the valve remains fully open. Below this value, the diaphragm is pulled away from the valve-opening electrode, and behavior is similar to the lifting mode.
图 14.通过单个造口板阀的平均流速 $(ΔP = 30 kPa、n= 3)$ 在施加电压的范围内。其行为在提升（真空优先）和闩锁（电压优先）模式下有所不同。(a) 提升：电压低于 200V 时，负压在这种相互作用中占主导地位，并使阀膜片保持关闭状态。超过这一点后，随着静电力将膜片从阀门出口抬起，气流呈线性增长。(b) 锁定：如果阀门在施加负压之前就已锁定打开，由于膜片距离缩短，静电力会更强。当电压高于 200V 时，阀门保持全开状态。低于此值时，膜片会被拉离阀门开启电极，其行为类似于提升模式。

While the lifting mode is arguably more dynamic, the latching mode allows us drive the board at lower voltages, and circumvents some of the dielectric charging issues that we discuss in Section 7. This is also the mode used in our push-pull control scheme (Figure 8). However, for completeness, we report the actuation characteristics for both lifting and latching modes.
虽然提升模式可以说更有活力，但锁存模式允许我们在较低的电压下驱动电路板，并避免了我们在第 7 节中讨论的一些介质充电问题。这也是我们的推挽式控制方案中使用的模式（图 8）。不过，为了完整起见，我们还是要报告升降模式和闭锁模式的致动特性。

To facilitate our measurements, we attached a rigid manifold to the top of a 19-cell Stoma-Board (in place of the transducer layer). With Luer lock fittings for each cell, we were able to quickly add and remove mass flow sensors for evaluating actuator performance (Figure 15).
为了方便测量，我们在 19 个单元的造口板顶部安装了一个刚性歧管（代替传感器层）。通过每个单元的鲁尔锁接头，我们可以快速添加和移除质量流量传感器，以评估致动器的性能（图 15）。

6.1 Opening Voltage
6.1 开启电压

The opening voltage is associated with the lifting mode - it is the point at which electrostatic forces upward surpass pneumatic forces downward, and air begins to pass through the cell.
开启电压与提升模式有关，即静电力向上超过气动力向下时，空气开始通过电池。

To measure the opening voltage for a given valve, we first applied a global negative pressure, which pulled the valve diaphragm closed. We then increased the voltage between the diaphragm and valve-opening electrode, in increments of $10 V$ , until the diaphragm was attracted upwards and significant air flow through the valve was observed $(25 mL/min)$ .
为了测量给定阀门的开启电压，我们首先施加全局负压，使阀门隔膜关闭。然后，我们增加膜片和阀门打开电极之间的电压，增量为 $10 V$ 、 $(25 mL/min)$ 直到隔膜被向上吸引，观察到大量气流通过阀门。

Figure 16a charts the Stoma-Board opening voltage as a function of pressure (the differential between valve inlets and the global reservoir). At higher pressures(80kPa), this approaches $300 V$ , which we chose as the limit of our system. Beyond this point, we noticed an increase in parasitic effects.
图 16a 显示了造口护板开启电压与压力（阀门入口和整个储气罐之间的差值）的函数关系。在较高压力（80kPa）下，该值接近于 $300 V$ ，我们选择该值作为系统的极限值。超过这一点，我们注意到寄生效应会增加。

Fig. 15. Test rig for measuring the flow characteristics of a 19-cell Stoma-Board. A 3D-printed manifold with Luer-lock fittings allows for individual connections to flow sensors. A vacuum pump acts as a global negative pressure source, which can be manually adjusted with a breaker valve. Valve inlets are left at atmospheric pressure.
图 15.用于测量 19 芯造口袋流量特性的测试装置。带有鲁尔锁接头的 3D 打印歧管可实现与流量传感器的单独连接。真空泵充当整体负压源，可通过断流阀进行手动调节。阀门入口处于大气压状态。

Fig. 16. Average opening voltage (lifting mode) and holding voltage (latching mode) across a range of pressure differentials. Valves were sampled uniformly from the 19-cell test rig in Figure 15. Error bars represent 25th and 75th percentiles (n=7).
图 16.不同压差下的平均开启电压（提升模式）和保持电压（闭锁模式）。从图 15 中的 19 单元测试台上均匀抽取阀门样本。误差条代表第 25 和 75 百分位数（n=7）。

Though the valves in our application examples all occupy discrete "on" and "off" states, we can achieve variable flow rates (between "fully on" and "fully off") by driving the system at higher or lower voltages respectively. Figure 17 shows this relationship for six valves at several operating pressures (sampled randomly from our test rig). Below 150 to 200 volts, the applied vacuum dominates this interaction. As the voltage increases beyond this point, air flow through the valve increases as electrostatic forces lift the diaphragm away from the valve outlet. We did not observe any pneumatic crosstalk during these tests - flow rates through neighboring valves stood unchanged.
虽然我们应用实例中的阀门都处于离散的 "开 "和 "关 "状态，但我们可以通过分别以较高或较低的电压驱动系统来实现可变流量（介于 "全开 "和 "全关 "之间）。图 17 显示了六个阀门在几种工作压力下的这种关系（从我们的测试台随机取样）。电压低于 150 到 200 伏特时，真空将主导这种相互作用。当电压升高到此点以上时，由于静电力将膜片从阀门出口抬起，通过阀门的气流增加。在这些测试中，我们没有观察到任何气动串扰 - 通过相邻阀门的流量保持不变。

Stoma-Board cells remain robust throughout repeated actuations. In Figure 18, we plot the average opening times for an additional six valves, over the course of one hundred trials. Operating at 300 volts, and subject to 80 $kPa$ , the average valve opens in less than 40 milliseconds. Notice that there is no degradation over repeated trials - the average opening time for the final 25 actuations(36ms)is comparable to the average opening time for the first 25 actuations (38 ms). We discuss reliability further in Section 8.
Stoma-Board单元在反复启动过程中始终保持稳健。在图 18 中，我们绘制了另外六个阀门在一百次试验过程中的平均打开时间。在 300 伏特电压下工作，并受到 80 $kPa$ ，阀门的平均打开时间不到 40 毫秒。请注意，反复试验的结果并没有降低--最后 25 次启动的平均打开时间（36 毫秒）与前 25 次启动的平均打开时间（38 毫秒）相当。我们将在第 8 节中进一步讨论可靠性问题。

Fig. 17. Flow rates for six randomly sampled Stoma-Board valves, as a function of opening voltage. Note that for one valve (middle, bottom) there was a flow rate spike at $30 kPa$ and $240 V$ . This anomaly did not reoccur during a second test of the same valve, but we include it here for transparency.
图 17.随机取样的六个造口护板阀门的流量与开启电压的关系。请注意，一个阀门（中、底部）在 $30 kPa$ 和 $240 V$ 。在对同一阀门进行的第二次测试中，这一异常情况没有再次出现，但为了透明起见，我们在此将其包括在内。

Fig. 18. Average opening times for six randomly sampled Stoma-Board valves, over 100 trials. (Opening times are averaged on a per-valve basis, and then these values are averaged to produce the green data points.) Note that opening times remain consistent throughout the experiment. Operating conditions: $80 kPa, 300 V$ . Error bars represent $25 th$ and $75 th$ percentiles.
图 18。随机抽样的六个造口护板瓣膜在 100 次试验中的平均打开时间。(每个瓣膜的打开时间取平均值，然后将这些值取平均值，得出绿色数据点）。请注意，开放时间在整个实验过程中保持一致。运行条件： $80 kPa, 300 V$ 。误差条代表 $25 th$ 和 $75 th$ 百分位数。

6.2 Holding Voltage
6.2 保持电压

Since our applications use an alternating pressure source, we are able to take advantage of the latching mode, and activate valves before a negative pressure is applied. In this context, the quantity of interest is the holding voltage - the minimum voltage required to keep the valve from closing (once the pressure in the global reservoir drops). This value is smaller than the opening voltage, due to the reduced distance between the diaphragm and the valve-opening electrode in the initial state.
由于我们的应用使用的是交变压力源，因此可以利用闭锁模式，在负压施加之前激活阀门。在这种情况下，我们所关注的量是保持电压，即保持阀门不关闭所需的最小电压（一旦全局储液器中的压力下降）。由于初始状态下膜片与阀门开启电极之间的距离缩短，因此该值小于开启电压。

To measure the holding voltage (Figure 16b), we first applied 300 volts to the valve of interest. We then applied a negative pressure, and recorded the steady-state flow rate. Finally, we progressively lowered the valve voltage (in increments of 10 volts), until the flow rate dropped below ten percent of the steady-state value. This drop-off does not happen gradually - as show in Figure 14, there is a "cliff" at which point the valve transitions from fully-open to nearly-closed.
为了测量保持电压（图 16b），我们首先在相关阀门上施加 300 伏电压。然后施加负压，记录稳态流速。最后，我们逐步降低阀门电压（增量为 10 伏），直到流速降至稳态值的百分之十以下。这种下降并不是逐渐发生的--如图 14 所示，在阀门从全开过渡到接近关闭的过程中会出现一个 "悬崖"。

7 PROGRAMMABLE STOMA-BOARD SURFACES
7 个可编程气孔板表面

From a stock piece of wood or plastic, a craftsperson can construct a multitude of objects, each with mechanical properties that are (in part) a function of the original workpiece. Porous sheets of fiberboard, for instance, can be shaped into a vacuum table; and compliant strips of bamboo can be woven into a flexible basket. Similarly, we envision a process in which a fabricator may start with a sheet of "raw" Stoma-Board, and through the addition of custom transducers, arrive at a variety of programmable surfaces and mechanisms. Importantly, the scalable production of this base material (i.e. patterned valves) is only made possible by the layer-driven manufacturing techniques that we employ.
手工艺人可以用一块木头或塑料制造出多种物品，每种物品的机械性能（部分）都是原始工件的函数。例如，多孔的纤维板可以制成真空桌；顺从的竹条可以编织成柔韧的篮子。同样，在我们的设想中，制造者可以从一张 "未加工 "的造口板开始，通过添加定制的传感器，制造出各种可编程的表面和机构。重要的是，只有我们采用的层驱动制造技术才能实现这种基础材料（即图案化阀门）的规模化生产。

In this section, we showcase four surfaces (using three types of transducers) that are built upon our "raw" Stoma-Board surface.
在本节中，我们将展示基于造口护板 "原始 "表面的四种表面（使用三种类型的传感器）。

7.1 Tactile Patterns from a Bistable Membrane
7.1 来自双稳态薄膜的触觉图案

7.1.1 Standard Pitch. Bistable mechanisms do not require an external energy source in order to maintain their state, which makes them an attractive transducer option in low-power applications [46]. For our first demo, we cast an elastic silicone membrane (Smooth-On Dragon Skin 30), composed of bistable, hemispherical cells (Figure 19). While it’s possible to attach to this membrane to the raw Stoma-Board directly, we opted to use a 3D-printed manifold as an intermediate layer for ease of mounting.
7.1.1 标准间距双稳态机构不需要外部能源来维持其状态，因此在低功耗应用中是一种极具吸引力的传感器选择[46]。在首次演示中，我们制作了一个由双稳态半球形单元组成的弹性硅胶膜（Smooth-On Dragon Skin 30）（图 19）。虽然可以将这层膜直接连接到未加工的造口导板上，但为了便于安装，我们选择使用 3D 打印歧管作为中间层。

Initially, all cells are in the raised state. To render a tactile pattern, we latch open the relevant valves, and apply a global negative pressure - this causes the selected cells to buckle into the collapsed state. To return the cells to the raised state, we apply a global positive pressure.
最初，所有细胞都处于凸起状态。为了呈现触感图案，我们打开相关阀门，并施加全局负压--这将使选定的单元格折叠成塌陷状态。要使细胞恢复到凸起状态，我们需要施加全局正压。

Fig. 19. We mount a cast array of bistable domes (b) on a 3D-printed manifold (a). By activating specific valves, we can render tactile patterns (c, d). Domes are $14 mm$ in diameter.
图 19。我们将双稳态穹顶铸造阵列（b）安装在 3D 打印的歧管（a）上。通过激活特定的阀门，我们可以呈现出触感图案（c、d）。穹顶直径为 $14 mm$ 。

7.1.2 Compact Pitch. By altering the channel structure of the upper manifold, we can modify the apparent density of the Stoma-Board surface. In our second demo (Figure 20), a set of converging pipes decreases the cell pitch to $2.5 mm$ (Braille spacing), such that six transducers can fit within the area of a human fingertip. At this scale, the raised domes are more readily perceived as a texture, as opposed to a group of distinguishable objects [26]. While the perimeter of the Stoma-Board is still determined by the electrode and membrane layers, this flexibility in piping can hasten the prototyping of fine-grained (and variable-pitch) tactile interactions.
7.1.2 紧凑型间距。通过改变上分流板的通道结构，我们可以改变造口板表面的表观密度。在我们的第二个演示（图 20）中，一组会聚管道将单元间距减小到 $2.5 mm$ （盲文间距），这样就可以在人类指尖的范围内安装六个传感器。在这种比例下，凸起的圆顶更容易被感知为一种纹理，而不是一组可区分的物体 [26] 。虽然造口护板的周长仍然由电极和膜层决定，但管道的这种灵活性可以加快细粒度（和可变间距）触觉交互的原型设计。

Fig. 20. A set of converging pipes, as seen in the manifold cross-section (a), shrink the transducer pitch to $2.5 mm$ (b). The Braille transducer (c, d) is cast silicone (Smooth-On Mold Star 30), and individual dots can be lowered when the corresponding Stoma-Board valves are opened.
图 20。如歧管横截面所示（a），一组会聚管道将传感器间距缩小到 $2.5 mm$ (b)。盲文传感器（c、d）是硅胶浇铸的（Smooth-On Mold Star 30），当相应的造口护板阀门打开时，各个点就会下降。

7.2 Bellows-Style Robotic Actuators
7.2 波纹管式机器人推杆

Among soft roboticists, the bellows-style actuator (Figure 3e, 3f) is well-established as a means of converting pneumatic energy into linear motion [10]. When pressurized, it expands along a single axis. When de-pressurized, it contracts. If two or more are connected in parallel, an applied pressure differential will result in a bending motion, which forms the basis for many soft robotic joints [17].
在软体机器人专家中，波纹管式致动器（图 3e、3f）作为一种将气动能量转化为线性运动的方法已得到广泛认可[10]。加压时，它沿单轴膨胀。减压时，它收缩。如果两个或两个以上并联，施加的压力差将导致弯曲运动，这构成了许多软机器人关节的基础 [17]。

Pneumatic routing is often a challenge when integrating these types of soft actuators. Since every bellows structure needs to be pressurized independently, many research prototypes rely on bundles of tubes, which tether the individual actuators to an external bank of valves.
在集成这些类型的软执行器时，气动路由通常是一项挑战。由于每个波纹管结构都需要独立加压，因此许多研究原型都依赖于管束，将各个执行器与外部阀门组连接起来。

With Stoma-Board as a base material, these valves can instead be embedded in the robot structure directly. In our third demo (Figure 21), three bellows-style transducers (SLA 3D-printed with Formlabs Elastic Resin 50A) are fixed to a raw Stoma-Board and used to drive a 2-DOF joint. By selectively opening valves and contracting individual transducers, we can determine the roll and pitch of an attached platform. These embedded valves may enable modular stacking, in a manner similar to the continuum robots by Robertson and Paik [45].
有了造口板作为基础材料，这些阀门就可以直接嵌入机器人结构中。在第三个演示中（图 21），三个波纹管式传感器（使用 Formlabs 弹性树脂 50A 进行 SLA 3D 打印）被固定在原始造口板上，用于驱动一个 2-DOF 关节。通过选择性地打开阀门和收缩单个传感器，我们可以确定连接平台的滚动和俯仰。这些嵌入式阀门可实现模块化堆叠，其方式与 Robertson 和 Paik 的连续机器人类似[45]。

Fig. 21. 3D-printed bellows-style actuators control the orientation of an attached platform.
图 21.三维打印的波纹管式致动器可控制连接平台的方向。

7.3 Spoke-Propelled Rimless Wheel
7.3 辐条推进式无缘轮

The "rimless wheel" is a rudimentary legged robot, suitable for traversing rough and uneven terrain [19]. In a typical implementation, the spokes of the wheel are passive elements, and a hub-mounted motor is used to drive the structure forward or backward [51]. To enable additional modes of locomotion, variants of this design have incorporated spokes that are independently actuated, which propel the robot by extending and contracting on command $[15, 24]$ . This modification eliminates the heavy, motorized hub, but requires a separate mechanism for each leg of the robot. Building such an assembly can be cumbersome.
"无轮辋车轮 "是一种初级的腿式机器人，适用于穿越崎岖不平的地形 [19]。在典型的实施方案中，轮辐是被动元件，轮毂安装的电机用于驱动结构前进或后退 [51]。为了实现更多的运动模式，这种设计的变体采用了独立驱动的辐条、 $[15, 24]$ 。这种改装省去了笨重的电动轮毂，但需要为机器人的每条腿配备单独的机械装置。制造这样的组件可能非常麻烦。

With a raw base of patterned valves, constructing this prototype becomes as simple as adding a custom transducer layer. In our fourth demo, we showcase a spoke-propelled rimless wheel (Figure 22), which can "walk" forward via a sequential extension of pneumatically-actuated legs. Note that in this example, the transducer layer and common cavity are swapped - we use a global pressure source instead of a pressure sink.
有了图案阀门这个原始基础，构建这个原型就变得非常简单，只需添加一个定制的传感器层即可。在第四个演示中，我们展示了一个由辐条推动的无缘轮（图 22），它可以通过气动腿的顺序延伸向前 "行走"。请注意，在这个示例中，传感器层和公共空腔是对调的，我们使用的是全局压力源而不是压力汇。

Fig. 22. An actuated rimless wheel, with spokes (syringes) that can extend independently. The syringe manifold is attached to a hexagonal Stoma-Board, which is connected to a single pressure source. In the stable position (a), two spokes maintain contact with the ground. When the left spoke is extended (by opening the appropriate Stoma-Board valve) the wheel tilts to the right (b). The wheel falls to a new stable position (c), and the extended spoke is retracted (d).
图 22.驱动无缘轮，辐条（注射器）可独立伸展。注射器歧管连接到六边形造口板上，造口板与单个压力源相连。在稳定位置（a），两个辐条与地面保持接触。当左侧辐条伸出时（打开相应的造口板阀门），车轮向右倾斜（b）。车轮下降到新的稳定位置 (c)，伸出的辐条缩回 (d)。

8 DISCUSSION, LIMITATIONS, AND FUTURE WORK
8 讨论、局限性和未来工作

8.1 Long-Term Use
8.1 长期使用

From a distance, electrostatic actuation appears deceptively simple - a straightforward mapping of an applied voltage to a resultant force. In reality, there are parasitic effects which can reduce the long-term reliability of such systems. The most significant of these, well-recognized by the MEMS community, is dielectric charging [23]. This is a molecular-scale phenomenon, which results from a displacement of polarized components within the material. If unaccounted for, this can lead to "sticky" switches (or in this context, valves).
从远处看，静电驱动似乎非常简单--将外加电压直接映射到结果力。实际上，寄生效应会降低此类系统的长期可靠性。其中最重要的，也是 MEMS 界公认的，就是介电充电 [23]。这是一种分子尺度的现象，源于材料内部极化成分的位移。如果不加以考虑，就会导致 "粘滞 "开关（在这里指阀门）。

In our Stoma-Board actuators, the dielectric layer is a thin coating of solder mask, which separates the conductive diaphragm from the valve-opening electrode. If a permanent charge develops in this dielectric layer, the diaphragm will always cling to the solder mask, and the valve will be unable to close. This parasitic charging often occurs after an extended period of exposure to a constant, applied voltage [14].
在我们的造口护板执行器中，介电层是一层薄薄的阻焊层，它将导电膜片与阀门开启电极隔开。如果电介质层中产生永久电荷，膜片就会始终粘附在阻焊层上，阀门将无法关闭。这种寄生充电通常发生在长时间暴露于恒定的外加电压之后 [14]。

We were able to mitigate this effect by driving our actuators with a bipolar square wave (as opposed to a DC source), and reducing the peak voltage (no higher than $300 V$ ). While this balancing of polarity over time was sufficient for our applications, it is possible that such adjustments may only reduce or delay this effect. Further reliability testing is needed in order to assess valve performance beyond the 100 trials described in Section 6.1.
我们使用双极方波（而非直流电源）驱动致动器，并降低峰值电压（不高于 $300 V$ ），从而减轻了这种效应。虽然这种随时间变化的极性平衡足以满足我们的应用需求，但这种调整有可能只会减少或延迟这种效应。为了评估第 6.1 节所述 100 次试验之外的阀门性能，还需要进一步的可靠性测试。

8.2 Towards Larger Surfaces
8.2 走向更大的表面

A second concern relates to pneumatic actuation, and arises when working with large transducer membranes. Since these membranes are cast from 3D-printed molds, the printer’s working area determines the maximum size of a cast membrane. Larger membranes can be assembled from these smaller sections, but discontinuities at the section boundaries can lead to air leakage, and unpredictable actuation behavior. Future revisions may benefit from a less-dense actuator packing (allowing for a thicker, more robust section boundary) or flexures between cells to mitigate PCB bowing (which can become significant at larger scales, such as our 127 valve array).
第二个问题与气动驱动有关，在使用大型传感器膜时会出现。由于这些膜是从 3D 打印模具中浇铸出来的，因此打印机的工作区域决定了浇铸膜的最大尺寸。较大的膜可以由这些较小的部分组装而成，但部分边界的不连续性会导致漏气和不可预测的致动行为。未来的改进可能会受益于密度较低的致动器填料（允许更厚、更坚固的截面边界）或单元之间的挠性结构，以减轻印刷电路板的弯曲（这在较大尺寸的情况下会变得很明显，例如我们的 127 阀阵列）。

In addition, the global cavity, instead of being 3D-printed, could itself be fabricated via a layer-driven approach. (Indeed, commercial manifolds $^{}$ exist that utilize this technique.) Stacking and bonding milled sheets may scale more easily than a purely additive procedure.
此外，全局腔体可以通过层驱动方法制造，而不是三维打印。(事实上，商业流形 $^{}$ 就是采用这种技术）。堆叠和粘合铣削薄片可能比纯粹的加法过程更容易扩展。

8.3 Towards Denser Surfaces
8.3 走向高密度表面

The electronic components that we use - in particular, the opto-isolated solid state relays - determine the minimum pitch of the raw Stoma-Board surface(18mm). It is worth noting that these particular components are overpowered for our application, capable of switching currents that are orders of magnitude larger than necessary. With more refined electrical engineering, it is conceivable that this pitch could be reduced. However, as the size of the electrostatic actuators decrease, so too does the force. The tradeoffs in this area should be evaluated.
我们使用的电子元件，特别是光隔离固态继电器，决定了 Stoma-Board 原始表面的最小间距（18 毫米）。值得注意的是，对于我们的应用而言，这些特定元件的功率过大，开关电流比所需电流大几个数量级。可以想象，如果电气工程更加精细，这个间距还可以缩小。不过，随着静电致动器尺寸的减小，力也会减小。应该对这方面的权衡进行评估。

8.4 Bidirectional Valves
8.4 双向阀

As noted in Section 4.4, valves in our system are designed to withstand pressure in only one direction. For many applications, such as those demonstrated in Section 7, this is sufficient. However, if bidirectional switching is necessary, a variation of this construction can be used. By adding an additional membrane (Figure 23), effectively placing two flap valves "back-to-back", we can block (and switch) pressure in both directions. Though we have built some early prototypes with this construction, these new valves have yet to be fully characterized - this is an area of future work.
如第 4.4 节所述，我们系统中的阀门只能承受一个方向的压力。对于许多应用（如第 7 节中演示的应用）而言，这已经足够。但是，如果需要双向切换，则可以使用这种结构的变体。通过增加一个膜片（图 23），有效地将两个翻板阀 "背靠背 "放置，我们就可以阻挡（和切换）两个方向的压力。虽然我们已经利用这种结构制造出了一些早期原型，但这些新阀门的特性还有待于充分验证，这是我们未来工作的一个领域。

Fig. 23. Concept for a bidirectional Stoma-Board valve, consisting of an upper and lower membrane (two switchable flap valves, back to back). Such a construction resists both positive and negative pressures.
图 23.双向造口板阀门的概念，由上下膜（两个背靠背的可切换瓣阀）组成。这种结构可抵御正压和负压。

8.5 Stoma-Board as a Raw Material
8.5 作为原材料的造口护板

Ultimately, we envision programmable surfaces that can function as "raw materials" (i.e. available for broad use by designers, not necessarily engineered for one particular application). An LED strip, for example, can be purchased, cut, and applied to an object - in the hands of a user, it is closer to a roll of decorative tape than a flexible circuit board. Such a future may be possible for tactile programmable materials as well, but not within the constraints of a module-driven design.
最终，我们设想的可编程表面可以发挥 "原材料 "的作用（即供设计师广泛使用，而不一定是为某一特定应用而设计）。例如，LED 灯条可以购买、切割并应用到物体上--在用户手中，它更像是一卷装饰带，而不是一块柔性电路板。触感可编程材料也有可能实现这样的未来，但不会受模块驱动设计的限制。

We see the four characteristics of these layer-driven programmable surfaces (outlined in Section 1) as branching points for subsequent research. For instance, while cell communication within Stoma-Board is neighbor-to-neighbor, the original messages are still generated upstream - a truly information-responsive material could perform this act internally. Future implementations might benefit from a transition towards fully distributed computation. Onboard pressure sources, such as electrostatic or piezoelectric micropumps, can also bring this closer to becoming a fully untethered programmable material.
我们认为，这些层驱动可编程表面的四个特点（第 1 节概述）是后续研究的分支点。例如，虽然 "造口板 "内的细胞通信是邻居之间的通信，但原始信息仍在上游生成--真正的信息响应材料可以在内部执行这一操作。未来的实施可能会受益于向完全分布式计算的过渡。板载压力源（如静电或压电微泵）也能使其更接近成为一种完全不受约束的可编程材料。

9 CONCLUSION
9 结论

We observe that a layer-driven fabrication process, characterized by patterning and stacking, can give rise to programmable surfaces that may scale more readily than their module-driven counterparts. Instead of building and assembling actuators individually, actuators in our framework are formed all at once, during the layup process. The resulting cells are composite mesostructures, cross-sections of which are distributed across the functional layers of our material.
我们发现，以图案化和堆叠为特征的层驱动制造工艺可以产生可编程表面，这种表面比模块驱动的表面更容易扩展。在我们的框架中，致动器不是单独制造和组装的，而是在层叠过程中一次性形成的。由此产生的单元是复合介质结构，其横截面分布在我们材料的各功能层中。

We introduce Stoma-Board as a programmable surface that exemplifies this model. In this particular implementation, the actuator cells are electrostatic valves, which communicate digitally with their neighbors, and regulate the flow of air between a pneumatic transducer layer and a global reservoir. The valves themselves are a novel structure that can resist human-scale pressures of $80 kPa$ (an order of magnitude larger than earlier variants). As the cells are ultimately responsive to information sources upstream, we are able to use Stoma-Board as a "raw material" to construct several dynamic, pneumatically-powered devices.
我们介绍的 Stoma-Board 就是这种模式的可编程表面。在这个特定的实施方案中，执行器单元是静电阀门，它们与相邻单元进行数字通信，并调节气动传感器层和全局储气罐之间的气流。阀门本身是一种新颖的结构，可以抵抗人体规模的压力 $80 kPa$ （比早期的变体大一个数量级）。由于细胞最终会对上游的信息源做出反应，因此我们可以将造口护板作为一种 "原材料"，用于构建多种动态气动装置。

Moving forward, research in discretely-actuated programmable surfaces may benefit from this layer-driven lens, adopting composite fabrication techniques and distributed computation paradigms from materials science and robotics.
展望未来，离散驱动可编程表面的研究可能会受益于这种层驱动透镜，采用材料科学和机器人学中的复合制造技术和分布式计算范例。

ACKNOWLEDGMENTS
致谢

The authors thank Alexandra Ion, whose comments and feedback improved this work.
作者感谢亚历山德拉-扬（Alexandra Ion），她的评论和反馈意见改进了本作品。

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