DE102022204443A1 - Mechanical systems with adjusted linearity - Google Patents

Abstract

A mechanical system includes a bending transducer structure configured to provide a bend in response to an applied electrical signal and/or to provide an electrical signal in response to an applied external force causing the bend, wherein a structural rigidity of the bending transducer structure for a first nonlinear mechanical stiffness contribution of the bending. The mechanical system includes an conforming structure that is mechanically coupled to the bending transducer structure through mechanical coupling to provide conforming deformation along with the bending. Structural stiffness of the conforming structure provides a second nonlinear mechanical stiffness contribution to the bending based on mechanical coupling during deformation.

Description

The present invention relates to mechanical systems that include a bending transducer and include an adjustment structure that provides a contribution to the bending of the bending transducer, for example to adjust the bending behavior of the bending transducer. The present invention further relates to modulating the response of flexural transducer systems based on elementary cell design.

A well-known concept for counteracting nonlinearity in a response of a transducer system using nonlinear mechanical stiffening is known in the art and publications (1-5). However, most of these solutions are highly design specific with limited application scope and performance levels. For example, the bending transducer systems that rely on nonlinear stiffening through contact formation and contact evolution, e.g. B. Zipper actuators (zipping actuators) based on electrostatic actuation, usually subject to movement hysteresis due to contact formation and breakage [4, 6-9], instabilities due to electrostatic attraction (or pull-in) [4, 6-8] , static friction problems, abrupt response change [6, 8, 10], necessary design based on complicated residual stress engineering [7], requirements for dedicated external structures [1, 2, 3, 5, 11], etc.

In most of the zipper configurations, directional deflection or movement of a specific structural area is used instead of bending curvature of the entire cell/component geometry. Simultaneous modulation/linearization of different system responses (bending curvature, bending moment, available force, capacitance change, motion resolution, frequency response, etc.) with an actuation signal in such configurations is difficult (most often only one or more than two responses are modulated in a particular design). In addition, electrostatic zipper actuators exhibit tightening instability, which makes controlling them challenging [12].

There is therefore a need for reliable and stable mechanical systems.

An object of the present invention is to provide reliable and stable mechanical systems. This task is solved by the subject matter of the present invention.

One insight of the present invention is that the behavior of a flexural transducer structure can be customized, i.e. H. in relation to an increase or decrease in linearity by a mechanical coupling of the bending transducer structure to an adapting structure which ensures a deformation together with the bending of the bending transducer structure, the deformation of the adapting structure resulting in forces acting on the bending transducer structure and thereby the bending behavior to adapt. By using such an adaptation structure, the behavior of the bending structure can be tailored to a desired property.

According to one embodiment, a mechanical system includes a bending transducer structure configured to provide a bend in response to an applied electrical signal and/or to provide an electrical signal in response to an applied external force causing the bend, wherein a structural rigidity of the bending transducer structure ensures a first nonlinear mechanical stiffness contribution from the bend. The mechanical system includes an conforming structure that is mechanically coupled to the bending transducer structure through a mechanical coupling to provide conforming deformation along with the bending. Structural stiffness of the conforming structure provides a second nonlinear mechanical stiffness contribution to the bending based on mechanical coupling during deformation. The combination of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution enables precise design and a reliable and stable structure.

According to an embodiment of the present invention, a mechanical system includes a bending transducer structure configured to non-linearly deform based on bending in response to an applied electrical signal and/or for non-linearly providing an electrical signal in response to an applied external force that the Bending caused. The mechanical system includes an accommodation structure mechanically coupled to the flexure transducer structure, the bending and deformation of the accommodation structure being causally correlated, the deformation accommodation structure providing a nonlinear force to the flexural transducer structure that reduces the magnitude of nonlinearity in the overall response . Based on the mechanical implementation, linearization can be obtained, but this is not necessary. Based on spring configurations, a desired increase in nonlinearity in parts of the response regime can be obtained. Nevertheless, this can be compared to systems without a spring also lead to a reduction in nonlinearity in the overall response.

Further embodiments relate to a method for producing and/or controlling a mechanical system.

Advantageous embodiments of the present invention are defined in the dependent claims.

• 1a zeigt eine schematische Seitenansicht eines Biegewandlersystems, das eine Anpassungsstruktur außerhalb eines aktiven Bereichs eines Biegewandlers aufweist, die konfiguriert ist zum Kontaktieren des aktiven Bereichs des Biegewandlers, gemäß einem Ausführungsbeispiel;
• 1b zeigt eine schematische Seitenansicht eines Biegewandlersystems, das eine Anpassungsstruktur außerhalb eines aktiven Bereichs eines Biegewandlers aufweist, die konfiguriert ist zum Nichtkontaktieren des aktiven Bereichs des Biegewandlers, gemäß einem Ausführungsbeispiel.
• 1c zeigt eine schematische Seitenansicht eines Biegewandlersystems, das eine Anpassungsstruktur in einem Volumen eines aktiven Bereichs eines Biegewandlers aufweist, die konfiguriert ist zum Kontaktieren des aktiven Bereichs des Biegewandlers, gemäß einem Ausführungsbeispiel;
• 1d zeigt eine schematische Seitenansicht eines Biegewandlersystems, das eine Anpassungsstruktur in einem Volumen eines aktiven Bereichs eines Biegewandlers aufweist, die konfiguriert ist zum Nichtkontaktieren des aktiven Bereichs des Biegewandlers, gemäß einem Ausführungsbeispiel;
• 2a zeigt eine schematische Draufsicht auf ein mechanisches System gemäß einem Ausführungsbeispiel, das zwei Biegeelemente als Teil der Biegewandlerstruktur aufweist, gemäß einem Ausführungsbeispiel;
• 2b-e zeigen unterschiedliche Konfigurationen von mechanischen Systemen gemäß Ausführungsbeispielen, eine Mehrzahl von Zellen gemäß 2a in unterschiedlichen Konfigurationen gemäß Ausführungsbeispielen;
• 2f-g zeigen unterschiedliche Modifizierungen des mechanischen Systems aus 2a gemäß Ausführungsbeispielen;
• 3a-d zeigen schematische Ansichten mechanischer Systeme gemäß Ausführungsbeispielen, die zumindest einen Teil der Anpassungsstruktur als eine Schicht auf einem Biegeelement der Biegewandlerstruktur aufweisen;
• 3f-g zeigen schematische Ansichten mechanischer Systeme gemäß Ausführungsbeispielen, die eine Anpassungsstruktur aufweisen, die zumindest einen Teil einer Nut/Feder-Struktur aufweist;
• 4a-b zeigen schematische Ansichten mechanischer Systeme gemäß Ausführungsbeispielen, die eine unterschiedliche Steifheit unterschiedlicher Biegeelementabschnitte der Biegewandlerstruktur aufweisen;
• 5a-b zeigen schematische Ansichten mechanischer Systeme gemäß Ausführungsbeispielen, die gekantete Biegeelemente der Biegestruktur aufweisen;
• 6a zeigt eine schematische Ansicht einer Doppelkuppel-Konfiguration eines mechanischen Systems gemäß einem Ausführungsbeispiel;
• 6b-e zeigen schematische Diagramme von Biegeverhalten des mechanischen Systems aus 6a;
• 7a-d zeigen schematische Ansichten von Biegewandlersystemen gemäß Ausführungsbeispielen, bei denen die Anpassungsstruktur außerhalb eines Volumens des aktiven Bereichs des Biegewandlers angeordnet ist;
• 8a-b zeigen schematische Ansichten mechanischer Systeme gemäß Ausführungsbeispielen, die eine Anpassungsstruktur aufweisen, die eine nichtlineare Feder aufweist;
• 8c zeigt ein schematisches Diagramm eines Biegeverhaltens des mechanischen Systems aus 8b;
• 8d zeigt eine schematische Ansicht eines mechanischen Systems gemäß einem Ausführungsbeispiel, das eine Anpassungsstruktur aufweist, die eine mehrschichtige nichtlineare Feder aufweist;
• 8e-g zeigen schematische Ansichten mechanischer Systeme gemäß Ausführungsbeispielen, bei denen die Anpassungsstruktur auf zwei äußeren Seiten der Biegewandlerstruktur angeordnet ist;
• 9a-c zeigen schematische Ansichten mechanischer Systeme gemäß Ausführungsbeispielen, die zumindest zwei Biegewandlerstrukturen aufweisen; und
• 10a-c zeigen schematische Ansichten mechanischer Systeme gemäß Ausführungsbeispielen, die unterschiedliche Betätigungsprinzipien implementieren.

Embodiments of the present invention are described in detail below with reference to the accompanying drawings, in which:

• 1a shows a schematic side view of a bending transducer system having a matching structure outside an active region of a bending transducer configured to contact the active region of the bending transducer, according to an embodiment;
• 1b 1 shows a schematic side view of a flexural transducer system that includes a matching structure outside an active region of a flexural transducer configured to non-contact the active region of the flexural transducer, according to an embodiment.
• 1c 1 shows a schematic side view of a flexural transducer system that includes a matching structure in a volume of an active region of a flexural transducer configured to contact the active region of the flexural transducer, according to an embodiment;
• 1d 1 shows a schematic side view of a flexural transducer system that includes an accommodation structure in a volume of an active region of a flexural transducer configured to non-contact the active region of the flexural transducer, according to an embodiment;
• 2a shows a schematic top view of a mechanical system according to an exemplary embodiment, which has two bending elements as part of the bending transducer structure, according to an exemplary embodiment;
• 2b-e show different configurations of mechanical systems according to exemplary embodiments, according to a plurality of cells 2a in different configurations according to exemplary embodiments;
• 2f-g show different modifications of the mechanical system 2a according to exemplary embodiments;
• 3a-d show schematic views of mechanical systems according to exemplary embodiments that have at least a part of the adaptation structure as a layer on a bending element of the bending transducer structure;
• 3f-g show schematic views of mechanical systems according to exemplary embodiments that have an adaptation structure that has at least part of a tongue and groove structure;
• 4a-b show schematic views of mechanical systems according to exemplary embodiments that have different stiffness of different bending element sections of the bending transducer structure;
• 5a-b show schematic views of mechanical systems according to exemplary embodiments that have folded bending elements of the bending structure;
• 6a shows a schematic view of a double dome configuration of a mechanical system according to an embodiment;
• 6b-e show schematic diagrams of the bending behavior of the mechanical system 6a ;
• 7a-d show schematic views of bending transducer systems according to exemplary embodiments in which the adaptation structure is arranged outside a volume of the active region of the bending transducer;
• 8a-b show schematic views of mechanical systems according to embodiments that include an adjustment structure that includes a nonlinear spring;
• 8c shows a schematic diagram of a bending behavior of the mechanical system 8b ;
• 8d shows a schematic view of a mechanical system according to an embodiment having an adjustment structure that includes a multi-layer nonlinear spring;
• 8e-g show schematic views of mechanical systems according to exemplary embodiments in which the adaptation structure is arranged on two outer sides of the bending transducer structure;
• 9a-c show schematic views of mechanical systems according to exemplary embodiments that have at least two bending transducer structures; and
• 10a-c show schematic views of mechanical systems according to execution examples that implement different operating principles.

The same or equivalent elements or elements with the same or equivalent functionality are provided with the same or equivalent reference numerals in the following description, even if they appear in different figures.

In the following description, a variety of details are presented to provide a more complete explanation of embodiments of the present invention. However, it will be apparent to those skilled in the art that embodiments of the present invention may be practiced without these specific details. In other instances, known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the present invention. In addition, features of the different exemplary embodiments described below can be combined with one another unless specifically stated otherwise.

Mechanical systems are described below. Part of the disclosure set forth below relates to micromechanical systems (MMS), and in particular to microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS). However, the present invention is not limited to micromachines. Embodiments of the present invention relate to influencing the bending behavior of a bending transducer structure that has a nonlinear deflection behavior with another structure that is mechanically coupled to the transducer structure to adjust the bending behavior by introducing additional forces. Such an influence can be implemented for micromechanical systems as well as for micromechanical systems or in general for mechanical systems.

Some of the figures presented below relate to bending transducers configured to deflect planarly with respect to a stack of layers, which is particularly illustrated in the technical field of MEMS. However, the embodiments presented herein are not limited to planar deflection. Based on a freely selectable configuration of a clamping and/or arching direction, any direction, e.g. B. planar or extra-planar.

1. A. MEMS-/NEMS-Bereich:
   1. 1. Isolator / dielektrische Schichten: Breite: 10 nm - 10 µm (Höhe und Länge sind normalerweise gleich wie die Biegezellenabmessungen)
   2. 2. Elektrodenabmessungen: Breite: 10 nm - 100 µm (Höhe und Länge sind normalerweise gleich wie die Biegezellenabmessungen)
   3. 3. Abmessungen von Luftzwischenräumen: Breite: 10 nm - 100 µm (Höhe und Länge sind normalerweise gleich wie die Biegezellenabmessungen)
   4. 4. Zellabmessungen: Länge: 10 nm - 10 mm; Breite: 50 nm - 500 µm; Höhe: 10 nm-10 mm, Länge ist normalerweise gleich wie die Biegezellenabmessungen;
2. B. Makroebene: alle Abmessungen können von wenigen mm bis mehrere cm reichen.

Typical dimensions (not necessarily the limits) of structures of various embodiments set forth herein are:

1. A. MEMS/NEMS area:
   1. 1. Insulator/dielectric layers: Width: 10nm - 10µm (Height and length are usually the same as the bending cell dimensions)
   2. 2. Electrode dimensions: Width: 10 nm - 100 µm (height and length are usually the same as the bending cell dimensions)
   3. 3. Air gap dimensions: Width: 10 nm - 100 µm (height and length are usually the same as the bending cell dimensions)
   4. 4. Cell dimensions: Length: 10 nm - 10 mm; Width: 50 nm - 500 µm; Height: 10nm-10mm, length is usually the same as the bending cell dimensions;
2. B. Macro level: all dimensions can range from a few mm to several cm.

Voltage ranges:

1. A. MEMS/NEMS: 0 - 500V
2. B: Macro-level designs: 0 - 10,000 V (typically until electrical breakdown of used insulator/air gap is achieved)

Materials:

1. 1. Elektroden: hochdotierte Halbleiter (Si, GaAs, usw.), Metalle (Aluminium (Al), Wolfram (W), TiAl, usw.), leitfähige Polymere / Polymere beschichtet mit Metall (bei Produktion basierend auf Additivherstellung), kunststoffbasierte Materialien, piezoelektrische Keramiken, usw.
2. 2. Dielektrikum: Al2O3, SiO2, Si3N4, Polymere (bei Produktion basierend auf Additivherstellung), usw.

A. Possible materials for MEMS/NEMS (those mentioned are mainly CMOS compatible, but this is not a necessary condition):

1. 1. Electrodes: highly doped semiconductors (Si, GaAs, etc.), metals (aluminum (Al), tungsten (W), TiAl, etc.), conductive polymers / polymers coated with metal (in production based on additive manufacturing), plastic-based materials , piezoelectric ceramics, etc.
2. 2. Dielectric: Al2O3, SiO2, Si3N4, polymers (for production based on additive manufacturing), etc.

1. 1. Elektroden: alle Metalle/Leiter (Stahl, Al, usw.) oder leitfähige Polymere / Polymere beschichtet mit Metall (bei Produktion basierend auf Additivherstellung)
2. 2. Dielektrikum: Al2O3, SiO2, Si3N4, Polymere (bei Produktion basierend auf Additivherstellung), Keramiken, usw.

B. Possible materials for macro level:

1. 1. Electrodes: all metals/conductors (steel, Al, etc.) or conductive polymers/polymers coated with metal (for production based on additive manufacturing)
2. 2. Dielectric: Al2O3, SiO2, Si3N4, polymers (for production based on additive manufacturing), ceramics, etc.

Possible production processes (but not the only ones):

1. 1. Planare Biegestrukturen: standardmäßige Mengenmikrobearbeitungsprozesse für einzelne kristalline Wafer (z. B. SOI-Wafer-DRIE, ALD, chemische Nassätzung über TMAH, usw.), hochauflösende Additivherstellung mit Drucken von leitfähigem Material / Metallbeschichtung von Polymeren zusammen mit konformen Abscheidungsprozessen für dielektrisches Material (z. B. ALD).
2. 2. Außerplanare Biegestrukturen: Oberflächenmikrobearbeitungsprozesse, Kristallines-Silizium-Wafer-Bonding von zwei Schichten und Strukturieren derselben durch DRIE und anisotrope TMAH-Ätzprozesse, hochauflösende Additivherstellung mit Drucken von leitfähigem Material / Metallbeschichtung von Polymeren zusammen mit konformen Abscheidungsprozessen für dielektrisches Material (z. B. ALD).

A. MEMS/NEMS:

1. 1. Planar bending structures: standard volume micromachining processes for one single crystalline wafers (e.g. SOI wafer DRIE, ALD, wet chemical etching via TMAH, etc.), high resolution additive manufacturing with conductive material printing/metal plating of polymers along with conformal dielectric material deposition processes (e.g. ALD) .
2. 2. Extra-planar bending structures: surface micromachining processes, crystalline silicon wafer bonding of two layers and patterning the same by DRIE and anisotropic TMAH etching processes, high-resolution additive manufacturing with printing of conductive material / metal coating of polymers along with conformal deposition processes for dielectric material (e.g .ALD).

1. 1. Additivherstellungsprozesse (mit Drucken von leitfähigem Material / Metallbeschichtung von Polymeren)
2. 2. Hochpräzise mechanische Herstellungsprozesse wie Spritzgießen, hochpräzise maschinelle Bearbeitung wie CNC, usw.

B. Macro scale:

1. 1. Additive manufacturing processes (with printing of conductive material / metal coating of polymers)
2. 2. High-precision mechanical manufacturing processes such as injection molding, high-precision machining such as CNC, etc.

A bending transducer system can be understood as a mechanical system or at least as part of it. Such systems described herein may include an active region that includes an electrostatic gap and potential-carrying electrodes, e.g. B. for NED, and / or potential-carrying electrodes for actuators, such as piezo configurations and thermal configurations or is defined thereby. It should be noted that matching structures described herein may still be part of the entire cell (=entire bending transducer structure) as compared to cases when they are not present (although they are still inactive parts of a cell as there may be no potential difference in it). reference to an active area and contribute primarily as loads or mechanical feedback systems) will always have a causal direct/indirect influence on the cell response to bending. The adaptation structure can thus be viewed as part of a cell, regardless of whether it is arranged or located inside or outside the active area.

Embodiments presented herein typically relate to a mechanical coupling of a flexural transducer structure to an accommodation structure. The embodiments may differ from each other based on several criteria. This includes the inclusion of the adaptation structure in a volume of the bending transducer structure, for example whether the adaptation structure is “in” the volume of the bending transducer structure or not. Another criterion is whether the adaptation structure is adapted for contact formation, e.g. B. zipper (or zipping) with a different structure, such as the bending transducer structure, or not, or alternatively, whether a coupling surface changes or not. The latter enables highly flexible adjustment of the mechanical system in terms of its behavior. In particular, a linearity or a nonlinearity of the overall mechanical system can also be influenced on the basis of whether it has (change in) contact formation or not.

Embodiments of the present invention relate to a flexural transducer structure. The mechanical coupling of the adaptation structure can, at least in some embodiments, refer to a coupling of the adaptation structure to two disjointed regions of the bending transducer structure, for example at both ends thereof. In such a case, the conforming structure may act as a type of parallel connection to the flexural transducer structure, rather than providing an additional support point or connection to a substrate or the like.

The invention is concerned with bending transducer configurations that can operate as an actuator, sensor or both and its scope is primarily in the field of microelectromechanical systems (MEMS), but is not limited thereto. The invention relates to all bending actuation principles such as electrostatic, piezoelectric, electrothermal, electroactive polymer actuators (e.g. dielectric elastomer actuators (DEAs), etc. and commonly used sensing mechanisms such as capacitive sensing, piezoresistive sensing, piezoelectric capture, etc.

In numerous bending transducer systems, e.g. B. in electrostatic bending transducers [13], the responses such as bending curvature, bending moment, deliverable force, capacitance change, etc. have a non-linear relationship with the applied transducer signal and/or a load condition. This often leads to complex activation, reading and/or control for such systems. The invention presents concepts for modulating the response of the bending system with the transducer signal and/or a load condition to eliminate or reduce the magnitude of the nonlinearity. This is achieved primarily by changing the mechanical stiffness (linear/nonlinear) of the elementary bending cells and/or the geometry of the electrodes, with the applied transducer signal and/or the loading condition. In the presented configurations there are also inherent possibilities of a detection mechanism with Linea rity or reduced magnitude of a nonlinearity. Thus, response modulation can be effectively used to simplify the required driving, sensing and/or control systems. Additionally, the present invention may also be used for bending transducer systems that need to modulate the generated response via changing a bending cell stiffness and/or geometry of the electrodes for a particular application requirement, e.g. B. a reduction of the generated available actual force in a specific range of an applied transducer signal for electrothermal bending transducers, which are known for generating high forces for small voltage changes, for better and controlled handling of sensitive biological samples.

One of the main advantages of the invention is that the required response modulation comes directly from the configuration of the elementary cells of the bending transducer, thus providing a high degree of freedom in the design and performance of the bending transducer. Additionally, the area/volume required to implement the system can be optimized more efficiently while achieving required performance levels, particularly when compared to configurations that use externally dedicated loading mechanisms to modulate a system response [1, 11 ].

Thus, the invention can be used to optimize any bending transducer scheme/mechanism that requires modulation of a system response and/or linearization with respect to an applied transducer signal (actuation and/or readout signal) and/or a load condition. Furthermore, the basic concepts presented to obtain response modulation at an elementary level in the invention are not only limited to bending configuration, but can also be extended to other transducer systems, especially where the system response is based on a change in mechanical stiffness (linear /nonlinear) and/or to modulate deformation of electrodes, which comes from the design of the basic element cells.

Since the invention is applicable to the basic elementary level of the transducer, it can be used in numerous applications and devices such as MEMS micropositioning systems, MEMS pumps, MEMS optical switches, MEMS capacitance diodes, MEMS energy harvesters, etc.

The invention relates specifically to electrostatic bending actuators such as nanoscopic electrostatic drives (NED, Nanoscopic Electrostatic Drive), which are described in the patent WO 2012/095185 A1 are described [14].

The different design configurations set forth in this invention provide the possibilities of solving the above problems. For the electrostatic configurations with contact-based operation in this invention, contact formation can be achieved with/without using a pull-in effect. For configurations without the use of a tightening effect, the tightening-based design challenges and associated design nonlinearities can be avoided, and a slow and smooth transition into the response modulation/linearization realm can be obtained. However, if an abrupt transition into the contact region is required for response modulation/linearization and a rapid contact break is needed to reduce probabilities of permanent stiction, a tightening effect can also be used. In the configurations based on a bending spring (with/without feedback to the cell electrodes), non-linear stiffening in a bending cell can be achieved even without contact formation, which means that there are no problems with frictional adhesion, contact-based motion hysteresis, etc. Furthermore, a frequency response in such configurations does not exhibit sudden disturbances due to contact formation.

The invention can be used to reduce nonlinearity and/or modulate an effect of motion hysteresis (particularly in configurations with mechanical feedback to cell electrodes) in DEAs and also piezo actuators. It can also be used to reduce the force provided and/or increase motion resolution for bending systems based on electrothermal actuators (if required for specific applications).

WO 2020 078541 A1 : In this paper, specific bending cell configurations based on control with specialized drive signals were implemented to achieve linearity in electrostatic bending actuator cells (which usually have a highly nonlinear response [13, 14]). Linearization is achieved using a specific cell geometry and operating it in a specific range of actuator response. A special configuration of drive signals with a very specific configuration with three or more electrodes is required (not necessarily required for the present invention). The usable area for linearization and response is in ver similar to the present invention, more limited. Additionally, forces achieved will be lower compared to contact-based configurations presented in this invention and thus higher bending curvatures and deflections can be achieved in the present invention.

patent US 7,679,261 B2 : In this document, a pivot configuration is used along with a zipper actuation to create multiple degrees of motion. The system requires special configuration and does not ensure reduction of nonlinearity of a system response. The present invention uses a very different approach to counteract nonlinearity and does not require the specific configuration discussed therein.

US 2021/061648 A1 : In this paper, electrodynamic levitation is used to counteract attraction effect and nonlinearity of electrostatic transducers. However, the system requires a very specialized design configuration (thus there is limited design freedom) and a complicated control scheme with very high drive voltages. The present invention uses a very different approach to counteract nonlinearity and does not require a complicated driving scheme.

US 10,693,393 B2 and US 2019/036463 A1 : In these documents, a tri-electrode configuration is used with a specific drive scheme to counteract a tightening effect and have reduced nonlinearity at reduced drive voltages. The present invention uses a very different approach to counteract non-linearity and does not require such a drive scheme, while the lowered drive voltage conditions can also be met if required. The configurations set forth in this invention also have a greater degree of design freedom.

The bending actuator responses, such as bending curvature, peak deflection, actual force available, bending moment, force generated, structural stiffness (localized or total), frequency response (mechanical and/or electrical, e.g. structural hardening and/or softening with mechanical movements higher frequency, change in cut-off frequency of the electrical actuation signal due to capacitance change, etc.), etc. can be modulated based on the geometric design and electrode configurations in the individual elements of the bending actuator (referred to as “bending cells”) when the actuation signal is applied. Response modulation is achieved primarily through linear/nonlinear stiffening at the elementary cell level using causal bending of the electrodes based on contact formation and/or an internal bending system.

1. 1. Strukturelle Versteifung (linear/nichtlinear) mit Zellbiegung auf der Basis von Kontaktbildung und ihrer Evolution in der Zellgeometrie:
   1. a. Kontaktformation und -evolution zwischen Elektroden in dem elektrostatischen Zwischenraum auf der Basis eines Materials eines elektrischen Isolators / dielektrischen Materials (z. B. Al2O3, SiO2, usw.).
   2. b. Kontaktbildung außerhalb des elektrostatischen Zwischenraums (elektrischer Isolator nicht notwendigerweise erforderlich).
2. 2. Strukturelle Versteifung (linear/nichtlinear) mit Zellbiegung auf der Basis einer Federkonfiguration in der Zellgeometrie;
   1. a. Biegefederkonfigurationen in der Zellgeometrie ohne Rückkopplungsschleife zu der Verformung der Biegeelektroden.
   2. b. Biegefederkonfigurationen in der Zellgeometrie mit direkter/indirekter Rückkopplungsschleife zu der Verformung der Biegeelektroden.

The configurations presented in this invention can generally be divided into the following basic variants:

1. 1. Structural stiffening (linear/nonlinear) with cell bending based on contact formation and its evolution in cell geometry:
   1. a. Contact formation and evolution between electrodes in the electrostatic gap based on an electrical insulator/dielectric material (e.g. Al2O3, SiO2, etc.).
   2. b. Contact formation outside the electrostatic gap (electrical insulator not necessarily required).
2. 2. Structural stiffening (linear/nonlinear) with cell bending based on a spring configuration in the cell geometry;
   1. a. Bending spring configurations in the cell geometry without a feedback loop to the deformation of the bending electrodes.
   2. b. Bending spring configurations in cell geometry with direct/indirect feedback loop on the deformation of the bending electrodes.

It is always possible to combine the different basic variants to form different cell configurations depending on the system response requirements.

The contact formation and its evolutions in the cell geometry with the applied signal can take place in the electrostatic gap between the cell electrodes or outside of it. The position of initial contact shape formation and evolution of contacts upon actuation depends on the geometry and topography of electrodes, material properties of the electrodes, the insulating layer in the electrostatic gap, maximum applicable voltage (insulator thickness required to withstand the voltage in the electrostatic gap ), etc. Based on the different factors that can be designed, the response of the bending actuator when voltage is applied can be designed and modulated depending on the requirements.

The internal bending system may be with/without direct connection to the geometry of the deforming electrodes to have a direct/or indirect effect on the electrode deformation. Thus, a feedback loop system is also possible to adjust the deformations of the electrodes based on mechanical deformations and forces generated in the cell geometry when the conversion signal is applied. For bending actuator cells with electrostatic/electroactive polymers (e.g. DEAs), the bending system with direct/indirect structural feedback loop to the electrodes can be used to deform, in addition to the geometric shape of the electrodes, the local/general shape of the electrostatic gap during bending, and thus also influencing the electrostatic forces generated in these gaps. This can be used to widen the feedback loop even further. For piezoelectric bending actuator cells, the structural feedback loop to piezoelectric layers will affect their actual mechanical deformation and a stress in the layers, which will effectively also affect the actual forces generated therein when voltage is applied.

One of the main advantages of the invention is that the response modulation can be obtained directly from the cell geometry itself, thereby avoiding the use of external spring mechanisms [2, 3], external mechanisms for nonlinear loading, articulated-end conditions [1], etc , and thus the overall system area is effectively reduced since the actuators can be easily stacked in series and parallel based on the cell geometry.

Furthermore, in the case of configurations of electrostatic bending actuators based on contact formation, larger forces can be achieved than conventional ones used only on the basis of air gaps without contact formation between electrodes (e.g. conventional NEDs [13, 14, 15]) . Due to the use of contact formation based on a dielectric material therebetween, much larger electrostatic forces (∝ ε _r ,g ² ) can be generated as a gap (g) is drastically reduced compared to typical minimum values of 1/3rd of an air gap (to avoid attraction between electrodes of conventional NEDs), and a higher effective relative permittivity (ε _r ) can be achieved in the electrostatic gap upon contact based on a high dielectric constant material.

In the configurations of the present invention, the dielectric material may be conformally applied to the electrodes or as detached layers between the electrodes (using special production processes) so that pre-deflection upon release in the cells due to residual stress is negligible. This dielectric deposition based approach can be used to reduce the effective electrostatic air gap between electrodes compared to the production resolution limitation, i.e. H. where directly produced electrostatic air gaps cannot be reduced beyond a certain dimensional limit, such as planar NED cells based on DRIE etching, where a minimum trench width is limited by a certain aspect ratio with respect to depth. This further allows the maximum forces generated to be increased by achieving a narrower effective electrostatic air gap between electrodes than given production limitations, thereby increasing the system area and/or voltage level required to achieve required force and displacement levels , be reduced. Another significant advantage is that it also enables actuation at voltages higher than the attraction voltage (lateral and/or vertical attraction) of the electrodes of the electrostatic bending actuators, in contrast to conventional NEDs. This makes it possible to compensate for any losses in target functionality due to variations introduced by production, load conditions, etc. by simply adjusting the applied voltage.

1. 1. Eine Kontaktbildung in einer einzelnen Zelle wird verwendet, um eine Biegeverformung einer gesamten Zellgeometrie zu erzielen, statt einer fortlaufenden Reißverschlussfunktion eines Aktors (was für gewöhnlich eine stationäre Elektrode und eine Reißverschluss-/Biege-Elektrode verwendet), zur Antwortmodulation bei angelegtem Signal. Somit können viele Zellen, mit mehreren Elektroden und Luftzwischenräumen, in Reihe und/oder parallel verwendet werden, um erforderliche Antwortparameter, wie etwa Auslenkung, Kraft, usw., bei einer geringeren effektiven Kontaktfläche im Vergleich zu herkömmlichen Reißverschlussaktoren zu erzielen. Dies reduziert die Wahrscheinlichkeit einer Reibungshaftung und Bewegungshysterese während der Lösung der Reißverschlussverbindung, da die Kontaktbildungsfläche erheblich reduziert sein kann, während ähnliche oder bessere Leistungsparameter erzielt werden.
2. 2. Biegeverformung auf der Basis limitierter Kontaktpunkte (oder bei einigen Konfigurationen sogar nur ein einzelner Kontaktpunkt) kann außerdem anstatt der kontinuierlichen kontaktbasierten Reißverschlussfunktion wie bei herkömmlichen Reißverschlussaktoren verwendet werden. Außer dem ersten Kontaktpunkt sind die weiteren Direktkontaktpunkte nicht dafür erforderlich, dass das Prinzip funktioniert, in den äußeren Ecken einer Biegezelle ist es sogar möglich, keine Kontaktposition aufzuweisen, während eine Modulation / Linearisierung aufgrund einer Biegung der gesamten Zellgeometrie erzielt wird. Dies reduziert Wahrscheinlichkeiten einer Reibungshaftung und Bewegungshysterese während der Lösung der Reißverschlussverbindung weiter und verbessert somit die Reproduzierbarkeit und Zuverlässigkeit der Leistung des Systems erheblich.
3. 3. Im Vergleich zur herkömmlichen elektrostatischen Reißverschlussaktoren ist eine elektrostatische Anziehung nicht erforderlich für eine erste Kontaktbildung oder ihre Evolution, womit ein reibungsloser Übergang in einen Kontaktbereich erhalten werden kann, ohne abrupte Bewegungen der Systemantwort während eines Überganges in einen Bereich einer Modulation / Linearisierung bei angelegtem Signal, und wobei außerdem anziehungsbezogene Instabilitäten zur Kontaktbildung vermieden werden. Falls ein plötzlicher Übergang erforderlich ist, um beispielsweise die Änderung in einem Bereich einer Modulation / Linearisierung zu kennzeichnen oder den Kontakt während eines Prozesses zur Lösung der Reißverschlussverbindung stark zu unterbrechen, um Haftreibungswahrscheinlichkeiten weiter zu reduzieren, kann ein Anziehungseffekt in den vorliegenden Konfigurationen auch je nach Anforderung verwendet werden.

Furthermore, the main advantages of the presented configurations based on contact formation (to achieve a change in flexural cell stiffness) with respect to conventional zipper actuators [1-8, 10-12] are as follows:

1. 1. Contact formation in a single cell is used to achieve bending deformation of an entire cell geometry, rather than a continuous zipping function of an actuator (which usually uses a stationary electrode and a zip/bend electrode) for response modulation when a signal is applied. Thus, many cells, with multiple electrodes and air gaps, can be used in series and/or parallel to achieve required response parameters, such as deflection, force, etc., with a smaller effective contact area compared to conventional zipper actuators. This reduces the likelihood of frictional adhesion and motion hysteresis during zipper connection release as the contact formation area can be significantly reduced while achieving similar or better performance parameters.
2. 2. Bending deformation based on limited contact points (or even just a single contact point in some configurations) can also be used instead of the continuous contact-based zipper function found in traditional zipper actuators. Apart from the first contact point, the further direct contact points are not necessary for the principle to work, in the outer corners of a bending cell it is even possible to have no contact position while modulation/linearization is achieved due to a bending of the entire cell geometry. This further reduces probabilities of frictional adhesion and motion hysteresis during zipper connection release, thereby significantly improving the repeatability and reliability of the system's performance.
3. 3. Compared to conventional electrostatic zipper actuators, electrostatic attraction is not required for initial contact formation or its evolution, whereby a smooth transition into a contact area can be obtained without abrupt movements of the system response during a transition into a modulation/linearization area when applied Signal, and in which attraction-related instabilities for contact formation are also avoided. If a sudden transition is required, for example to mark the change in a region of a modulation/linearization or to sharply break contact during a zipper release process to further reduce stiction probabilities, an attraction effect in the present configurations may also vary depending on requirement can be used.

For configurations based on contact formation, the potential problems arising due to stiction between electrodes could be caused by increasing the roughness of the contact surfaces (e.g. sidewall undulations from DRIE etching), texturing of contact surfaces, and/or use of anti-stick coating therebetween , e.g. B. conformal FDTS (perfluorodecyltrichlorosilane) single-layer coatings deposited with ALD (atomic layer deposition) can be reduced.

Dielectric charging of electrical insulation may occur in present configurations due to limited dielectric material volume and interface usage, reduced areas for effective contact formation (particularly for insulation contact-based configurations), floating electrodes (for charging and/or discharging dielectric areas for response regulation), etc. can also be reduced and/or regulated. This further helps to increase system response reproducibility and reduce probability of stiction due to dielectric charging between the contact surfaces.

The linearization/modulation of the bending cell response can also be read out using a detection signal, and due to a reduction in detected nonlinearity of the response, the required detection system can also be simplified. The detection can be based on inherent response changes such as a change in capacitance between the bending electrodes (e.g. change in capacitance in the electrostatic gap can also be linearized or modulated to a lower order linearity, along with the curvature of the cell upon cell bending). structural deformation and/or stress in electrodes (e.g. causing a change in resistance based on a piezoresistor (material such as crystalline silicon), or generating a voltage due to the piezoelectric effect), etc. take place.

1a shows a schematic side view of a mechanical system 10 ₁ , e.g. B. a bending transducer system, according to one embodiment. The mechanical system includes a bending transducer structure configured to provide bending, e.g. B. along a bending direction 14. The bending direction 14 is according to a non-restrictive Cartesian coordinate system along a z-direction, which can be planar or extra-planar in the sense of a MEMS. Without limiting the examples described herein, when referring to a MEMS, an x/y direction may be referred to as a planar direction, while a direction along the z coordinate may be referred to as an extra-planar bend or movement.

The bending transducer structure may be configured as an actuator to bend in response to an electrical signal 16. This can include, for example, electrostatic and/or electrodynamic actuators as well as capacitive actuators or piezoelectric actuators. However, the energy provided with the electrical signal 16 can also be converted, for example, into other types of energy, e.g. B. thermal energy, magnetic forces or the like.

Alternatively or additionally, the bending transducer structure may be operative to provide the electrical signal 16 in response to an applied force F, the force F causing the bending. That is, the bending transducer structure can also work as a sensor. Both functions can be carried out in an either/or manner, that is, the bending transducer structure can be a sensor or an actuator. However, a combined mode of operation may also be possible if, for example, the bending transducer structure is operated sequentially as a sensor during a first period of time and is used as an actuator during an unrelated second period of time. Another way of using both mechanisms, functioning as a sensor and functioning as an actuator, can be present, for example, if the bending transducer structure is activated by providing the electrical signal 16, for example by using a control unit and/or an amplifier or the like, and by evaluating the electrical signal 16 (or another signal) is operated or controlled with regard to a superposition or modulation caused by the force F, the functioning as a sensor and the functioning as an actuator can therefore be carried out simultaneously.

The flexural transducer structure 12 may have a structural stiffness that may be based on a material and geometry of the flexural transducer structure. The structural stiffness S ₁ of the bending transducer structure can provide a nonlinear mechanical stiffness contribution of the bend, that is, based on a changing deflection of the bending transducer structure, an additional force F can provide an increased or reduced deflection amount and/or the deflection behavior can be in With regard to a linear amplitude of the electrical signal 16, it may not be linear.

The mechanical system 10 ₁ has an adaptation structure 18 that is mechanically coupled to the bending transducer structure 12 through the use of a mechanical coupling. That is, the adaptation structure 18 is mechanically connected to the bending transducer structure 12. The conforming structure 18 is configured to provide conforming deformation along with the bending of the bending transducer structure. That is, the force F and/or the electrical signal 16 causes a bending of the bending transducer 12 and thereby the deformation of the adaptation structure 18. A mechanical stiffness S ₂ of the adaptation structure 12 ensures a further nonlinear mechanical stiffness contribution to the bending of the transducer structure the basis of the mechanical coupling. For example, the adaptation structure 18 can absorb or use up a portion of the force F or the force generated by electrical signals 16. Through the nonlinear behavior of the mechanical stiffness S _{2 ,} the behavior caused by the mechanical stiffness S ₁ of the bending transducer structure 12 can be influenced to increase an overall linearity compared to the nonlinear contribution of the stiffness S ₁ . However, it may be desirable to increase the nonlinearity, which is possible without specific limitation, by selecting a respective mechanical stiffness S ₂ or a behavior thereof. This can be achieved by selecting an appropriate material and/or geometry. Both the bending transducer structure 12 and the conforming structure 18 may be configured for deformation. That is, a certain amount of elasticity may be included in both the flexural transducer structure 12 and the conforming structure 18. With respect to a MEMS structure, semiconductor-based materials and/or dielectric materials or metal-containing materials may be suitable. With regard to micromechanical systems, other types of material may be used in addition to a metal material or other dielectric or conductive materials, such as wood, plastic or the like.

At the in 1 In the example presented, the adaptation structure 18 is adapted to form a mechanical contact on a contact surface 22a and on a contact surface 22b of the bending transducer structure, ie the contact boundaries are used to provide mechanical contact. A force generated by the contact between the contact surfaces 22a and 22b may be variable or non-constant during contact formation and with respect to an increase or decrease in amplitude along the bending direction. For example, a size of a contact area in which the contact areas 22a and 22b contact each other may increase or decrease.

1b shows a schematic side view of a mechanical system 10 ₂ according to an embodiment, in which the adaptation structure 18 is adapted to provide the second nonlinear mechanical stiffness contribution without any additional contact beyond the mechanical coupling or other fixed or constant connections to the bending transducer structure 12 is formed. While the contact in the contact surfaces 22a and 22b of the mechanical system 10 ₁ is such a variable or changeable contact, the mechanical system 10 ₂ is implemented without such contact surfaces.

1c shows a schematic side view of a mechanical system 10 ₄ according to an exemplary embodiment. Compared to the mechanical systems 10 ₁ and 10 ₂ which have the adjustment structure 18 outside of a volume 24 enclosed by the outer sides of the flexural transducer structure 12, the mechanical system 10 ₃ has a configuration in which the adaptation structure 18 is arranged in the volume 24. This can be understood to mean that the adaptation structure is arranged outside an active area of the bending transducer. At the in 1c In the example provided, the adjustment structure 12 may be clamped between flexures 26 ₁ and 26 ₂ , which may be attached to each other at ends thereof, not excluding optional connections therebetween. For example, the bending element 26 ₁ and 26 ₂ can be active elements such as electrodes, thermoactive elements, piezoelectric elements or the like. This may make it possible to obtain pairs of contact surfaces 22a and 22b, 22c and 22d, of which no contact is formed, for example in a scenario such as that illustrated, or based on a deflection of the bending transducer structure along a positive or negative bending direction 14, only one of the pair of contact surfaces 22a and 22b on the one hand or 22c and 22d on the other hand ensures mechanical contact. Instead of making the mechanical contact in one of the pairs of contact surfaces 22a/22b or 22c/22d, it may be possible to form a contact in both pairs simultaneously, e.g. B. based on sufficient bending amplitude.

1d shows a schematic side view of a mechanical system 10 ₄ according to an embodiment that is comparable to the mechanical system 10 ₃ , while the adaptation structure 18 is adapted, at least during normal operation, to provide no additional contact surfaces other than the mechanical coupling, for example by a Clamping 28 ₁ and/or 28 ₂ can be implemented at ends of sections or the entire bending elements 26 ₁ and 26 ₂ .

The exemplary embodiments according to 1a-d can be assigned to different groups of structures. While the mechanical systems 10 ₁ and 10 ₃ provide temporary additional contacts in the contact surfaces 22a, 22b or optionally 22c and 22d, the mechanical systems 10 ₂ and 10 ₄ are formed without such contact formations. This does not exclude mechanical couplings that remain constant over time.

A further grouping can be such that the adaptation structure 18 is arranged outside the volume 24 or within the volume 24.

2a shows a schematic top view of a mechanical system 20 ₁ according to an exemplary embodiment. The Cartesian coordinates x, y and z are shown as a non-limiting example. According to the illustrated configuration, the bending direction 14 is planar. As can be seen from the structure of the mechanical system 10 ₂ , the structure can be rotated in space, which also rotates the bending direction 14.

Bending elements 26 ₁ and 26 ₂ can have a substantially parallel course. For example, in an unactuated state or a reference state of a sensor implementation, the flexure elements 26 ₁ and 26 ₂ , which may be formed as flexure beams, may each have curved shapes that are parallel to one another. An unactuated state can be understood as a reference state without application of an electrical signal 16 in an actuator configuration or a force F in a sensor configuration. The unactuated state can still allow the bending transducer structure 12 to be deflected forward.

A neutral axis 27 ₁ of the bending element 26 ₁ runs essentially parallel to a neutral axis 27 ₂ of the bending element 26 ₂ . Based on a respective configuration, surfaces 26 ₁ A and 26 ₂ B are also substantially parallel to each other, as are outer surfaces 26 ₁ B and 26 ₂ A, by way of non-limiting example.

As in 2a As shown, the bending transducer structure 12 may have at least two bending elements 26 ₁ and 26 ₂ that are mechanically coupled parallel to one another and form a gap 38 with an adjacent bending element of the bending transducer structure. For example, the adaptation structure 18 can be arranged in the gap 38, at least in part, in order to separate the gaps into gaps 38 ₁ and 38 ₂ .

Clamps 28 ₁ and 28 ₂ fasten the bending elements 26 ₁ and 26 ₂ to one another and ensure a distance between them, e.g. B. as a spacer element. The clamps 28 ₁ and 28 ₂ may be formed by a single integral element, but may also be formed by multiple elements, as in 2a is shown. For example, the clamping 28 ₁ can have spacer elements 28a ₁ and 28b ₁ , which are part of the bending elements 26 ₁ and 26 ₂ , respectively. For example, the spacer element 28a ₁ may be formed integrally with the bending element 26 ₁ , and the spacer element 28b ₁ may be formed integrally with the bending element 26 ₂ . This may enable ease of manufacture, particularly in the case that the bending elements 26 ₁ and 26 ₂ are conductive, so that a conductive spacer element 28a ₁ and 28b ₁ may enable electrical contact to be provided, for example with an operating potential that shown by GND and +V to be contacted, which may enable an operating voltage, e.g. B. based on an electrical signal nals 16, between the bending elements 26 ₁ and 26 ₂ , which can lead to an attraction between the bending elements 26 ₁ and 26 ₂ and thereby to movement components 34 ₁ and 34 ₂ of the bending elements 26 ₁ and 26 ₂ to one another.

The matching structure 18 may include a dielectric material and may be configured to contact at least two elements of the flexural transducer structure 12 and to isolate them based on the flexure, e.g. B. the bending elements 26 ₁ and 26 ₂ . Preferably, an insulator 36 ₁ is arranged between the conductive spacers 28a ₁ and 28b ₁ . Accordingly, it is preferred to arrange an insulator 36 ₂ between the spacer elements 28a ₂ and 28b ₂ in order to avoid short circuits between the respective spacer elements. However, according to another example, at least the spacers 28a ₂ and 28b ₂ may be implemented by using a dielectric material, allowing the insulator 36 ₂ to be avoided. If the mechanical system 20 ₁ is created as a layered structure, it is still possible to provide the insulator 36 ₁ /36 ₂ as a layer of the system without complicated additional steps.

One of the advantages provided by the conforming structure 18 as a separate layer in the electrostatic air gap, e.g. B. instead of being produced directly on the electrodes 26 ₁ and / or 26 ₂ is that the areas with interfaces from conductor / metal to dielectric / insulator material are significantly reduced. Such interfaces, especially in typical material systems and production processes in the area of MEMS and nanoelectromechanical systems, NEMS, are known from the literature as good charge trapping points that can increase the dielectric charging effect and thus the static friction probabilities between contact surfaces, especially with frequent contact-based actuation. Reducing these interfaces can help to reduce the hysteresis of the system response, as well as to have better functional reliability and reproducibility of the system response.

Since the dielectric layer is standalone in the cell space, the overall self-stress in the thin film structures of the cell due to production, especially for the MEMS and NEMS area, can be significantly lower than compared to cases where dielectric layers are on the electrodes , especially for a non-uniform (e.g. 3b) Configuration, due to a reduced area of interfaces between two or more different types of material systems (conductor/metal to dielectric/insulator material). This can facilitate design because more complex technology to compensate for self-stress is not required and cells have negligible pre-deflection after structures are released during production.

On the other hand, the production of such stand-alone dielectric layers as a structure 18, particularly in the MEMS and NEMS area at the minimum resolution limits of the production process (i.e. at the smallest electrostatic air gaps that can be produced for the lowest possible actuation voltages), can be accompanied by a comparatively increased complexity, and it is difficult in practice to adequately control their dimensions during production at such resolution limits.

Additionally, it may be difficult to maintain structural integrity and sufficient robustness of stand-alone dielectric/insulator layers 18 at lower thicknesses for a given design, particularly at the resolution limits of MEMS and NEMS production processes. Thus, a minimum thickness of the structure 18 may be applied to maintain the shape of a thin stand-alone dielectric layer, particularly to withstand contact-based high electrostatic compressive forces multiple times during operation without mechanical and/or electrical failure. This may limit the minimum thickness of the structure 18 that can be used even if an electrical breakdown voltage limit has not been reached for the dielectric layer at the required operating voltage. This in turn may limit downscaling of the system to minimum usable air gaps, and thus require a higher voltage for actuation compared to cases where dielectric layers are directly on the electrodes (e.g. 3a-c , etc.), in which case the minimum thickness of the dielectric layer on the electrode is limited only by the limit of electrical breakdown at the required operating voltage (since the required structural integrity and robustness comes from the electrodes on which a dielectric layer is produced ).

The adjustment structure 18 may be clamped between the flexures 26 ₁ and 26 ₂ , as illustrated for the mechanical systems 10 ₃ and 10 ₄ . The adaptation structure 18 can be formed in one piece with the insulators 36 ₁ and/or 36 ₃ . An insulating property of the adaptation structure 18 may be advantageous, but is optional in a case where the bending elements 26 ₁ and/or 26 ₂ are electrically insulated, for example if they have an insulating layer arranged thereon sen and/or if they are operated non-electrically, e.g. B. thermal.

Based on actuation using the electrical signal 16 and/or in response to the force F, the spaces 38 ₁ and 38 ₂ can change their extent. For example, the gaps 38 ₁ and 38 ₂ can become smaller at least in a region of the contact surfaces 22a/22b between the bending element 26 ₁ and the adaptation structure 18 and/or between the adaptation structure 18 and the bending element 26 ₂ in the contact surfaces 22c and 22d.

Starting from a vertex of the course, for example a position at which the plane AA' is arranged, the contact surfaces 22a-d can increase along contact evolution directions 44 ₁ and 44 ₂ . Increasing the contact area may enable an increase in the mechanical resistance provided by the conforming structure 18 through the mechanical stiffness contribution thereof to counteract nonlinearities in the possible electrostatic actuation of the flexures 26 ₁ and 26 ₂ .

The mechanical system 20 ₁ can be used as a single actuator/sensor, but can also be used in conjunction with other mechanical systems, for example as a set thereof. In other words shows 2a an exemplary base cell configuration with an insulator layer 18 between the electrodes, in place of the electrostatic air gap 38 ₁ /38 ₂ , in a planar bend top view and an extra-planar bend side view, respectively.

The exemplary basic cell configuration may refer to an electrostatic bending actuator (NED) for response modulation based on contact formation between the electrodes (26 ₁ , 26 ₂ ) in the electrostatic gap via a detached dielectric / insulator layer (18) having a cell geometry is connected to the spacer areas (28) by electrical insulation (36 ₁ , 36 ₂ ) of the electrodes. When a potential difference is applied to the electrodes, the cell bends in the direction 14 (based on the NED principle) along the neutral fiber of the cell geometry. The greatest movement in the electrodes 26 ₁ , 26 ₂ will occur in the center of the cell (AA plane) along directions 34 ₁ and 34 ₂ , respectively. Beyond a certain voltage (not necessarily an attraction voltage of the cell geometry), based on cell design parameters such as electrode thickness, length, cell topography angle, etc., the electrodes will come into contact with the dielectric layer (18), resulting in initial contact formation and which thus starts the transition into a region of a modulated response.

After the first contact formation, the contact evolution will take place along the cell length in the directions 5a and 5b and thus result in increased stiffness of the cell geometry, especially in the cell bending direction, which counteracts the nonlinearity of the cell response when the actuation voltage signal is applied. Cell symmetry (along the AA plane) helps simplify actuator design and control, but is not essential for the principle to work. The geometry can be realized through the use of different production processes, such as bulk micromachining, surface micromachining, 3D printing, etc., or through their combinations, both planar and extra-planar.

2 B shows the schematic top view of a mechanical system 200 ₁ , which has a plurality of cells 20 ₁ according to 2a having. The cells 20 ₁ are arranged in series one along the other and connected to the respective clamp 28 ₂ of a previous cell. As a result, an amplitude of a deflection along the bending direction 14 at a non-clamped end 46 can be increased compared to a single cell. 2c shows a schematic top view of a mechanical system 200 ₂ according to an exemplary embodiment, with a second half 84 ₂ of cells 20 ₁ being rotated, for example, by 180 degrees. For example, while all of the cells of the mechanical system 20 ₁ may have a curvature along the +y direction, half 48 ₁ of the cells of the mechanical system 200 ₂ are arranged accordingly and the second half 48 ₂ have curvatures along the -y direction . In comparison to the mechanical system 200 ₁ , a so-called s-configuration can thus be obtained, which makes it possible to at least partially avoid rotation of the end 46 and at least partially avoid a rectilinear movement of the end 46. The groups or halves 48 ₁ and 48 ₂ can also be arranged in reverse and/or cells with a curvature along the +y direction and along the -y direction can be arranged alternately. Furthermore, any sequence or type of grouping can be carried out.

2d shows a schematic top view of a mechanical system 200 ₃ that has a double-clamped configuration, ie both ends of the chain of cells are clamped. This may make it possible to obtain deflection of the mechanical system 200 ₃ along the bending direction 14 more at a center or center of the mechanical system 200 ₃ .

2e shows a schematic top view of another mechanical system 200 ₄ according to an exemplary embodiment. Starting from a center 48 of the mechanical system 200 ₄ or the deflectable part thereof, a symmetrical number of, for example, two cells 20 ₁ is preferably arranged in such an orientation that the curvature occurs along the y-direction, and then this is followed by a preferably symmetrical one Number of cells 20 ₁ that have an alternative curvature along the +y direction. The number of cells having the direction of curvature along the +y direction and along the -y direction may be equal. Embodiments also provide for structures in which, starting from the center 48, the cells are arranged asymmetrically with respect to a number of cells and/or with respect to the structure of cells and/or with respect to the orientation thereof.

Although the mechanical systems 200 ₁ to 200 ₄ are illustrated as having eight cells, the number thereof may vary, for example at least 2, at least 3, at least 4, at least 8, or even higher. Mechanical systems according to embodiments may have different implementations of individual cells thereof, with these cells being implemented similarly or differently. That is, each mechanical system described herein may be used individually or in combination with at least one cell or a greater number of cells, the cells being of the same type or embodiment or of a different type or embodiment. Same or different configurations can be combined in any way or with any concept.

In other words, show 2 B until 2e exemplary bending beam configurations. 2 B shows a clamp-free configuration, 2c shows a clamp-free S configuration, 2d shows a double-clamped configuration, and 2e shows a double-clamped S configuration, each in a top view for a planar bend or in a side view for an out-of-planar bend. 2b-2e show basic bending actuator beam configurations for the example cell shown in 2a illustrating: (i) clamp-free configuration: all cells bend in the same direction, resulting in a bending movement in one direction 14 of the free end of the beam; (ii) Clamp-free S configuration: Cells of a group 48 ₁ and cells of a group 48 ₂ bend in opposite directions to form an S configuration when actuated to avoid rotation of the free end of the beam and allow rectilinear movement in to enable direction 14; (iii) double-clamped configuration: all cells bend in the same direction, resulting in movement in the direction 14 of the beam center; (iv) double-clamped S-configuration: cells that bend along +y and cells that bend along -y bend in opposite directions to form an S-configuration on each side of the center of the beam when actuated form to achieve a rectilinear movement in the direction 14.

2f shows a schematic top view of a mechanical system 20 ₂ , which, in comparison to the mechanical system 20 ₁ , has a multi-layer adaptation structure, in which a plurality of layers 18 ₁ and 18 ₂ , optionally additional layers, a respective gap 38 ₃ between adjacent layers 18 ₁ and 18 ₂ , wherein the gap 38 ₃ is partially closed in a deflected state of the bending transducer structure 12. The adaptation structure 18 may have a layer structure that is arranged in a planar manner between the first bending element 26 ₁ and the second bending element 26 ₂ . The different layers 18 ₁ and 18 ₂ may have a continuous gap therebetween, or may have a discontinuous gap, for example when contacted with each other at discrete positions.

In other words shows 2f an exemplary base cell configuration with multiple insulator layers between the electrodes in the electrostatic air gap for possibilities of forming multiple contacts in a top view for a planar bend and in a side view for an extra-planar bend. The exemplary base cell configuration has multiple detached dielectric/insulator layers (18 ₁ , 18 ₂ ) between the electrodes (26 ₁ , 26 ₂ ) in the electrostatic air gaps (38 ₁ -38 ₃ ) for possibilities of forming multiple contacts upon actuation. Depending on the stiffness (thickness, elastic modulus, etc.) of the dielectric layers in the bending direction and the positioning of the separate insulator layers with respect to a neutral fiber of the cell geometry (i.e. how far the dielectric layer will expand or contract with respect to the electrodes ) different configurations for contact formation and evolution can be achieved depending on the requirements. Contact formation and evolution only between the insulator layers 18 ₁ and 18 ₂ is also possible through their movement in directions 34a ₃ and 34b ₃ with contact evolution in directions 44a ₃ and 44b ₃ . This helps reduce the chances of dielectric charging since electrodes with a potential are not in contact with the surfaces of the dielectric layer to non-linearly stiffen a cell via a contact pattern when operated. Alternatively, contact formation of all electrodes (26 ₁ , 26 ₂ ) and the dielectric layers (18 ₁ , 18 ₂ ) as a whole can be achieved with contact evolution in the cell bending directions (44) in order to achieve higher cell stiffness when a voltage signal is applied together with higher electrostatic forces that can be provided to obtain.

The configuration 2f provides advantages, e.g. B. compared to 2a , since even with the same cell, different linear regimes with different slopes can be obtained on the basis of occurrence of different contact formation and propagation regimes and their superposition only by increasing the actuation voltage. The dimension of electrodes, dielectric layers and air gaps can be of the same order of magnitude as in 2a However, the overall stiffness of the cell must be reduced accordingly or the actuation voltage must be increased in order to be off 2f same bending range as in 2a since the presence of multiple layers and air gaps increases the total gap between the electrodes 26 ₁ and 26 ₂ (particularly at the production resolution limits of the production process used), which will reduce the overall electrostatic forces (which can be achieved by reducing the overall cell bending stiffness or by increasing the actuation voltage can be compensated). Cell bending stiffness can usually be reduced by using thinner and/or longer electrode/dielectric layers with higher dome angles.

2g shows a schematic top view of a mechanical system 20 ₃ according to an exemplary embodiment, wherein the adaptation structure 18 has a variable distance to at least one bending element 26 ₁ and/or 26 ₂ of the bending transducer structure 12, for example when comparing the mechanical system 20 ₃ with the mechanical system 20 ₁ , a layer 52 of the adaptation structure 18 may have one or more elevations 54 ₁ , 54 ₂ on one or both sides of the layer 52, a position of a elevation 54 ₁ and/or 54 ₂ being symmetrical or asymmetrical with respect to the side, which points to the bending element 26 ₁ , and the side which points to the bending element 26 ₂ , and/or may be along the direction x. That is, a number of elevations 54i, 54 ₂ on a first side 52A and on a second, opposite side 52B of the layer 52 may be the same or different, a height of the elevations 54 ₁ and 54 ₂ may be the same or different based on the design criteria be different. Through the elevations 54 ₁ and 54 ₂ , a variable distance of the adaptation structure to at least one of the bending elements 26 ₁ and 26 ₂ can be obtained along an axial direction thereof.

The elevations 54 ₁ and/or 54 ₂ can consist of the same material as the layer 52 or of a different material. Forming the layer 52 and the ridges 54 ₁ , 54 ₂ from the same, possibly dielectric, material may allow for ease of manufacture. The ridges 54 ₁ and 54 ₂ may make it possible to reduce stiction effects by reducing the area on which contact is formed. From another perspective, the contact surface 22a/22b on the one hand and/or 22c/22d on the other hand can be separated or structured.

2g thus shows an exemplary base cell configuration with a structured insulator layer in an electrostatic air gap between the electrodes to reduce contact points during actuation, in a top view for planar bending and a side view for extra-planar bending, respectively.

In other words, the exemplary base cell configuration includes a patterned dielectric/insulator layer 52 in the electrostatic air gap between the electrodes to provide an effective contact area between the dielectric layer 52 and the electrodes 26 ₁ and 26 ₂ upon contact formation and evolution in the directions 44 ₁ , 44 ₂ to reduce when actuated.

A main advantage of the configuration 2g , for example compared to 2a or 2f , may be due to the presence of a low number of contact points, which can greatly reduce the static friction probabilities and also the dielectric charging of the dielectric layers due to the changing contact with the electrodes. The configuration 2g can achieve reduction of nonlinearity of cell response only by initial contact at the AA' plane and extending electrodes in the bending direction. To achieve this, continuous contact propagation is not required, and other structured areas are not necessarily required to reduce response nonlinearity. The other contact points (54 ₁ and/or 54 ₂ ) may be used for better guidance and greater stiffness gain when contact formation occurs thereon while generating a higher electrostatic force due to a higher effective relative permittivity.

Alternatively, the two electrodes 26 ₁ and 26 ₂ may also be structured (in a tongue and groove configuration) to have a reduced contact area for easier production. The The electrical layer and the electrodes can even be tongue-and-groove at the same time or manufactured into surfaces with a higher roughness (e.g. using DRIE etching processes of crystalline silicon to create deep corrugations on sidewalls of Si electrodes and Si- to create trenches that are filled with the conformal dielectric material, for example Al2O3, using an atomic layer deposition (ALD) process to take the shape of the trench and have a high surface roughness when released).

The dimension of the electrodes, dielectric layers and air gaps can be in the same size arrangement as in 2a However, the overall stiffness of the cell must be reduced accordingly or an actuation voltage must be increased in order to be off 2g same bending range as in 2a since the presence of structured dielectric layers and air gaps will increase the total gap between electrodes 26 ₁ and 26 ₂ (particularly at the production resolution limits of the production process used, which will reduce the overall electrostatic forces), which is achieved by reducing the overall bending stiffness of the cell or the Increasing the actuation voltage can be compensated for). Cell bending stiffness can usually be achieved by using thinner and/or longer electrode/dielectric layers with higher dome angles.

3a shows a schematic top view or side view of a mechanical system 30 ₁ which, for example in comparison to the mechanical system 20 ₂ , has layers 18 ₁ to 18 ₄ of the adaptation structure 18 in order to cover the bending elements 26 ₁ and/or 26 ₂ on both sides, which can, for example, result in a number of four layers. That is, instead of a plurality of gaps as the mechanical system 20 ₂ has, a single gap 38 can be obtained.

In other words shows 3a an exemplary base cell configuration with a dielectric/insulator layer on all sides of the electrodes as a top view for a planar bend and a side view for an extra-planar bend, respectively. The exemplary basic cell configuration has a dielectric/insulator layer on all sides of the electrodes for a high dielectric constant in an electrostatic gap (for higher forces) and for complete and secure electrical isolation (even with an adjacent outer bar electrode). Furthermore, the intrinsic stress is inherently lower in such a configuration, particularly in the case of a homogeneous dielectric layer, which can be achieved via conformal deposition processes such as atomic layer deposition (ALD). For a system with a compact stacking of the bending cell beams ( 2b-e ) in a parallel manner, contact formation with external electrodes of cells from adjacent bars can also be achieved using a cell geometry as shown in 3a shown (via the outermost insulation layer on electrodes) to modulate the stiffness of the entire stack of actuator beams (in addition to contact formation and evolution in the electrostatic gap of the cell).

The structure according to 3a In addition to those already mentioned, e.g. B. compared to 2a or 2f , for more benefits.

For example, it provides simple and more controllable production of dielectric layers (18 _1-4 ) with a required thickness on the electrodes, in particular using standard MEMS and NEMS production processes and materials. Based on conformal deposition processes such as ALD, the dielectric layers can also be deposited to obtain much smaller air gaps than the production resolution limits by coating the cell geometry after production to have lower actuation voltages.

Furthermore, the limit of structural integrity is not a limiting factor of the required minimum thickness of the dielectric layer, the only main limit is the electrical breakdown limit at the maximum operating voltage.

However, there are significantly more areas with conductor/metal to dielectric/insulator material interfaces, which can lead to higher charging effects and increasing frictional adhesion probabilities between contact surfaces. For higher charging effects that lead to frictional adhesion problems, which can be solved by design methods such as stiffer electrodes with electrostatic attraction and/or repulsion effects (pull-in or pull-out) for contact formation or their easier opening, conformal non-stick friction coatings can be used , such as an ALD-deposited FDTS (perfluorodecyltrichlorosilane) layer, or the system can be operated via amplitude-modulated AC electrical signals at much higher frequency than a cell's maximum mechanical response frequency to rapidly electrically discharge the cells and any Reduce charging effects.

3b shows a schematic view of a mechanical system 30 ₂ in which only the internal adaptation structure layers 18 ₁ and 18 ₂ are arranged compared to the mechanical system 30 ₁ , as a non-limiting example. The second nonlinear mechanical stiffness contribution can thus be different compared to the mechanical system 30 ₁ . However, electrical insulation can still be maintained.

In other words shows 3b an exemplary base cell configuration with an insulator layer on electrodes only on the side of the electrostatic gap between the electrodes to reduce dielectric charging, in a top view for a planar bend and a side view for an extra-planar bend, respectively. The exemplary basic cell configuration has an insulator layer on electrodes only on the side of the electrostatic gaps between the electrodes to reduce probabilities of possible dielectric charging and associated stiction probabilities, while having a high dielectric constant in the electrostatic gap (for higher forces) and a required electrical Isolation should be maintained.

Compared to the structures 2a , 2f and or 3a can have advantages according to the structure 3b , in addition to those already mentioned, is that the structure is an intermediate compromise configuration between 2a and 3a is - which has less charging, static friction and interfaces compared to 3a while still having the mechanical structural integrity of dielectric layers coming from the electrodes, as opposed to 2a . However, due to the absence of counteracting self-stresses from reversed interfaces, the total self-stress will be higher than 2a and 3 exhibit,.

3c shows a schematic view of a mechanical system 30 ₃ , which, starting from the mechanical system 30 ₂ , has only one of the adaptation structures 18 ₁ and 18 ₂ , for example the adaptation structure 18 ₁ . This can further reduce the dielectric charge while still providing insulation between the electrodes 26 ₁ and 16 ₂ . The second nonlinear stiffness contribution can advantageously be applied to one of the bending elements 26 ₁ and 16 ₂ , thereby providing a further degree of freedom. Compared to the mechanical system 20 ₁ in which the adjustment structure 18 is symmetrical between the flexures 26 ₁ and 26 ₂ , different spacings can be implemented with respect to the flexures 26 ₁ and 26 ₂ , with one of the spacings possibly being reduced to zero , as shown for the mechanical system 30 ₃ .

In other words shows 3c an exemplary base cell configuration with an insulator layer only on an electrode on the side of the electrostatic gap between the electrodes to reduce a dielectric charge, in a plan view for a planar bend and a side view for an extra-planar bend, respectively. The exemplary basic cell configuration includes an insulator layer only on one electrode on the side of the electrostatic gap between the electrodes to further reduce probabilities of potential dielectric charging and associated stiction probabilities, while having a high dielectric constant in the electrostatic gap (for higher forces) and a required electrostatic insulation can be made possible.

Instead of applying a single adaptation structure 18 ₁ on the bending element 26 ₁ , the layer can also be applied on the outer side thereof and/or on the inner or outer side of the bending element 26 ₂ .

Compared to 3b can the structure 3c advantageously ensure fewer interface areas and thus less charging, as well as usually lower overall self-stress in the cell for the same design parameters (since self-stress of interfaces is usually more dominant). Furthermore, even better structural integrity and robustness of the dielectric layer can be obtained for lower thickness values, especially at the resolution limits of the production processes in the MEMS and NEMS area, compared to 3b , since to obtain the same level of electrical breakdown limit (which determines the maximum voltage that can be applied) the thickness of the dielectric layer on an electrode is different 3c the total thickness on each electrode 3b should be.

On the other hand, due to the increased required thickness of the dielectric layer on an electrode, the local self-stress on that specific electrode would be higher due to the higher thickness of the dielectric layer. Thus, local machining to compensate for self-stress on this electrode may be required for certain designs. Additionally, if traditional conformal but slow deposition processes such as ALD are used to deposit the dielectric layer, this will increase the deposition time by two times like to achieve the same level of dielectric thickness on one side of the electrode.

3d shows a schematic view of a mechanical system 30 ₄ according to an embodiment in which a single adaptation structure layer is applied, as described for the mechanical system 30 ₃ , the single layer being structured such that it forms an interrupted structure between the first Bending element 26 ₁ and the second bending element 26 ₂ is arranged.

In comparison to the mechanical system 30 ₃ , a structuring of the adaptation layer 18 ₁ , which, as a non-limiting example, is arranged in the mechanical system 30 ₄ at the bending element 26 ₂ , enables the implementation of a defined behavior of the nonlinear mechanical stiffness contribution on the one hand and a further reduced dielectric charge on the other hand, together with a low risk of frictional adhesion. The adaptation elements 56 ₁ , 56 ₂ , ..., which are obtained by structuring the adaptation structure 18, can be on a single bending element 26 ₂ and/or at least in parts on an opposite side, e.g. B. the bending element 26 ₁ , may be arranged.

In other words shows 3d an exemplary base cell configuration with a patterned insulator layer on only one electrode on the side of the electrostatic gap between the electrodes to reduce dielectric charging and contact points during actuation, in a top view for a planar bend and in a side view for an extra-planar bend, respectively. The exemplary base cell configuration includes a patterned insulator layer on only one electrode on the side of the electrostatic gap between the electrodes to further reduce dielectric charging and stiction probabilities by reducing the required dielectric material and contact points upon actuation.

Compared to 3c can the structure 3d advantageously ensure less interface areas and dielectric base material, thus less charging. Additionally, it can also provide a reduced number of contact points with the other potential electrode. There is therefore a significant overall reduction in the probabilities of static friction. Furthermore, a lower overall internal stress in the cell can be obtained for the same design parameters due to interrupted interfaces and reduced amount of base material.

However, due to the patterned dielectric layer resulting in dielectric islands/regions (56 ₁ , 56 ₂ ), probabilities of delamination between the electrode and the dielectric regions are higher compared to a continuous dielectric layer during contact formation and its propagation in each cycle all contact forces will be locally concentrated directly at the base of each region and must be sustained by the local interface between the electrode and the dielectric region.

For the same cell design, the electrostatic forces at a given voltage will be reduced because the effective relative permittivity (compared to the continuous dielectric layer) in the electrostatic gap is lowered due to a reduced amount of dielectric material with higher relative permittivity than air.

3e shows a schematic view of a mechanical system 30 ₃ according to an exemplary embodiment, wherein a groove structure with one or more grooves 58 ₁ is arranged in the intermediate space 38 and a spring structure with one or more springs 62 is arranged. The groove structure and the spring structure can form mechanical contact in a deflected state of the mechanical system 30 ₄ and avoid relative movement of the spring structure and the groove structure relative to each other along the x-direction that is perpendicular to the bending direction 14 of the bending transducer structure. With an increase in bending along the bending direction 14, an increased number of springs can form mechanical contact with the opposing groove, which can be understood, for example, as a discrete number of steps of contributions to the nonlinear stiffness behavior.

The groove structure and/or the spring structure can, for example, be provided by the adaptation structure 18, e.g. B. the adaptation elements 56 of the mechanical system 30 ₄ , whereby the grooves can also be implemented in a continuous or interrupted layer, for example in the layer 18 ₁ or 18 ₂ of the mechanical system 30 ₂ .

The groove structure and/or the spring structure can be formed from a material of one of the bending elements, for example the bending element 26 ₁ . Springs 58 ₁ and/or 58 ₂ can have the same material and can be formed in one piece with the bending element 26 ₁ and 26 ₂ . In an implementation in which the bending elements 26 ₁ and 26 ₂ are charged with an electrical potential, preferably at most one of the groove structure or the spring structure is formed by the electrode material of the bending element 26 ₁ or 26 ₂ , or as an alternative or in addition to this, an insulating material is arranged between them.

On the other hand, both the groove structure and the spring structure can be formed from a continuous or interrupted layer of the adaptation structure, for example from the layers 18 ₁ and 18 ₂ of the mechanical system 30 ₂ .

In other words, an exemplary base cell configuration with a patterned insulator layer on one electrode and a patterned opposing electrode for a flex locking mechanism for better contact locking and to improve effective stiffness increase with contact propagation while reducing dielectric charging and contact points upon actuation is shown in a top view for one planar bend or shown in a side view for an extra-planar bend. The exemplary base cell configuration includes a patterned insulator layer on one electrode and a patterned opposing electrode for a flex locking mechanism for better contact locking and to improve effective stiffness increase with contact propagation and a simultaneous reduction in dielectric charging and contact points upon actuation.

The structure 3e can compared to 3d provide increased displacement robustness, even if the same compared to 3d requires a larger gap between the cell electrodes in order to produce the required structures in the gap. Thus, the overall stiffness of the cell must be reduced or the actuation voltage must be increased in order to be off 3e same bending range as 3d to obtain. Compared to 3d can the structure 3e be made more easily.

3f shows a schematic view of a mechanical system 30 ₆ which, compared to the mechanical system 30 _3, has additional connecting elements 64 ₁ , 64 ₂ , ... which enable a further contribution to the second non-linear stiffness. The connecting elements 64 can have the same material as the adaptation elements 56, e.g. B. a dielectric material.

In other words shows 3f an exemplary base cell configuration with structured and linked insulator layer elements on one electrode and a structured opposing electrode for bend locking for better contact locking and improving effective stiffness increase with contact spreading and for simultaneous reduction of dielectric charging and contact points when actuated in a plan view for planar bending or in a side view for an out-of-plane bend. The exemplary base cell configuration includes a patterned and bonded insulator layer on one electrode and a patterned opposing electrode for a flex locking mechanism for better contact locking and improving effective stiffness increase with contact propagation and for simultaneous reduction of dielectric charging and contact points upon actuation.

Compared to 3e it can according to the structure 3f allow to reduce the probabilities of delamination due to mechanical bonding of the dielectric layer, also compared to 3e and or 3d , as the contact forces are now also distributed along the cell length up to the edge insulator 36 and are shared by side link elements (while still having a reduced area of interfaces) rather than simply concentrating locally directly at the base of each region (as in 3e and 3d ). However, this effect can cause it to be compared to 3e a larger gap between the cell electrodes is required to produce the required structures in the gap with the bending layer 64, particularly at the minimum production resolution limits of the typical MEMS and NEMS production processes. Thus, the overall stiffness of the cell must be reduced or an actuation voltage must be increased in order to operate 3e same bending range as in 3d to obtain. Compared to 3f can the structure 3e be made more easily.

3g shows a schematic view of a mechanical system 30 ₇ according to an exemplary embodiment, in which the connecting elements 64 are formed by a different material compared to the adaptation elements 56, e.g. B. a material of the bending elements 26 ₁ and 26 ₂ , e.g. B. a conductive material. Since the contact formation in the present example is provided exclusively in the area of the grooves 58 and tongues 62, a risk of a short circuit is still prevented while at the same time a low amount of dielectric charging is present. Optionally, a material of the connecting elements 64, which are insulated from the bending elements 26 ₁ , _{26 2 by} an insulating material on the clamp 28 ₁ and 28 2 , can be arranged in a region of the insulator 36 and 36 ₂ .

In other words shows 3g an exemplary basic cell configuration with a structured insulator layer on an electrode with floating electrodes, and a structured opposing electrode (spring structure) for a bend locking mechanism for better contact locking and to improve effective stiffness increase with contact spreading and a simultaneous reduction of dielectric charging and contact points when actuated in a planar bending plan view and in a respectively Side view for an extra-planar bend. The exemplary basic cell configuration includes a patterned insulator layer on one electrode associated with floating electrodes 64 (which may be used to charge and/or discharge the associated insulator structures to stabilize/modulate a system response in or after/before each cycle of operation), and a patterned opposite one Electrode for a bend locking mechanism for better contact locking and to improve effective stiffness increase with contact spreading and at the same time reduce dielectric charging and contact points when actuated.

Compared to 3f can the structure 3g advantageously provide better performance due to mechanical interconnection of dielectric regions/islands via standard electrode material, which usually has better mechanical properties such as higher breaking strength, elasticity, reduced plastic deformation or creep, etc. compared to standard dielectric materials (compare to 3f) , especially in the MEMS and NEMS area, and thus well-defined behavior can be obtained.

However, the structure can be made from 3g have mechanical connections based on an electrode/dielectric interface between island-linking bends (compared to 3f , where the same dielectric material is used) and thus probabilities of delamination may be higher (compared to 3f) , especially at the minimum production resolution limits of typical MEMS and NEMS production processes. Additionally, the effective relative permittivity will be lower due to less dielectric material. Thus, the overall stiffness of the cell must be reduced or an actuation voltage must be increased in order to operate 3g same bending range as in 3f to obtain what is a basis for a compromise. Compared to 3g production can be carried out according to the structure 3f be easier.

The exemplary embodiments described herein relate, among other things, to a mechanical coupling of the bending transducer structure and the adaptation structure. Such mechanical coupling may include a fixed placement of one element to another, for example, by using the rigidity of a substrate 66 and/or an insulating material and/or another material that conforms different elements to one another. The mechanical coupling between the conforming structure and the bending transducer structure may be adjusted to combine the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution to control the bending of the bending transducer structure based on a combination of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution. In the in 2a until 3g In the examples provided, the first nonlinear mechanical stiffness contribution and/or the second nonlinear mechanical stiffness contribution may be based on a mechanical contact between a first element and a second element of the mechanical system, for example between the bending transducer structure and the adaptation structure. Other contacts are possible and described herein. The mechanical contact may provide a variable magnitude of mechanical forces acting on the bending transducer structure and/or the adjustment structure, with an increase in bending amplitude, for example along or opposite to direction 14.

With regard to the provisions herein in connection with 2a until 3g In the embodiments described, a mechanical system may be configured to provide mechanical contact between the bending transducer structure 12 and the adjustment structure 18, for example by contacting opposing contact surfaces 22. The bending transducer structure 12 and the adjustment structure 18 are arranged to provide a contact surface with one another upon an increase in bending to enlarge the transducer structure, wherein the contact surface that is formed between the adaptation structure and the bending transducer structure, see for example 2a , and/or between a first element of the adaptation structure connected to the first element of the bending transducer structure and a second element of the adaptation structure connected to the second element of the bending transducer structure, such as in 3b is shown.

As in 2a until 3g is shown, in a non-deflected state of the bending transducer structure, a first neutral axis of the first bending element 26 ₁ can run substantially parallel to a second neutral axis of the second bending element 26 ₂ , in particular in a case in which both elements have a similar shape and run parallel to each other. Alternatively or additionally, a surface of the bending element 26 ₁ that faces the bending element 26 ₂ may be essentially be parallel to a surface of the element 26 ₂ that points to the bending element 26 ₁ .

As in 2a until 3g As shown, the adaptation structure 18 can be arranged partially or completely between a first section of the bending transducer structure and a second section of the bending transducer structure, each of which is formed, for example, by a respective bending element 26 ₁ and 26 ₂ . The adaptation structure can be arranged therebetween along a bending direction of the bending transducer structure. Like for example in 2a As shown, the bending transducer structure may have at least two bending elements 26 ₁ and 26 ₂ that are mechanically coupled in parallel and form a gap 38 or more gaps with an adjacent bending element of the bending transducer structure or the adaptation structure or a part thereof. At least part of the adaptation structure is arranged in the intermediate space and mechanically coupled in parallel to the adjacent bending elements via the mechanical contact. Bending of the bending transducer structure along direction 14 may cause mechanical contact between the conforming structure 18 and at least one of the adjacent bending elements in the gap, either directly with the element or with a layer attached thereto. For example, assuming the mechanical system 20 ₁ , a mechanical system according to embodiments may further include three or more bending elements 26 that are mechanically coupled in parallel to form at least a first gap between a first bending element and a second bending element and at least one other To form a space between the second bending element and a third bending element. For example, the mechanical system 20 ₁ may have at least a third bending element 26 ₃ , which is arranged, for example, to clamp the bending element 26 ₂ between the bending element, not shown, and the bending element 26 ₁ . Different parts of the matching structure may be located in the different spaces to form different contacts, either simultaneously or at different times.

4a shows a schematic view of a mechanical system 40 ₁ according to an exemplary embodiment. Compared to other mechanical systems described herein, for example mechanical system 20 ₁ or 30 ₁ , the flexures 26 ₁ and 26 ₂ may have different shapes and/or different properties. Although neutral axes of the bending elements 26 ₁ and 26 ₂ in the example 4a do not run parallel, the sides 26 ₁ A and 26 ₂ B of the bending elements 26 ₁ and 26 ₂ run essentially parallel in the unactuated state shown.

Similar to other embodiments, actuation and/or an external force F may cause contact to be formed in the contact surfaces 22a/22b between the conforming structure layers 18 ₁ and 18 ₂ , increasing along the directions 44 ₁ and 44 ₂ the deflection increases.

In other words shows 4a an exemplary cell configuration with fully insulated electrodes and straight bottom electrodes for downward bending along the direction 14 in a top view for a planar bend and in a side view for an extra-planar bend, respectively. The term downward bend refers to a direction of view 4a and is not necessarily linked to an orientation of the mechanical system 40 ₁ in space. It will be apparent to those skilled in the art that terms such as up, down, left, right, front, back, or the like may change arbitrarily in space as a mechanical system 40, or other embodiments, rotates.

Despite the presence of a planar or straight element 26 _2, the bending direction 14 can be influenced at least by the shape or structure of the bending element 26 ₁ . The exemplary cell configuration includes fully insulated electrodes and straight bottom electrodes for downward bending. A straight electrode geometry is particularly useful for creating extra-planar S-configuration bending beams, as an ordinary straight bottom electrode can be used to create up and down bending cells in the cell beam for ease of production. Furthermore, the use of deposition-based conformal dielectric layers required for isolation-based contact formation (34 ₁ and 34 ₂ ) and their evolution (44 ₁ and 44 ₂ ) in an electrostatic gap reduces the achieved effective air gap much more than the typical production limit of the physical one air space. This significantly increases the electrostatic forces due to an increase in the effective dielectric constant in the electrostatic gap. It also increases the electrical reliability of the system against electrical short circuits between electrodes against accidental contact formation. The straight electrode side (planar and extra-planar) can also be used directly if required for certain applications, such as those applications requiring well-defined formation of borders based on a straight wall such as micropumps, microvalves, microspeakers, etc .require to effectively control the fluid pressure distribution.

4a shows, among other things, another embodiment of the present invention, according to which the inventive concept is not limited to a geometry of curved electrodes/dome electrodes. Other advantages provided include, for example, that this type of geometry can be more easily produced at the wafer level compared to curved electrodes/dome electrodes to achieve an extra-planar, e.g. B. downward bending system using standard wafer-level MEMS production processes (e.g. wafer bonding and patterning of the electrodes via volume micromachining processes) due to the planar nature of the electrode geometry. Due to the use of wafer bonding and bulk micromachining processes, the prestress in these structures can be significantly lower compared to out-of-plane configurations formed by surface micromachining, which require thin film deposits. A general design constraint (but not absolute) for effective bending behavior is that the local electrode thickness is thinner in areas such that bending in that particular direction is facilitated.

4b shows a schematic view of a mechanical system 40 ₂ according to an exemplary embodiment, which can be viewed as complementary to the mechanical system 40 ₁ . While the mechanical system 40 ₁ may have increased stiffness at a center of the flexure 26 ₁ along an axial path, a flexure 26 ₁ may have a thinning 68 in the center, thereby locally weakening the structure or reducing mechanical stiffness. Compared to the mechanical system ₄₀₁ , the bending direction 14 is reversed in direction. While the flexure 26 ₁ of the mechanical system 40 ₁ and 40 ₂ may have complementary properties, as a non-limiting example, the flexure 26 ₂ is planar in both ways, with a non-planar implementation also selected for the mechanical system 40 ₁ and 40 ₂ and can be implemented.

In both configurations, the bending transducer structure may include at least two bending elements 26 ₁ and 26 ₂ which may be secured to one another at discrete positions, such as clamps 28 ₁ and 28 ₂ . Along a bending direction 14 along which the bending transducer structure 12 is configured to provide the bend, a stiffness of one of the bending elements differs compared to the other bending element.

That is, local stiffness may be variable from section to section of the electrodes to achieve upward or downward bending while having a specific desired planar electrode topology on one side of the transducer element.

In other words shows 4b an exemplary configuration with fully insulated electrodes and straight bottom electrodes for upward bending in a top view for a planar bend and in a side view for an extra-planar bend, respectively. The exemplary cell configuration includes fully insulated electrodes and a straight bottom electrode for upward bending. The cell configuration 4a can be used together with this configuration to create a cantilever with extra-planar/planar S configuration using an ordinary straight-bottom electrode.

4b illustrates another embodiment of the present invention, according to which the concept is not limited to a geometry of curved electrodes/dome electrodes. Other advantages achieved are that this type of geometry can be more easily produced at the wafer level (compared to curved electrodes/dome electrodes) to achieve an extra-planar, e.g. B. upward, bending system using standard wafer-level MEMS production processes (e.g. wafer bonding and patterning of the electrodes via volume micromachining processes) due to a planar nature of the electrode geometry. Due to the use of wafer bonding and bulk micromachining processes, the prestress in these structures can be significantly lower compared to out-of-planar configurations formed by surface micromachining, which requires thin film deposition. A general design constraint (but not absolute) for effective bending behavior is that the local electrode thickness is thinner in areas such that bending in that particular direction is facilitated.

While other embodiments have been described as having, in a non-deflected state of the mechanical system, one or more bending elements with a curved path between a first end and a second end of the bending element 26 ₁ /26 ₂ to the direction 14 of the bend define, it is also possible to implement angular gradients, such as in 5a is shown, which illustrates a schematic view of a mechanical system 50 ₁ . In a symmetrical or asymmetrical manner, curved but possibly straight elements of the bending elements 26 ₁ and 26 ₂ arranged with an angle α between them, the angle α being, for example, a value of less than 170° or more than 190°. For example, in comparison to the mechanical system ₂₀₁ , this can lead to contact formation on two separate surfaces 22a/22b on the one hand and 22c/22d on the other hand, next to a central plane A-A', indicated by the planes BB' and C-C'. This allows the amount of the second nonlinear mechanical stiffness contribution to be adjusted, e.g. B. be increased.

A strong dependence of α can be seen with respect to the distance of the contact formation planes BB' and CC' from the symmetry plane AA' (as well as on the bending effect/curvature achieved when voltage is applied). For example, as α increases (and other dimensions remain almost constant), the B-B' and C-C' planes may come closer to the A-A' plane (at one point they will almost overlap, as in 2a , when the system becomes flat “enough” and the first contact will occur almost at the A-A' plane of symmetry). However, this is only a general case and there may be exceptions for asymmetrical designs or extreme α values.

In other words, to show another embodiment of the present invention, according to which the concept is not limited only to a geometry of dome electrodes/straight electrodes or to formations of centralized single point contacts and their distribution 5a an exemplary cell configuration with fully isolated electrodes and multiple non-centralized physical contact formation sites and proliferation of contacts in a top view for a planar bend and in a side view for an extra-planar bend, respectively. The exemplary cell configuration includes fully isolated electrodes and multiple non-centralized physical contact formation sites and proliferation of contacts. Although symmetrical for the present geometry (around the A-A' plane), the contact formation sites do not need to be symmetrical for the stiffening principle to work to allow an order of nonlinearity in the system's responses to be reduced. The contact locations and distribution of contacts can be changed asymmetrically based on a cell geometry (e.g. asymmetrical cell design) and/or by changing the loading conditions (e.g. asymmetrical load distribution on the cell structure).

5b shows a schematic view of a mechanical system 50 ₂ according to an exemplary embodiment. In comparison to the mechanical system 50 ₁ , the findings associated with the mechanical systems 40 ₁ and 40 ₂ are combined, that is, at least one of the bending elements 26 ₁ and 26 ₂ can have a variable stiffness and/or a variable thickness along the Have an axial course along the x direction.

A key difference between the structures 5b and 5a may be that a bottom electrode stiffness can be increased by making it thicker (filling an empty roof), as a possible way to further shift the contact formation planes towards the quarter length of the cell (since then the higher stiffness regimes are usually reached much more quickly to modulate the contact propagation lengths on both sides of the contact plane to tune the ranges of linear regimes as required.

It should be noted that a ground electrode with bending systems (as in 8a shown by elements 84 ₁ and 84 ₂ ) or a different roof angle α can also be used to change the location of the plane of the contact formations.

However, for a given air gap, the increase in the stiffness of the bottom electrode may be compensated for by a corresponding reduction in the overall stiffness of the cell, or the actuation voltage must be increased to achieve this 5b same bending range as in 5a to obtain.

In other words shows 5b an exemplary cell configuration with fully isolated electrodes and multiple non-centralized physical contact formation sites and a proliferation of contacts due to a bottom electrode geometry in a top view for a planar bend and in a side view for an extra-planar bend, respectively. The exemplary cell configuration has fully isolated electrodes and multiple non-centralized physical contact formation sites and a proliferation of contacts compared to 5a are symmetrically shifted (C-C' and B-B' planes), with the cell design being based on a bottom electrode geometry of the cell.

6a shows a schematic view of a mechanical system 60 ₁ , which has three, optionally a higher number, bending elements 26 ₁ , 26 ₂ and 26 ₃ as components of the bending transducer structure. Between adjacent bending elements 26 ₁ and 26 ₂ on the one hand and 26 ₂ and 26 ₃ on the other hand, adaptation structure layers 18 ₁ and 18 ₂ are arranged, which ensure a respective contact formation area 22 ₁ and 22 ₂ with an increase in movement 34 ₁₁ to 34 ₂₂ . For example, by a number of three electrodes is present, these can be connected to different or grouped potentials, for example a reference potential GND on the outer electrodes 26 ₁ and 26 ₃ and a potential difference thereof on an inner element 26 ₂ . Any other configuration is also possible. This can enable jointly or selectively controlled pairs of electrodes 26 and 26 ₂ on the one hand and 26 ₂ and 26 ₃ on the other. The pairs of elements 26 ₁ and 26 ₂ on the one hand and 26 ₂ and 26 ₃ on the other hand can each form a dome-like structure, which leads to an at least two-domed structure.

Although the bending elements 26 ₁ , 26 ₂ and 26 ₃ are shown as having a curved shape along the axial direction x, they may alternatively or in combination have an angular shape.

In other words shows 6 an exemplary two-dome base cell configuration with insulator layers between the electrodes for both electrostatic air gaps 38 ₁ /38 ₂ and 38 ₃ /38 ₄ in a top view for a planar bend and in a side view for an extra-planar bend, respectively. The exemplary two-dome base cell configuration has insulator layers between the electrodes for both electrostatic air gaps. A dual-dome cell design experiences higher bending curvatures and deliverable forces for a given voltage and chip area relative to standard single-dome structures air gaps with the shape of two domes used in a compact form factor. With the use of contact formations and their evolution based on a deposited dielectric layer in the electrostatic gaps, even higher bending curvatures and deployable forces can be obtained along with a reduced magnitude of nonlinearity in the system's response.

A structure according to 6a ensures the advantage that, in view of their high performance, two-coupled cells can best be used in planar NED structures for numerous components in practice.

6b shows a schematic diagram with a normalized stress on the abscissa and a normalized curvature of a mechanical system, for example the mechanical system 60 ₁ , on the ordinate. The curves 74 ₁ and 74 ₂ show different behaviors, with the curve 74 ₂ showing a non-linear response of the bending transducer structure, ie coupled bending elements 26 ₁ and 26 ₂ , without forming contact with the matching structure, which is caused, for example, by a low insufficient thickness of the insulating layer in the air gaps can be obtained. In comparison, diagram 74 ₁ shows an increased thickness of the insulating layer allowing contact between the conforming structure and the flexural transducer structure. It can be seen that a linearized behavior of version 2 starting from the first contact formation at a normalized voltage of 0.8 is higher than compared to 3 , showing the linearized behavior after initial contact formation at a normalized voltage of 0.5.

The term "sufficient" insulator thickness may refer to a thickness that can withstand the voltage applied across it throughout the operating range without electrical breakdown upon contact formation and its distribution.

For a given cell design, contact formation can always be achieved at a certain higher voltage (with/without attraction) until the insulator thickness allows such a particularly high voltage to be applied across it without electrical breakdown. The only thing that changes is the location of the formation of the first contact in relation to the applied voltage and the length of the linear regime. If contact formation at lower voltages is desired, the stiffness of the cell electrodes can be reduced to allow easier movement of the electrodes towards each other at lower voltage, or narrower gaps between the electrodes can be used (for higher electrostatic forces to move the electrodes towards each other and for less distance that electrodes have to move before contact with the insulation layer occurs).

The general optimum thickness of the insulator layer may be a minimum value at a location or tolerance range that can withstand the maximum possible operating stress of the entire regime, while also having the structural integrity and mechanical robustness required to withstand the high compressive forces during contact formation and -to withstand spread without mechanical breakage (and thus possible electrical breakdown).

For a fixed gap between the electrodes (usually as small as possible, the minimum value at the production resolution limit is best), the thicker the electrical insulation, the less the electrodes have to move in order to achieve contact formation and in one linearization regime. In the case of dielectric layers, the total electrostatic forces due to an increase in the effective dielectric con The constant of the electrostatic gap increases as the layer is thicker, which also helps in faster contact formation for a given voltage. Thus, insulator thickness can be used to control contact formation and the amount of contact propagation allowed before electrical breakdown occurs therein.

To obtain smooth/abrupt transition to a linear regime: Normally, an insulator/dielectric layer thickness of more than 2/3 of a total gap between electrodes can be used to obtain contact formation before a tightening phenomenon for a smooth transition to a linear regime occurs. If attraction is desired for reasons mentioned above, then larger air gaps can be used if the insulator thickness is already at the limit of electrical breakdown or mechanical structural integrity and cannot be reduced for the maximum operating voltage required.

It should be noted that in addition to the insulator thickness, contact formation and propagation also depends on a local stiffness of the contact surface during bending (which depends on the electrode thickness, length, geometric topology, topology angle (if any), etc., and the actuation forces, which are generated in the region of contact formation and propagation (which depends on the applied voltage, the electrostatic air gap, the effective dielectric constant, etc.).

A similar principle for combining nonlinear behavior can be implemented in any other mechanical system described herein. That is, a mechanical system according to embodiments may include a bending transducer structure configured to nonlinearly deform based on a bend in response to an applied electrical signal and/or to nonlinearly provide an electrical signal in response to an applied external force causing the bend . The mechanical system includes an adjustment structure that is mechanically coupled to the bending transducer structure, the bending and a deformation of the adjustment structure being causally correlated with one another, the deformation of the adjustment structure providing a nonlinear force for the bending transducer structure that has the magnitude of the nonlinearity in an overall response of the mechanical system is reduced, for example the bend is linearized, i.e. H. results in a linear spring or ensures a desired non-linearity. In the case of spring configurations, linearization is not necessarily obtained for the complete response regime in every case. However, compared to systems without a spring, i.e. H. springless systems, a reduction of non-linearity in the overall response is present.

In other words shows 6b an exemplary cell bending curvature compared to an actuation voltage (normalized with respect to maximum values) from a finite element method (FEM) simulation of identical two-dome cell geometries with sufficient (T2) / insufficient (T1) thicknesses of the insulator layer in the air gaps to achieve a Contact formation / no contact formation in the area of the applicable voltage. The exemplary cell bending curvature is then plotted against the actuation voltage (normalized with respect to maximum values) from FEM simulations of identical two-coupled cell geometries (same cell as in 6a shown) with sufficient (T2) / insufficient (T1) thicknesses of dielectric / insulator layer in the identical air gaps and a cell geometry shown to obtain contact formation / no contact formation in the range of the applicable voltage. It is important to note that for most of the operating voltage range, the achieved curvature in the contact formation region is higher due to contact-based operation through a sufficiently thick dielectric layer (T2) compared to a system without contact formation (T1), even with linearized response.

6c shows a schematic diagram corresponding to the diagram 6b similar, with an additional curve 74 ₃ a version 2 of the two-domed cell geometry 6b where the version which does not perform contact formation due to insufficient thickness of the insulator layer is referred to as version 1, and the curve 74 ₁ which shows high linearity is shown as a version 3.

In other words shows 6c an exemplary cell bending curvature compared to an actuation voltage (normalized with respect to maximum values) from an FEM simulation of different versions of two-coupled cells to obtain a design-based adjustable position of a first contact formation in the range of the applicable voltage. The exemplary cell bending curvature is shown versus the actuation voltage (normalized with respect to maximum values) from FEM simulations of different versions of two-coupled cells to have a design-based adjustable position of the first contact formation in the range of the applicable voltage. Versions 1 and 3 balance the T1 and T2 cell designs 6b , while version 2 has a similar cell design to version 3, but with larger air gaps, to move the first contact formation point with respect to the applied voltage. This exemplary case demonstrates the high flexibility in design possibilities of the present configurations of this invention to easily tune the response of the system.

6d shows a schematic diagram with the normalized voltage on the ordinate and the normalized curvature on the abscissa to show the behavior of a produced test sample of the two-coupled cell, such as in 6a is shown to illustrate with regard to deformation hysteresis. As can be seen, there is only a small difference between a positive cycle start-up behavior shown in curve 78 ₁ and a positive cycle run-off behavior shown in curve 78 ₂ , that is, there is a small hysteresis , which is consistent with the FEM simulation illustrated in curve 78 ₃ . The curves 78 ₁ , 78 ₂ and 78 ₃ refer to version 3, for example 6c .

In other words shows 6d an exemplary cell bending curvature compared to an actuation voltage (normalized with respect to maximum values) from a FEM simulation and experimental measurements of produced test samples of a two-coupled cell, which demonstrates negligible curvature hysteresis in a forward and backward evolution of a contact during voltage startup and decay. The exemplary cell bending curvature is shown versus the actuation stress (normalized with respect to maximum values) from an FEM simulation and experimental measurements of a produced test sample of a two-coupled cell (same geometry as 6a , 6b-T2 and 6c , version 3), demonstrating negligible bending curvature hysteresis in a forward and backward evolution of a contact with voltage start-up and release. The experimental results practically demonstrate that the expected negligible motion hysteresis (which usually occurs due to stiction between contacting surfaces or charging problems during zipper operation and zipper release cycles), and also demonstrates reproducibility and reliability of performance of the systems.

6e shows a schematic diagram again showing the normalized stress on the ordinate and the normalized curvature of the mechanical system 60 ₁ , curves 78 ₁ and 78 ₂ 6d , shows. In other words shows 6e an exemplary cell bending curvature compared to an actuation voltage (normalized with respect to maximum values) of test samples produced from experimental measurements of a two-coupled cell, demonstrating a negligible charging effect in successive runs of positive and negative voltage cycles. The exemplary cell bending curvature is shown in comparison to the actuation voltage (normalized with respect to maximum values) from experimental measurements of test samples produced from a two-coupled cell (same geometry as 6a , 6b-T2 and 6c , version 3), which demonstrates a negligible charging effect in successive runs of positive and negative voltage cycles.

While at least some of the embodiments described above show the adaptation structure 18 being disposed at least partially or even completely within the volume 24 defined by the flexure transducer structure, such an implementation is not required, for example in connection with 1a and 1b is described.

7a shows a schematic view of a bending transducer or a mechanical system 70 ₁ according to an exemplary embodiment, in which the adaptation structure 18 is at least partially arranged outside the volume 24 or an active area of the transducer. For example, the adaptation structure 18 may have one or more bending beam structures 84 ₁ , 84 ₂ of the same or different thickness, ie an extension along the y-direction. Both ends thereof are connected to the bending transducer structure 12, which includes, for example, having the common areas of the clamp 28 ₁ and 28 ₂ , with at least a first end 86 ₁ connected to the clamp 28 ₁ or being part of the clamp 28 ₁ can also be connected to the common substrate 66 without losing the advantages of the present invention. Even if the end 86 ₁ is contacted with the substrate 66, this should still be understood to mean that the end 86 ₁ is connected to the bending transducer structure 12, for example via the substrate 66. The adaptation structure 18 is configured to provide adaptation formation, e.g. B. bend, as a bend of the bending beam structures 84 ₁ and 84 ₂ .

As has been described in other embodiments of contact formation between the conforming structure and the flexure transducer structure, contact formation in the mechanical system 70 ₁ between the flexure beam structures 84 ₁ and 84 ₂ may occur based on movements 34 ₁ and 34 ₂ along a same direction (+ y) to ensure, for example, contact formation at the plane AA', which increases along contact evolution directions 44 ₁ and 44 ₂ . At one point a contact formation In contact surfaces 22a/22b, for example plane AA', the bending elements 26 ₁ and 26 ₂ can move towards one another, as shown by the direction of movement arrows 88 ₁ and 88 ₂ . The bending elements 26 ₁ and 26 ₂ can, for example, provide contact therebetween, but this is not necessary. Whether or not contact is provided may depend at least in part on the amplitude of the deflection along the bending direction 14 and/or a size of the gap 38, for example a distance between the bending elements 26 ₁ and 26 ₂ along the +y direction.

It is a general condition that 84 ₂ should be thinner than 84 ₁ . For example, the outermost bend 84 ₂ , due to its furthest position from a neutral fiber of the cell (particularly compared to 84 ₁ ), may experience the maximum compressive bending moment, and thus its inward bend will be stronger than compared to 84 ₁ , especially if it has a bending stiffness lower than 84 ₁ . If 84 ₂ is thinner, it will have a much lower stiffness to bending, and thus its inward bending will be significantly stronger than that of 84 ₁ , and thus contact formation with 84 ₁ will be achieved in a reliable and rapid manner when flexed (which in turn is necessary to increase cell stiffness in a non-linear manner upon bending).

The air gap 92 will affect two important points: 1) The larger the gap 92, the greater 84 ₂ experiences a compressive bending moment with respect to 84 ₁ (and thus the inward deflection amount for a fixed bending stiffness of each bend/flexion), on the other hand : 2) The larger the gap, the more the bend 84 ₂ must move inward with respect to 84 ₁ to obtain initial contact formation.

Typically, the most effective case of cell bending and contact formation is when both gaps 92 and 38 are as small as possible (depending on the manufacturing process used) and a gap 92 is smaller than 38 so that contact formation occurs at lower voltages and higher electrostatic forces , and thus a higher bending moment, can be generated at lower applied voltages (for the gap 38). Additionally, the inward deflection of 84 ₂ is significantly increased by using a much thinner 84 ₂ with a longer length compared to 84 ₁ to provide faster and reliable contact formation. This is also shown in 7a .

A gap 92, which is arranged between the bending elements 84 ₁ and 84 ₂ of the adjustment structure 18, can be adjusted with respect to the distance between the bending beams 84 ₁ and 84 ₂ along the +y direction in order to determine the amplitude of the deflection, which ensures the first contact and thus the linearization effect. During bending of the bending transducer structure 12, the adjustment structure 18 is configured to form contact between the bending beam structures 84 ₁ and 84 ₂ in a contact area 22a/22b that increases with an increase in a bending amplitude of the bending transducer structure along the bending direction. Contacting the ends 86 ₁ and 86 ₂ with the clamping and/or with the material of a bending element 26 ₁ or 26 ₂ may allow the bending beam elements 84 ₁ and/or 84 ₂ to be more flexible in comparison to the adjacent bending element 26 _1, 26 ₂ are at the same potential. However, this is not a problem because mechanical contact does not lead to short circuits or the like.

In other words shows 7a an exemplary cell configuration with a dedicated structure for contact formation and evolution outside the electrostatic air gap and avoiding mandatory insulator-based contact for flexible design options and further reducing friction probabilities between contact surfaces due to any direct charging in a planar bend plan view, respectively a side view for an extra-planar bend. The exemplary cell configuration has a dedicated structure for contact formation and evolution outside the electrostatic gap and avoids mandatory insulator-based contact for flexible design options and further reduction of stiction probabilities between contact surfaces due to charging of a dielectric layer or electrostatic charging of a contact surface Contact surfaces will be at the same voltage without any dielectric layer between them. As a cell bends upon actuation, both structural beams 84 ₁ and 84 ₂ bend inward (34 ₁ and 34 ₂ respectively). The inward movement of 84 ₂ (34 ₂ ) will be greater than that of 84 ₁ (34 ₁ ) because 84 ₂ is designed to have a much lower stiffness (with reduced width, longer length, etc.) than 84 ₁ , and is also placed further from the neutral fiber of the cell geometry compared to 84 ₁ , and thus undergoes greater bending in the 34 ₂ direction compared to 84 ₁ . This results in contact formation at a required actuation voltage level due to cell bending. Contact formation and its propagation (44 ₁ and 44 ₂ ) upon cell actuation and subsequent cell bending results in an increase in overall cell stiffness, which can be used to counteract the nonlinearity resulting from the increase the electrostatic forces arise in the electrostatic gap 38 when the actuating voltage is applied. The contact surfaces in this case have significantly reduced probabilities of stiction because the contact surfaces have no dielectric between them and are also maintained at the same voltage level, thereby negating probabilities of stiction due to dielectric charging or electrostatic forces originating from any retained potential difference. Stiction due to adhesion between the contacting surfaces can be reduced, if necessary, through the use of structured surfaces (similar to the texturing described in 3d , 3e , 3f or 3g is shown) can be further reduced to limit the effective contact surface.

7b shows a schematic view of a mechanical system 70 ₂ that has shorter bending beams 84 ₁ and 84 ₂ compared to the mechanical system 70 ₁ , which can lead to offsets 94 ₁ and/or 94 ₂ so that the adjustment structure 18 the bending transducer structure 12 closer contacted to a center, for example closer to the A-A' plane. The offsets 94 ₁ and 94 ₂ can be implemented independently, that is, only one or both offsets can be present and/or the offsets 94 ₁ and 94 ₂ can differ in size, providing a further degree of freedom in terms of normalization a combination of cells 70 ₂ , for example in combination with other cells.

In other words shows 7b an exemplary cell configuration with a shifted position of the dedicated contact forming structure outside the electrostatic air gap 38 to change the occurrence of the first contact and its evolution with the applied actuation voltage, in a top view for a planar bend and in a side view for an extra-planar bend, respectively . The exemplary cell configuration includes a shifted position of the dedicated structure (for contact formation outside the electrostatic air gap) to postpone the occurrence of the first contact and its evolution with the applied actuation voltage. This is achieved with the help of a cumulative effect of positional displacement of the bending beams 84 ₁ and 84 ₂ with respect to a neutral fiber of the cell and a direct influence on the bending of the bottom electrode at the applied voltage, as the contact formation and propagation (44 ₁ and 44 ₂ ) will also limit the bending deformation of the bottom electrode 1b when voltage is applied, especially at the highest deformation of the electrostatic gap (38) on the plane AA in the direction 88 ₂ . This affects the system response primarily in two ways, firstly due to an increase in the overall cell stiffness upon contact formation and its propagation, and secondly by limiting the generation of the electrostatic force in the gap 38 by limiting the local gap reduction, particularly from the direction 88 ₂ at the AA' plane, compared to cases where there is no direct feedback of mechanical coupling with cell bending to limit the localized deformation of the bottom electrode, and thus the electrostatic gap, such as in 7a .

It can appear as a difference between structures 7b and 7a can be considered to be the overall bending stiffness of the cell 7b (compared to 7a) can increase more non-linearly with respect to an applied voltage (assuming that contact formation occurs at the same voltage as in 7a occurs, by reducing the stiffness of the contacting diffractions), while also reducing the rate of reduction of the gap between the electrodes at higher voltage due to mechanical feedback to the bottom electrode, so that a rate of increase in the generated electrostatic forces is also reduced - thus by moving the Dedicated structure position inward usually the higher stiffness regimes are obtained, while a rate of generated electrostatic forces is also restricted - this helps to modulate the regimes of reduced magnitude nonlinearities depending on the requirement in the same cell area (compared to 7a) . In addition, cell bars can be compared to 7a stacked more closely in parallel, providing optimal space utilization and better compactness at the system level.

With regard to the mechanical systems 70 ₁ and 70 ₂ , the number of two bending beams 84 ₁ and 84 ₂ coupled in parallel is selected as an example only. The number can be different, for example more than two, for example 3, 4, 5 or a higher number. According to one embodiment, the number of bending elements can also be 1 if, for example, a spring structure is included, as in connection with 7c is described, which shows a schematic view of a mechanical system 70 ₃ , wherein the adjustment structure 18 includes the bending beam structures 84 ₁ and 84 ₂ arranged in series and having a spring structure 96 arranged therebetween. The spring structure 96 can be adapted to locally reduce a distance from the bending transducer structure 12 in a non-deflected state of the mechanical system like, for example by pointing locally to the bending transducer structure 12. For example, the spring structure 12 may have two or more curved deformable elements 96 ₁ , 96 ₂ which, for example, have a curved shape. The curved shapes may contact each other to form a peak in the contact area, with the peak pointing towards the bending transducer structure 12 in the example shown.

The spring structure 96 may have a linearized spring characteristic, for example, by implementing a double-curve implementation shown with a zipper contact surface in the gap 92. The spring structure 96 may be configured to form mechanical contact with the bending transducer structure 12, for example by making the amplitude of the deflection along the bending direction 14 high enough. From the state shown, a deflection along the bending direction 14 based on the mechanical coupling with the adaptation structure 18 can lead to a bending of spring elements 96 and 96 ₂ due to the transport of forces via the bending beams 84 ₁ and 84 ₂ . It should be noted that the elements 84 ₁ and 84 are advantageously flexible in order for the mechanical system 70 ₃ to have high strength, but that a rigid structure can also be arranged to transport forces to the spring structure 96. Bending the bending transducer structure 12 along the bending direction 14 can cause movements 34 ₁ and 34 ₂ of the spring elements 96 ₁ toward one another to increase the area of contact formation 22. At the same time, the spring structure, for example a tip thereof, can move along a direction 44 towards the bending transducer structure 12, for example until mechanical contact occurs, the mechanical contact being possible but not necessary.

In other words shows 7c an exemplary cell configuration with a dedicated structure for contact formation outside the electrostatic air gap 38 with a guided contact formation and an evolution for faster initial contact formation with the applied actuation voltage in a top view for a planar bend and in a side view for an extra-planar bend. The exemplary cell configuration has a dedicated structure (for contact formation outside the electrostatic air gap) with guided contact formation and evolution for faster initial contact formation at the applied actuation voltage. The guidance in the beam structure (84 ₁ /84 ₂ ) helps with a smooth and rapid transition to contact formation (34 ₁ and 34 ₂ ) and contact distribution (44) in the gap 92. Based on the guided mold curvature and thickness 84 ₁ /84 ₂ contact formation and propagation and their effect on cell bending stiffness can be regulated.

An advantage of the structure according to the 7c compared to that 7a-b may be due to the fact that the contact formation is demonstrated by the elements 96 ₁ , 96 ₂ and is faster, by the same amount of bending deflection as in 7a-b to reach. In addition, the rate of increase in stiffness with bending is related to contact propagation 7a usually be higher for similar thickness diffractions.

7d a schematic view of a mechanical system 70 ₄ according to an exemplary embodiment. In comparison to the mechanical system 70 _3, a further bending beam 84 ₃ is arranged between the bending beams 84 ₁ , 84 ₂ , with a spring structure 96 on one side and the bending transducer 12 on the other side. This may be equivalent to the placement of the spring structure 96 in the flexural beam member 84 ₂ of the mechanical system 70 ₂ , possibly in conjunction with increasing a distance between the flexural beams 84 ₁ and 84 ₂ therein. Compared to the mechanical system 70 ₃ , the spring structure 96 may not contact the flexural transducer structure 12 but contact the flexural beam element 84 ₃ to provide the second nonlinear mechanical stiffness contribution. The spring structure 96 of the mechanical system 70 ₃ and 70 ₄ may have two bending elements 96 ₁ and 96 ₂ that face each other and are connected to one another at a connection region 98. The spring structure 96 is configured to increase a contact area between the two bending elements 96 ₁ and 96 ₂ with an increase in the bending of the bending structure 12, for example starting from the connection region 98.

The conforming structure 18, which includes the spring structure, may be mechanically attached to the flexural transducer structure 12 and supported on the substrate 66 that supports the flexural transducer structure 12. This can be achieved, for example, if the bending transducer structure 96 is included in the adaptation structure 18, which contacts the bending transducer structure 12 or the substrate 66, in order to be mechanically contacted in parallel with the bending transducer structure 12.

In other words shows 7d an exemplary cell configuration with a dedicated structure for contact formation outside the electrostatic gap 38 through contact formation and evolution for faster initial contact formation and with mechanical bending coupling to a bending electrode to limit faster propagation of contact evolution and an order of magnitude of cell stiffening nonlinearity function when actuated, in a top view for a planar bend or in a side view for an extra-planar bend. The exemplary cell configuration has a dedicated structure (for contact formation outside of the electrostatic air gap) with guided contact formation and evolution for faster initial contact formation and with a mechanical bending coupling to a bending electrode to limit faster propagation of contact evolution and an order of magnitude nonlinearity of cell stiffening increase when actuated. The beam structure 84 ₃ limits the generation of the electrostatic force in the gap 38 during bending by limiting the local gap reduction, in particular from the direction 88 ₂ on the A-A' plane, due to a direct coupling with the bottom electrode 26 ₂ . Compared to 7c the structure according to 7d ensures an advantageous integration of mechanical feedback.

8th shows a schematic view of a mechanical system 80 ₁ according to an embodiment showing a different implementation of a spring structure 102. The spring structure 102 can be implemented as a bending beam structure that is coupled in parallel to at least one bending beam structure 26 ₁ or 26 ₂ of the bending transducer structure 12. In the examples of the mechanical system 80 ₁ , the bending beam structure formed by a series connection of different bending beams 84 ₁ , 84 ₂ and 84 ₃ may have local stiffening, for example based on increased stiffness of the bending beam element 84 ₂ . This allows the bending beam element 84 ₂ to be stiffer compared to the bending beam elements 84 ₁ and 84 ₃ . Similar or complementary behavior can be obtained to implement local weakening instead of local stiffening between ends 86 ₁ and 86 ₂ .

The local stiffening implemented in the beam element 84 ₂ may enable contact formation with the bending transducer structure 12 to be avoided.

In other words shows 8a an exemplary base cell configuration with a nonlinear spring configuration 102, which consists of a structural material of the electrode/cell, in the cell geometry to create a nonlinear stiffening of the cell without contact formation or contact evolution in a top view for a planar bend and in a side view for an extra-planar bend . The exemplary basic cell configuration includes a nonlinear spring configuration 102, which consists of a structural material of the electrode/cell, in the cell geometry to create a nonlinear stiffening in the cell without contact formation or contact evolution. The nonlinearity of the spring configuration can be regulated in the bending direction by different design parameters of the spring configuration, for example by the thickness and length of the sections 84 ₁ , 84 ₃ and 84 ₂ . This configuration is particularly useful when the stiffness of the cell needs to be increased without contact-based operation, for example when there is no need for perturbation in the frequency response of the cell that may occur due to sudden contact formation or its propagation, during the nonlinearity of the cell's response upon actuation is counteracted.

8b shows a schematic view of a mechanical system 80 ₂ according to an exemplary embodiment. In comparison to the mechanical system 80 ₁ , a spring structure 102' has a plurality of layered bending beam structures or a layered arrangement of bending beam structures, the arrangement between supporting bending beams 84 ₁ or 84 ₂ and the bending transducer structure being contacted.

Connecting elements 104 ₁ to 104 ₅ can be adapted to connect different layers of the bending beam elements 84 ₁ /84 ₂ on the one hand and 84 ₃ on the other hand and/or to connect bending beams to the bending transducer structure. The connecting elements 104 ₁ to 104 ₅ can be flexible or rigid. A gap between bending beam elements 84 ₁ and 84 ₂ , closed off-planar by bending beam element 84 ₃ , allows edges 106 ₁ and 106 ₂ of bending beam elements 84 ₁ and 84 ₂ to be diagonal or inclined along directions 108 ₁ and 108 _2, respectively move.

In other words shows 8b an exemplary cell configuration with a nonlinear spring configuration consisting of structural material of the electrode/cell in the cell geometry with a mechanical bending coupling to bending electrodes to create a nonlinear stiffening in cells without contact formation or contact evolution in a top view for planar bending and in a side view, respectively for an extra-planar bend. The exemplary cell configuration includes a nonlinear spring configuration 102', composed of structural material of the electrode/cell, in the cell geometry with a mechanical bending coupling to the bending electrode to create a nonlinear stiffening in the cell without contact formation or contact evolution. The mechanical coupling (84 ₁ and 84 ₂ ) has a direct influence on the bending of the bottom electrode at the applied voltage and limits the bending deformation of the bottom electrode 26 ₂ at the applied actuation voltage, especially at the highest deformation mung of the electrostatic gap (38) at the plane AA' in the direction 88 ₂ . This again affects the system response primarily in two ways, firstly due to an increase in the overall cell stiffness upon bending of the non-linear spring and secondly by limiting the generation of the electrostatic force in the gap 38 by limiting the localized gap reduction, particularly from the direction 88 ₂ on the A-A' plane, compared to cases when there is no direct mechanical coupling feedback with cell bending to limit the localized deformation of the bottom electrode and thus the electrostatic gap, for example as in 8a .

8c shows a schematic diagram for comparing curves 112 ₁ and 112 ₂ , with bending curvatures versus normalized stress illustrated on the abscissa and normalized curvature illustrated on the ordinate of the diagram. While curve 112 ₁ shows a coupled bend thickness T1 that is less than a coupled bend thickness T2 in curve 112 ₂ and relates to the mechanical system 80 ₂ , it can be seen that the highly nonlinear response of the smaller Thickness T1 in curve 112 ₂ becomes more linear, so that there are linear regions 114 ₁ and 114 ₂ in which the behavior is strongly linear. Although this results in a lower amplitude of curvature, the behavior is advantageously linear.

In other words shows 8c a cell bending curvature compared to an actuation stress normalized with respect to maximum values from FEM simulations in 8b Shown exemplary cell configurations with identical cells but mechanical bending couplings of lower and higher thicknesses to change the magnitude of a nonlinearity response in a required voltage range. The bending couplings refer, for example, to elements 84 ₁ and 84 ₂ . The example cell bending curvature is shown compared to the actuation stress (normalized with respect to the maximum values) from FEM simulations of a in 8b shown exemplary cell configuration with identical cells but mechanical bending couplings (84 ₁ and 84 ₂ ) of uniformly smaller (T1) and larger thicknesses (T2) to change the magnitude of nonlinearity of the response in a required voltage range. The mechanical coupling can be designed to have different thicknesses and meeting locations of its parts in order to modulate the reduction in the magnitude of nonlinearity depending on the requirement in a certain range. Although the achieved bending curvature is always lower in the case of reduced nonlinearity for these structures (since there is no dielectric/insulator based contact formation in the electrostatic gap used), it is important to note that the magnitude of the nonlinearity can be significantly reduced while there is no contact-based operation, i.e. without any possibility of problems of stiction or dielectric charging, along with higher stiffness when the actuation signal is applied.

8d shows a schematic view of a mechanical system 80 ₄ according to an exemplary embodiment. In comparison to the mechanical system 80 ₂ , a plurality of spring structures 102' are arranged, for example three spring structures 102' ₁ to 102' ₃ . These can be connected via a bending beam structure 84 ₁ , which can have a straight or, as shown, a curved curvature. Because the bending beam element 84 ₁ connects and supports the spring structures 102' ₁ to 102' ₃ as a curved structure, possibly substantially parallel compared to the bending beam elements 26 ₁ to 26 ₂ , movements 116 ₁ , 116 ₂ and 116 ₃ can be achieved, for example Base sections of the spring elements 102' ₁ to 102' ₃ be directed essentially towards the normal of the bending transducer structure 12.

A number of spring elements 102' can be 1, 2 or 3, or a higher number. As shown, the conforming structure 18 may include a spring structure that is mechanically attached to the flexural transducer structure 12 and supported by a flexural beam structure 84 ₁ that is adapted to flex in concert with the flexural transducer structure 12. The bending transducer structure 12 can in turn have a conductive material, like the adaptation structure 18. The materials can be the same or at least comparable.

In other words shows 8d an exemplary cell configuration with a distributed nonlinear spring configuration, which consists of a structural material of the electrode/cell, in the cell geometry with a mechanical bending coupling to bending electrodes to create a nonlinear stiffening in a cell without contact formation or contact evolution in a plan view for a planar bend or in a side view for an extra-planar bend. The exemplary cell configuration includes a distributed nonlinear spring configuration consisting of an electrode/cell structural material in the cell geometry with a mechanical bending coupling to a bending electrode to create a nonlinear stiffening in the cell without contact formation or contact evolution. Due to the distributed structures (84 ₂ - 84 ₄ and 84 ₁ ), the mechanical feedback can vary with the increasing bending deformation Request can be transmitted (e.g. in the directions 116 ₁ -116 ₃ ) to extend the feedback effect to the localized deformation of the bottom electrode, thus to the localized deformation of the electrostatic gap, in addition to increasing the structural cell stiffness. The geometries of the distribution structures can be changed and/or used in higher numbers for a more uniform/non-uniform distribution of the mechanical feedback as required.

Compared to 8b ensures the structure accordingly 8d for an advantageous integration of a conformal bend with a mechanical feedback coupling. Conformal springs/structures provide the advantage that the cell beams can be stacked more closely in parallel compared to non-compliant spring configurations, thereby providing optimal area utilization and better compactness at the system level.

8e shows a schematic view of a mechanical system 80 ₅ according to an exemplary embodiment, which has a symmetrical arrangement of an adaptation structure 18 outside the bending transducer structure 12. Starting from the gap 38 as an inner portion of the mechanical system 80 ₅ , a sequential arrangement of thinned flexural elements 84 ₁ and thicker elements 84 ₂ that provide local stiffening is present, as in conjunction with 8a is described, arranged along a curved path in order, for example, to have essentially constant gaps 92 ₁ and 92 ₃ on one side of the bending elements 26 ₁ and 26 ₂ opposite the gap 38. This can be understood as a sequential arrangement of spring elements 102 along a curved path. In other words shows 8e an exemplary base cell configuration with a nonlinear spring configuration that is conformal with respect to the geometry of the electrode and consists of a structural material of the electrode/cell, in the cell geometry for creating a nonlinear stiffening in a cell without contact formation in a plan view for a planar bend or .in a side view for an extra-planar bend. The exemplary base cell configuration includes a nonlinear spring configuration that is conformal to the geometry of the electrode and consists of a structural material of the electrode/cell in the cell geometry to create a nonlinear stiffening in a cell without contact formation. Cell stiffening is achieved due to higher elongation/bending of bends (84 ₁ ) relative to electrodes, as these will experience the greatest bending (they are furthest from the neutral fiber of the cell). The conformal shape of the bends helps to make optimal use of the cell area, and the parallel cell bar stacking can be made more compact. It is important to note that contact formation between the bends (84 ₁ ) and electrodes (26 ₁ , 26 ₂ ) can always be used to further modulate cell stiffness upon actuation.

Compared to the structure from 8d can have a structure according to 8e provide the advantage of better shape conformability and less area utilization along with the possibility of closer stacking (accompanied by a contact formation possibility, as in connection with 8f described). Conformal springs/structures offer the advantage of allowing cell beams to be stacked more tightly in parallel compared to non-conformal spring configurations, providing optimal area utilization and better compactness at the system level.

8f shows a schematic view of a mechanical system 80 ₆ according to an exemplary embodiment. For example, compared to the mechanical system 80 ₅ , external bending elements 84 ₁ and 84 ₂ may have a continuous or constant thickness and/or stiffness. At discrete locations 118 ₁ and 118 _2, the bending elements 84 ₁ and 84 ₂ of the adjustment structure 18 can be mechanically attached to the bending beam elements 26 ₁ and 26 ₂ or can contact the same. This allows relative bending or movement 116 towards the bending transducer structure with a highest amplitude between the attached locations, e.g. B. at the levels BB' or C-C'.

The flexural transducer structure 12 may include first and second elements 26 ₁ and 26 ₂ coupled in parallel. The adaptation structure 18 may include at least a first adaptation element 84 ₁ and a second adaptation element 84 ₁ or 84 ₂ , optionally the other element shown. These adjustment elements can be mechanically coupled in parallel to the bending element 26 ₁ or 26 ₂ , while the same form gaps 92 ₁ and/or 92 ₂ . The mechanical system 90 ₆ can be implemented with or without contact formation at the levels BB' and/or CC'. For example, contact formation can be used in the gaps 92 ₁ and 92 ₂ to control the change in cell stiffness upon bending (increase or decrease depending on the contact formation), spreading and its effect on the increase in the electrostatic gap 38 due to the mechanical Feedback from the external structure that presses against the internal electrodes. Due to the mechanical pressure, the local air gap in the electrostatic gap 38 may reduce at one point, thereby increasing the nonlinearity rather than reducing it due to the local minimization of the gap due to the contact will dominate more than the increase in mechanical stiffness after a certain period of time. For example, the configuration in normal operation may not use contact formation in an alternative implementation. For example, in such a configuration there are only extensible conformal springs to increase stiffness in a linear or nonlinear manner with mechanical expansion (outermost/innermost structures will expand the most) due to bending.

Non-contacting operation can be understood as a normal operation in which the non-contacting configuration or mechanical elements are to be used (e.g. merely as extensible conformal springs) to provide stiffness (linear/nonlinear) under mechanical expansion (outermost/ innermost structures will expand the most) due to bending.

Conformal springs/structures offer the advantage of allowing cell beams to be stacked more closely in parallel compared to non-conforming spring configurations, providing optimal area utilization and better compactness at the system level.

However, contact formation in these spaces can also be used to alter the change in cell stiffness upon bending. However, whether the nonlinearity of the response will increase or decrease in a particular operating range depends on contact formation, propagation, and its effect on reducing the electrostatic gap 92 ₁ due to mechanical feedback from an external structure pressing against the internal electrodes. Due to the mechanical pressure, the local air gap in the region of the electrostatic gap may decrease at one point, thereby increasing the nonlinearity rather than decreasing it, since the local minimization of the gap due to contact will dominate more than the increase after a certain period of time the mechanical stiffness. The change in overall response depends largely on the geometric design of the cell (air gaps used, thickness of electrodes, spring design, etc.), applied voltage, localized contact formation, local pressure and its effect on 92 ₁ , etc. Based on this, the nonlinearity of the response can be tuned to be more or less large for a certain range of applied voltage after contact formation.

If the designs have a compliant spring configuration (e.g. 8f or 8e) with designs of contact formation cells (e.g. as in 2a or 6a shown) are to be combined, then alternatively, contact formation in external spring gaps can be used to produce initial contact formation in the electrostatic gap 92 ₁ more quickly (since the pressure on the local air gaps helps to achieve contact earlier), while Higher overall cell stiffness in bending can be achieved due to contact formation and propagation in the outer spring and in an inner electrostatic gap, ensuring even faster and effective linearization. However, the advantage of reduced charging can be taken advantage of 8f at least partially lost.

In other words shows 8f an exemplary base cell configuration with nonlinear spring configuration compliant with respect to the electrodes and with direct structural connection to bending electrodes and consisting of structural material of the electrode/cell in the cell geometry to create a nonlinear stiffening in the cell without contact formation, in a plan view for a planar Bend or in a side view for an out-of-plane bend. The exemplary base cell configuration includes a nonlinear spring configuration conforming to the electrodes and a direct structural connection with bending electrodes and consisting of electrode/cell structural material in the cell geometry to create a nonlinear stiffening in the cell without contact formation. Cell stiffening is achieved primarily by higher elongation/bending of bends (84 ₁ , 84 ₂ ) relative to electrodes as they experience the greatest bending (they are farthest from the neutral phase of the cell), and with a faster transition into a regime of nonlinear bending stiffness due to a structural connection with electrodes (118 ₁ , 118 ₂ ) that can act as quasi-clamping, compared to cases without this, e.g. b. 8e . The conformal shape of the bends helps to make optimal use of the cell area, and the parallel stacking of the cell bars can be done more compactly. It is important to note that contact formation between the bends (84 ₁ , 84 ₂ ) and electrodes (26 ₁ , 26 ₂ ) can always be used to further modulate cell stiffness upon actuation.

Compared to the structure from 8e provides the structure 8f for the advantage that for similar dimensions a higher rate of increase in stiffness in bending can be obtained and/or nonlinearity regimes of reduced magnitude can be better tuned depending on the requirements (along with a possibility of contact formation at several points as well as due to a structural connection with electrodes, as in connection with 8f described).

8g shows a schematic view of a mechanical system 80 ₇ that has a stacked configuration of flexures 84 of the adjustment structure 18. That is, multiple layers of flexural elements may form an accommodation structure on one or both sides of the flexure transducer structure 12. Although mechanical systems 80 ₆ and 80 ₇ are shown as having portions of the conforming structure on both sides of the flexural transducer structure, it may also be located on only one or both sides.

Based on an increased amount of bending, the further outwardly the elements of the adjustment structure are arranged, the less stiffness they can provide in one embodiment, for example by implementing them thinner compared to internal elements, such as when comparing the beam elements 84 ₁ and 84 ₃ or the elements 84 ₂ and 84 ₄ is shown.

The multiple layers can be connected with a single discrete element at locations 118 ₁ or 118 ₂ or with separate elements. Furthermore, additional elements can be arranged along the course of the bending elements 26 ₁ and 26 ₂ .

In other words shows 8g an exemplary base cell configuration with multiple parallel nonlinear spring configurations conforming to the geometry of the electrodes and structural connection with electrodes and consisting of structural material of the electrode/cell in the cell geometry to create a nonlinear stiffening in the cell without contact formation, however contact formation is also possible . The illustration from 8g is a top view for a planar bend or a side view for an off-planar bend. The different layers shown for the mechanical system 80 ₇ may have the same configuration as shown, but may also implement different configurations. For example, the inner or outer or even an additional layer can have a configuration according to 8e or the like. An additional arrangement of spring elements is also possible. The exemplary basic cell configuration includes multiple parallel nonlinear spring configurations conforming to the geometry of the electrodes and a structural connection with electrodes consisting of structural material of the electrode/cell in the cell geometry to create a nonlinear stiffening in the cell without contact formation. Cell stiffening is achieved primarily due to higher elongation/bending of bends (84 ₁ -84 ₄ ) relative to electrodes as they experience the most bending (since they are farthest from the neutral fiber of the cell), and with a faster Transition to a regime of nonlinear bending stiffness due to a structural connection with the electrodes (118 ₁ , 118 ₂ ), which can act as a quasi-clamp, compared to cases without it, for example in 8e . The conformal shape of the bending points helps to make optimal use of the cell area, and the parallel stacking of the cell bars can be made more compact. It is important to note that a contact formation option between the bends (84 ₁ -84 ₄ ) and/or electrodes (26 ₁ , 26 ₂ ) can always be used to further modulate cell stiffness. Different possibilities for contact formation and evolution in the air gaps 92 ₁ , 92 ₂ (without feedback to the bending electrodes) and/or 92 ₃ , 92 ₄ (with feedback to the bending electrodes), in particular at the levels CC' and/or B-B ', can be set up based on a bend design (thickness, length, topology, etc.).

Compared to the structure from 8f provides the structure 8g for the advantage that for similar dimensions a higher rate of stiffness increase in bending can be obtained and/or reduced magnitude nonlinearity regimes can be better tuned depending on the requirement (along with multiple contacts as well as due to a structural connection with the electrodes and multiple bending layers).

9a shows a schematic view of a mechanical system 90 ₁ according to an exemplary embodiment. The bending transducer structure can have a first transducer section 12a, which has, for example, bending elements 26 ₁₁ together with bending elements 26 ₁₂ , which work, for example, as described for the mechanical system 80 ₁ . A second transducer section 12b can be arranged, which has, for example, bending elements 26 ₂₁ and 26 ₂₂ which can operate correspondingly to the transducer section 12a. The transducer section 12a and/or the transducer section 12b may be arranged in a symmetrical or asymmetrical manner with respect to each other.

The transducer sections 12a and 12b can be controlled independently through the use of electrical signals 16 ₁ and 16 ₂ by applying a potential indicated as V ₁ and V ₂ simultaneously or at different times, as compared to the illustration out of 9a an assignment of different electrode elements 26 ₁₁ to 26 ₂₂ can be switched to a reference potential GND or a control potential.

Compared to the mechanical system 80 ₁ , the matching structure 18 may be isolated from internal electrodes 26 ₁₂ and 26 ₂₂ through the use of insulators 36 ₂ , 36 ₃ , 36 ₆ and 36 ₇ . However, these elements are optional, but may make it possible to detect a deflection of the adaptation structure 18, for example when using piezoelectric materials as bending element 84 ₂ or bending elements 84 ₁ or 84 ₃ or in different components thereof. This can make it possible to obtain a readout signal 16 ₃ (V _read-out ). The mechanical system 90 ₁ combines two modifications. On the one hand, the bending transducer structure 12 of the mechanical system 80 ₁ can be combined with a second section of the obtained structure, for example the transducer structure 12b, in order to provide a different, for example opposite, bending direction 14 ₁ and 14 ₂ . Furthermore, a deflection in one or more of the elements of the adaptation structure 18 can be detected through the use of a respective electrical signal 16 ₃ , which can also be implemented in the mechanical system 80 ₁ , for example, using suitable materials and by isolating possible used electrodes from the bending transducer structure 12 can be.

As in 9a As shown, the adjustment structure 18 may include a flexural transducer structure that is mechanically coupled in parallel to the first transducer section 12a and second transducer section 12b and between both sections 12a and 12b.

Optionally, the bending transducer structure of the adaptation structure 18 can have a local stiffener 84 ₂ , for example in a central region of the bending transducer structure.

A deflection or bending of the bending transducer structure 18 can be detected, for example, when capacitive movements and/or piezoelectric measurements or other principles are used.

In other words shows 9a an exemplary base cell beam configuration with identical electrodes for bending in both directions and nonlinear spring configurations consisting of the material of the electrode/cell in the cell geometry to create a nonlinear stiffening of the cell without contact formation or contact evolution in a top view for a planar bend and in a side view for a extraplanar bending. The exemplary bimorph base cell configuration optionally includes a configuration of identical electrodes for bending in both directions and a nonlinear spring configuration consisting of the structural material of the electrode/cell in the cell geometry for creating a nonlinear stiffening in the cell without contact formation or contact evolution in the electrostatic gap. For the cell bending in the direction 14 ₁ or 14 ₂ , a corresponding cell part is actuated with V1 or V2 actuation signals. While one side is actuated, the other side of the cell acts as a passive load, which can also be designed to be a non-linear load in the bending direction in addition to the bends (84 ₁ , 84 ₂ , 84 ₃ ). Alternatively, the passive cell portion (for a particular bending direction) can also be partially actuated to make it an active load that can be used to further counteract the nonlinearity in the cell's response to the bending direction. The deformation in the bend (84 ₁ , 84 ₂ , 84 ₃ ), electrically isolated from the electrodes of the cell, can be used for sensing purposes using materials in a bend region that exhibit piezoresistive and/or piezoelectric effects. The bends may be set to produce a sense signal (V _read-out ) that is linear or has a lower magnitude of non-linearity at applied actuation voltages (V1, V2). It is important to note that options for insulator/dielectric-based contact formation and evolution between the cell electrodes (bending elements _{26 11} -26 ₂₂ ) in the electrostatic air gap (38 ₁ , 38 ₂ ) can always be used to achieve cell stiffness upon actuation to further modulate while also achieving higher actuation forces.

9b shows a schematic view of a mechanical system 90 ₂ according to an exemplary embodiment. Compared to the mechanical system 90 ₁ , the conforming structure 18 includes two opposing flexure beam elements 84 ₁ and 84 ₂ implemented to include a conductive material to form electrodes, at least in a portion of the flexure elements 84 ₁ and 84 ₂ . In order to avoid short circuits, an insulator 122 can be arranged at least in a central region of the adaptation structure 18 between the bending beam elements 84 ₁ and 84 ₂ , for example in regions in which mechanical contact can occur in the absence of the insulator 122. A similar function is implemented through the use of insulators 36 ₃ and 36 ₃ in the area of the clamps 28 ₁ and 28 ₂ , whereby it could be advantageous to implement a gap 92 at least partially between the electrodes in order to prevent deflection of the adaptation structure 18 improve.

The matching structure 18 may include an electrode structure having electrodes 84 ₁ and 84 ₂ and an insulating material 122 therebetween. The electrode structure may form at least a portion of the bending beam structure of the conforming structure, and the conforming deformation may result in deformation of the electrode structure, wherein the mechanical system 90 ₂ may be adapted to provide one or more electrical signals corresponding to the conforming deformation. By using two electrodes isolated from each other, such a signal 16 ₃ can be a difference between the potential V _read-out and V _{read-out_GND} , which can change due to the deflection.

In other words shows 9b an exemplary bimorph base cell configuration with a configuration of identical electrodes for bending in both directions 14 ₁ and 14 ₂ and non-linear spring configurations with multiple isolated bending points consisting of the material of the electrode for creating a non-linear stiffening in a cell together with a possibility for feedback through capacitive sensing, to estimate bending deformation to actively control cell deformation, in a top view for a planar bend or in a side view for an extra-planar bend. The exemplary bimorph base cell configuration includes a configuration of identical electrodes for bending in both directions and a nonlinear spring configuration with multiple isolated bending points consisting of the material of the electrode to create a nonlinear stiffening in the cell along with a capability for feedback through capacitive sensing to prevent bending deformation active control of cell deformation. The change in capacitance between bends 3n and 3o can be detected using the readout signals V _read-out and V _{read-out_GND} . The bends may be designed to have a capacitance change that is linear or has a lower magnitude of nonlinearity at applied actuation voltages (V1, V2).

Both systems 90 ₁ and 90 ₂ enable control of an actuator that is configured to deflect in response to electrical signals 16 ₁ and/or 16 ₂ . As mentioned, a measurement principle that, among other things, enables regulation can be implemented in another system described herein by appropriate provision of the functionality, preferably in the adaptation structure 18.

9c shows a schematic view of a mechanical system 90 ₃ in which the bending transducer section 12b is formed asymmetrically compared to the bending transducer section 12a, allowing a different deflection behavior compared to an equal amplitude of signals 16 ₁ and 16 ₂ , and thus an additional degree of freedom. Furthermore, by forming an asymmetrical relationship between the distances 12a and 12b, external effects such as gravity or a permanent load can be taken into account, for example with regard to a desired reference deflection.

According to embodiments, the bending transducer structures described herein may be configured to bend in response to an applied electrical signal, wherein the mechanical system includes a controller 115 configured to provide the electrical signal. This can make it possible to use at least parts of the mechanical system as an actuator. Alternatively or additionally, the mechanical system may be implemented such that the bending transducer structure is configured to provide the electrical signal in response to the applied external force F causing the bend, and the mechanical system includes a readout circuit 117 configured to provide the electrical signal. The control unit 115 and/or the readout circuit 117 may be part of or connected to other mechanical systems described herein. The control unit 115 and the readout circuit 117 can be part of the same unit, for example a control unit or the like.

In other words is in 9c a bimorph exemplary base cell configuration with a configuration of different electrodes for bending in both directions and compensating for nonlinearity in the other response for a particular bending direction for the same applied voltage, together with a nonlinear spring configuration with multiple isolated bends consisting of the material of the electrode to create a nonlinear stiffening of the cell and a capability for feedback through capacitive sensing to estimate bending point deformation for actively controlling cell deformation, shown in a top view for a planar bend and in a side view for an extra-planar bend, respectively.

10a shows a schematic view of a mechanical system 100 ₁ having a configuration in which the flexure transducer structure 12 includes flexures 26', and 26' ₂ that include an electrothermal material that may be configured to act in response to the electrical signal 16 ₁ and/or 16 ₂ to expand or contract. For such a purpose, clamps 28 ₁ and 28 ₂ can also be conductive ges material to transport electrical charges to the electrothermal material. Although the clamp 28 ₂ is shown to have a reference GND potential, it should be noted that this potential may also be a supply voltage, ie the signal 16 ₁ and/or 16 ₂ for a base cell connected to the mechanical system 100 ₁ is connected, such as in 2b-2e is shown.

The matching structure may include flexures 84 ₁ and 84 ₂ , which may include a structural electrode material, ie, a conductive material, such as a MEMS semiconductor conductive material or a metal material. A gap 38 may allow relative movement of bending elements 26' ₁ , and 26' ₂ with respect to one another during bending along the bending direction 14 ₁ or 14 ₂ . A structural dielectric insulator material 36 can provide electrical insulation and thermal insulation.

In other words shows 10a an exemplary bimorph base cell configuration based on an actuator principle of electrothermal bending and fully insulated electrodes for contact formation and evolution for capacitive sensing possibilities in a top view for a planar bend and in a side view for an extra-planar bend. The exemplary bimorph base cell configuration is based on an actuator principle of electrothermal bending and fully insulated electrodes for contact formation and evolution to enable capacitive sensing in the electrostatic gap 38. The electrothermal actuator electrodes 26' ₁ , or 26' ₂ can be actuated to use corresponding actuation voltages (V1, V2) in directions 14 ₁ or 14 ₂ . For example, when V1 is activated (V2 is off), electrode 26' ₁ expands (due to thermal expansion) and, for contact formation and evolution, 84 ₁ moves toward 34 ₁ while 84 ₂ moves toward 34 ₂ ( passive contraction) (in the directions 44 ₁ and 44 ₂ ). The capacitance readout electrodes (84 ₁ , 84 ₂ ) come into contact and modulate the stiffness of the entire cell to tune the actual usable force and capacitance change produced (for sensing) at the applied actuation voltage signal.

10b shows a schematic view of a mechanical system 100 ₂ that, compared to the mechanical system 100 ₁ , has a piezoelectric material instead of an electrothermal material to implement an actuator and / or sensor function. This means that the bending elements 26'' ₁ and 26'' ₂ can have a piezoelectric material, at least in part. The piezoelectric material may preferably be covered on two opposite sides with conductive layers 124 to apply the voltage to activate and/or evaluate the contraction or expansion of the piezoelectric material.

In other words shows 10b an exemplary bimorph base cell configuration based on an actuator principle of piezoelectric bending and fully insulated electrodes for contact formation and evolution for the possibility of capacitive sensing in a top view for a planar bend or in a side view for an extra-planar bend. The exemplary bimorph base cell configuration is based on the actuator principle of piezoelectric bending and fully isolated electrodes for contact formation and evolution to enable capacitive sensing in the electrostatic gap 38. The piezoelectric actuator electrodes (124 ₁ to 124 ₄ ) can be actuated to move using appropriate actuation voltages ( V1, V2) to bend in directions 14 ₁ or 14 ₂ . For example, when V1 is activated (V2 is off), the piezoelectric material (26'' ₁ ) expands (due to the piezoelectric effect) and, for contact formation and evolution, the electrode 84 ₁ moves toward 34 ₁ while 84 ₂ moves (in directions 44 ₁ and 44 ₂ ) toward 34 ₂ (passive contraction). The capacitance readout electrodes (84 ₁ and 84 ₂ ) come into contact and modulate the stiffness of the overall cell to match the actual usable force and capacitance change generated (for detection) at the applied actuation voltage signal. Since it is a piezoelectric actuation system, the piezoelectric material layers 26" ₁ and/or 26" ₂ can be designed to also contract depending on design requirements.

10c shows a schematic view of a mechanical system 100 ₃ , which may substantially correspond to the mechanical system 100 ₂ , wherein instead of a piezoelectric material, a dielectric elastomer material is arranged in the bending elements 26''' ₁ and 26''' ₂ .

In other words shows 10c an exemplary bimorph base cell configuration based on an actuator principle of bending a dielectric elastomer and fully insulated electrodes for contact formation and evolution for the possibility of capacitive sensing in a top view for a planar bend or in a side view for an extra-planar bend. The exemplary bimorph base cell configuration is based on an actuator principle of bending a dielectric elastomer and on fully insulated electrodes for contact formation and evolution to enable capacitive sensing in the electrosta table gap 38. The DEA electrodes (124 ₁ to 124 ₄ ) can be actuated to bend in the directions 14 ₁ and 14 ₂ , respectively, using appropriate actuation voltages (V1, V2). For example, when V1 is activated (V2 is off), the dielectric elastomer material (26''' ₁ ) expands (depending on the actuation principle of the dielectric elastomer) and moves for contact formation and evolution (in directions 44 ₁ and 44 ₂ ). the electrodes 84 ₁ move in the direction of 34 ₁ while 84 ₂ moves in the direction of 34 ₂ (passive contraction). The capacitance readout electrodes (84 ₁ , 84 ₂ ) come into contact and modulate the stiffness of the overall cell to match the generated usable actual force and capacitance change (for detection) at the applied actuation voltage signal.

Embodiments described herein make it possible to combine a first nonlinear contribution of a deflection provided by the bending transducer structure with a second nonlinear contribution provided by a deflection of the adaptation structure. The combination of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution can be implemented to compare to the first nonlinear contribution, such as in 6b , 6d and 6e in combination with 6e is shown to ensure high linearity.

Mechanical systems described herein include the flexural transducer structure to have an electrostatic configuration, a piezoelectric configuration, an electrothermal configuration, and/or an electroactive polymer configuration. How out 10a , 10b and 10c As can be derived, the implementation of the bending transducer structure to any of the configurations described herein may be applied to any structure of the mechanical system described herein. That is, the mechanical systems described herein in connection with an electrostatic or electrodynamic configuration can be easily implemented with other configurations of actuator/sensor principles. Electrostatic configurations described herein refer to a combination of electrode structures. Whether these structures are used to be excited in an electrostatic or electrodynamic manner may be a matter of implementation.

Some embodiments described herein relate to a mechanical system, which is a micromechanical system, MMS, in particular a MEMS. As described herein, the bending transducer structure may be adapted to provide the bending planar with respect to a layer arrangement or out-of-planar with respect to a layer arrangement.

Like for example in 2b-2e As shown, a mechanical system described herein may include multiple cells arranged mechanically in series, with each cell configured in accordance with embodiments described herein. Cells can be designed to be the same or similar, but this is not necessary.

The basic concept of counteracting nonlinearity in a transducer system response using a nonlinear mechanical stiffener is known from the prior art and publications [1-5]. However, most of these solutions are highly design specific with a limited scope of application and limited performance level. For example, the bending transducer systems that rely on nonlinear stiffening through contact formation and contact evolution, such as zipper actuators based on electrostatic actuation, usually suffer from motion hysteresis due to contact formation and breakage [4, 6-9], electrostatic attraction instabilities [4, 6-8 ], static friction problems, abrupt response change [6, 8, 10], a design necessarily based on complicated self-stress processing [7], dedicated requirements for external structures [1-3, 5, 11], etc.

In most of the zipper configurations, direct tip deflection or movement of a specific structural area is used instead of bending curvature of the entire geometry of the cell/component. Simultaneous modulation/linearization of the system's different responses (bending curvature, bending moment, available force, capacitance change, motion resolution, frequency response, etc.) upon actuation signal in such configurations is difficult (most often one or two responses are modulated in a particular design). Furthermore, electrostatic zipper actuators exhibit attraction instabilities that make controlling them challenging [12].

• • Ein Aktor- und/oder Sensor-Mechanismus mit Steifheitsmodulation auf der Basis einer elementaren Gestaltung bei angelegtem Betätigungssignal in der Richtung der Biegung/Bewegung, um einer Nichtlinearität in der Antwort der Zelle entgegenzuwirken und/oder zur linearen / nichtlinearen Last. Eine Biegung einer gesamten Zelle wird in Bezug auf die neutrale Faser der elementaren Zelle verwendet.
• • Steifheitsmodulation über Kontaktbildung und ihre Evolution auf der Basis einer Isolator/Dielektrikum-Schicht in dem elektrostatischen Zwischenraum (für elektrostatischen Aktor/kapazitives Auslesen) mit Zellbiegung bei Betätigung.
• • Isolationsschicht und/oder Elektrodenkonfigurationen in dem elektrostatischen Zwischenraum (zentriert, ALD-beschichtet, usw.) können dazu verwendet werden, das Auftreten von Kontaktbildung und ihre Evolution bei Betätigungssignal zu modulieren, bevor eine Kontaktierung einer gesamten reißverschlussfähigen Elektrodenlänge oder eine Durchschlagspannung der Isolatorschicht erreicht wird.
• • Elementare Gestaltung auf Basis der Steifheit von Elektroden und/oder Isolator, um Kontaktbildung vor einer Anziehung von Elektroden für einen kontinuierlichen reibungslosen Übergang zu einer linearisierten Zellantwort oder einer Zellantwort mit Nichtlinearität einer reduzierten Größenordnung zu ermöglichen. Alternativ kann auch ein plötzlicher Übergang mit der Nutzung einer Anziehung hergestellt werden.
• • Die kontaktbasierten Konzepte in elektrostatischen Zwischenräumen ermöglichen eine Betätigung und eine Bewegung über Anziehungsspannungen von Elektroden hinweg, eine Erhöhung einer erreichbaren Gesamtkrümmung (bei einer gegebenen Spannung aufgrund von einer höheren relativen Permittivität, insbesondere nützlich im Fall eines Mindestluftzwischenraums aufgrund einer Produktionsbeschränkung).
• • Haftreibungseffekt kann mit Folgendem entgegengewirkt werden: erhöhte Oberflächenrauheit von Kontaktoberflächen (z. B. Wölbungen), strukturierte Elektrodenoberflächen (Kontaktstellen, usw.) zum Reduzieren einer effektiven Kontaktfläche, Strukturierung von Isolator/Dielektrikum-Material (minimiertes Volumen, minimierte Materialschnittstellen, usw.), um Kontaktfläche zu reduzieren, und zurückgehaltene elektrostatische Aufladungen, und/oder durch ALD-basierte Antihaftreibungsbeschichtung (z. B. FDTS).
• • Versteifung einer Zelle bei Betätigung durch Verwendung von Federn / Biegesystemen - mit Kontaktbildung außerhalb des elektrostatischen Zwischenraums.
• • Versteifung einer Zelle bei Betätigung durch Verwendung von Federn / Biegesystemen - ohne Kontaktbildung.
• • Biegesystem in Zellgestaltung mit Rückkopplung einer Biegebewegung auf Basis mechanischer Kopplung zur Verformung von Elektroden - um Steifheit zu erhöhen sowie lokalisierte Reduzierung des elektrostatischen Zwischenraums einzuschränken, insbesondere an den Punkten höchster Elektrodenbiegung/-verformung.
• • Versteifung auf der Basis von Komplementierung von Biegeabschnitt auf gegenüberliegender Seite in der Zelle (kann aktiv oder inaktiv auf der Basis der Gestaltung abgestimmt werden).
• • Nutzung mehrerer Isolatorschichten in dem elektrostatischen Zwischenraum für kontaktbasierte Versteifungsfunktionsweisen mit unterschiedlichen Kontaktbildungsmöglichkeiten, z. B. Isolator-Isolator/Elektrode-Isolator-Elektrode, usw.
• • Nutzung mehrerer beschichteter Zellelektroden mit Luftzwischenräumen für biege- und/oder kontaktbasierte Versteifungsmöglichkeiten.
• • Das Konzept ist auch anwendbar auf unterschiedliche Zellgeometrien, Betätigungsprinzipien, und Kombinationen unterschiedlicher steifheitserhöhender Verfahren, die in der Erfindung dargelegt werden, sind möglich.

Some embodiments relate to a desired low-cost application (approximately 20 claims). The possible claims are as follows:

• • An actuator and/or sensor mechanism with stiffness modulation based on an elementary design with an actuation signal applied in the direction of bending/movement to counteract non-linearity in the response of the cell and/or to linear/non-linear load. A bend in a total th cell is used in reference to the neutral fiber of the elementary cell.
• • Stiffness modulation via contact formation and its evolution based on an insulator/dielectric layer in the electrostatic gap (for electrostatic actuator/capacitive readout) with cell bending upon actuation.
• • Insulation layer and/or electrode configurations in the electrostatic gap (centered, ALD coated, etc.) can be used to modulate the occurrence of contact formation and its evolution upon actuation signal before contacting a full length of zip-able electrode or reaching a breakdown voltage of the insulator layer becomes.
• • Elementary design based on electrode and/or insulator stiffness to allow contact formation prior to electrode attraction for a continuous smooth transition to a linearized cell response or a cell response with nonlinearity of a reduced magnitude. Alternatively, a sudden transition can be made using attraction.
• • The contact based concepts in electrostatic gaps allow actuation and movement across attractive voltages of electrodes, increasing achievable total curvature (at a given voltage due to higher relative permittivity, particularly useful in the case of a minimum air gap due to a production limitation).
• • Stiction effect can be counteracted with the following: increased surface roughness of contact surfaces (e.g. bulges), structured electrode surfaces (contact points, etc.) to reduce an effective contact area, structuring of insulator/dielectric material (minimized volume, minimized material interfaces, etc. ), to reduce contact area and retained electrostatic charges, and/or through ALD-based anti-friction coating (e.g. FDTS).
• • Stiffening of a cell during actuation by using springs / bending systems - with contact formation outside the electrostatic gap.
• • Stiffening of a cell during actuation through the use of springs / bending systems - without contact formation.
• • Cell design bending system with feedback of bending motion based on mechanical coupling to deform electrodes - to increase stiffness as well as limit localized reduction in electrostatic gap, particularly at the points of highest electrode bending/deformation.
• • Stiffening based on complementation of bending section on opposite side in cell (can be tuned actively or inactively based on design).
• • Use of multiple insulator layers in the electrostatic gap for contact-based stiffening functionality with different contact formation options, e.g. B. Insulator-insulator/electrode-insulator-electrode, etc.
• • Use of multiple coated cell electrodes with air gaps for bending and/or contact-based stiffening options.
• • The concept is also applicable to different cell geometries, actuation principles, and combinations of different stiffness-increasing methods set forth in the invention are possible.

Although some aspects have been described in the context of a device, it will be appreciated that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Similarly, aspects that have been described in the context of a method step also provide a description of a corresponding block or element or feature of a corresponding device.

The embodiments described above are merely illustrative of the principles of the present invention. It will be appreciated that modifications and variations of the arrangements and details described herein will occur to those skilled in the art. It is further intended that they be limited only by the scope of the appended claims and not by the specific details set forth by way of the description and explanation of the exemplary embodiments herein.

bibliography

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• [2] J. Li, “Electrostatic zipping actuators and their applications to MEMS,” MASSACHUSETTS INSTITUTE OF TECHNOLOGY, 2004. Accessed: June 14, 2021. [Online]. Available: https://dspace.mit.edu/handle/1721.1/33678
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• [6] P. Gebbers, C. Grätzel, L. Maffli, C. Stamm and, H. Shea, “Zipping it up: DEAs independent of the elastomer's electric field,” breakdown Proceedings of SPIE - The International Society for Optical Engineering, Issue 8340 , 61-, 2012, DOI: 10.1117/12.915020.
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• [11] B. Rivlin and D. Elata, “Design of nonlinear springs for achieving a linear response in gap-closing electrostatic actuators,” International Journal of Solids and Structures, Issue 49, No. 26, pp. 3816-3822 , 2012, DOI: 10.1016/j.ijsolstr.2012.08.014.
• [12] RS Diteesawat, A. Fishman, T. Helps, M. Taghavi, and J. Rossiter, "Closed-Loop Control of Electro-Ribbon Actuators," Frontiers in Robotics and AI, Issue 7, p. 144 , 2020, DOI: 10.3389/frobt.2020.557624.
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QUOTES INCLUDED IN THE DESCRIPTION

This list of documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• WO 2012/095185 A1 [0029]
• WO 2020078541 A1 [0032, 0237]
• US 7679261 B2 [0033]
• US 2021061648 A1 [0034]
• US 10693393 B2 [0035]
• US 2019036463 A1 [0035]
• WO 2012095185 A1 [0237]
• EP 5048320110114 [0237]
• EP 7829820181016 [0237]

Non-patent literature cited

• B. Rivlin, S. Shmulevich, Inbar Hotzen, and D. Elata, "A gap-closing electrostatic actuator with a linear extended range," 2013 Transducers & Eurosensors XXVII: The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII), pp. 582-585 [0237]
• J. Li, “Electrostatic zipping actuators and their applications to MEMS,” MASSACHUSETTS INSTITUTE OF TECHNOLOGY, 2004. Accessed: June 14, 2021. [Online]. Available: https://dspace.mit.edu/handle/1721.1/33678 [0237]
• Jian Li, M. P. Brenner, J. H. Lang, A. H. Slocum, and R. Struempler, "DRIE-fabricated curved-electrode zipping actuators with low pull-in voltage," in TRANSDUCERS '03. 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Digest of Technical Papers (Cat. No.03TH8664), 2003, 480-483 [0237]
• R. Legtenberg, J. Gilbert, S. D. Senturia and M. Elwenspoek, “Electrostatic curved electrode actuators,” Journal of Microelectromechanical Systems, Issue 6, No. 3, pp. 257-265 [0237]
• X. Xiang, X. Dai, K. Wang, Z. Yang, Y. Sun, and G. Ding, "A Customized Nonlinear Micro-Flexure for Extending the Stable Travel Range of MEMS Electrostatic Actuator," J. Microelectromech. Syst., Issue 28, No. 2, pp. 199-208 [0237]
• P. Gebbers, C. Grätzel, L. Maffli, C. Stamm and, H. Shea, “Zipping it up: DEAs independent of the elastomer's electric field,” breakdown Proceedings of SPIE - The International Society for Optical Engineering, Issue 8340 [ 0237]
• J. Felder, E. Lee, and D. L. DeVoe, “Large Vertical Displacement Electrostatic Zipper Microstage Actuators,” J. Microelectromech. Syst., Issue 24, No. 4, pp. 896-903 [0237]
• L. Maffli, S. Rosset, and H. R. Shea, “Zipping dielectric elastomer actuators: characterization, design and modeling,” Smart Mater. Struct., Issue 22, No. 10, p. 104013 [0237]
• S. H. Pu et al., “RF MEMS Zipping Varactor With High Quality Factor and Very Large Tuning Range,” IEEE Electron Device Lett., Issue 37, No. 10, pp. 1340-1343 [0237]
• B. Rivlin and D. Elata, “Design of nonlinear springs for achieving a linear response in gap-closing electrostatic actuators,” International Journal of Solids and Structures, Issue 49, No. 26, pp. 3816-3822 [0237]
• R. S. Diteesawat, A. Fishman, T. Helps, M. Taghavi and J. Rossiter, “Closed-Loop Control of Electro-Ribbon Actuators,” Frontiers in Robotics and AI, Issue 7, p. 144 [0237]
• H. Conrad et al., “A small-gap electrostatic micro-actuator for large deflections,” Nature communications, issue 6, p. 10078 [0237]

Claims (43)

A mechanical system that has the following features: a bending transducer structure (12) configured to provide a bend in response to an applied electrical signal (16) and/or to provide an electrical signal (16) in response to an applied external force (F) causing the bend, wherein a structural stiffness (52) of the bending transducer structure (12) provides a first nonlinear mechanical stiffness contribution to the bend; an adjustment structure (18) mechanically coupled to the bending transducer structure (12) by mechanical coupling to provide an adjustment deformation together with the bend, wherein a structural stiffness (52) of the adjustment structure (18) for a second nonlinear mechanical stiffness contribution to the bending based on the mechanical coupling during deformation. The mechanical system according to Claim 1 , wherein the mechanical coupling is adapted to combine the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution to control the bending of the bending transducer structure (12) based on a combination of the first nonlinear mechanical stiffness contribution and the to obtain the second nonlinear mechanical stiffness contribution. The mechanical system according to any one of the preceding claims, wherein at least one of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution is based on a mechanical contact between a first element and a second element of the mechanical system, the mechanical contact ensures a variable magnitude of mechanical forces that act on the bending transducer structure (12) and / or the adaptation structure (18) when a bending amplitude increases. The mechanical system according to Claim 3 configured to provide mechanical contact between the flexure transducer structure (12) and the accommodation structure (18), the flexural transducer structure (12) and the accommodation structure (18) being arranged to provide a contact area between each other upon an increase in flexure increase the bending transducer structure (12), the contact surface being formed between one of: • the adapting structure (18) and the bending transducer structure; • a first element of the adaptation structure (18) connected to the first element of the bending transducer structure (12); and a second element of the adjustment structure (18) connected to the second element of the bending transducer structure. The mechanical system according to one of the Claims 3 until 4 , wherein in a non-deflected state of the bending transducer structure (12), a first neutral axis of the first bending element is substantially parallel to a second neutral axis of the second bending element; or wherein in a non-deflected state of the bending transducer system, a first surface of the first bending element pointing towards the second bending element is substantially parallel to a second surface of the second bending element pointing towards the first bending element. The mechanical system according to one of the Claims 2 until 5 , wherein the adaptation structure (18) has an interrupted structure which is arranged between the first bending element and the second bending element. The mechanical system according to one of the Claims 3 until 6 , wherein the adaptation structure (18) comprises a dielectric material; wherein the matching structure is configured to contact at least two elements of the bending transducer structure (12) and to isolate them from each other based on the bending. The mechanical system according to one of the Claims 3 until 7 , wherein the adaptation structure (18) has a layered structure which is arranged in a planar manner between the first bending element and the second bending element. The mechanical system according to Claim 8 , wherein the adaptation structure (18) has a plurality of layers which have a gap (383) between adjacent layers which is partially closed in a deflected state of the bending transducer structure (12). The mechanical system according to one of the Claims 3 until 9 , wherein the adaptation structure (18) has a variable distance from at least one bending element (26 ₁ , 26 ₂ ) of the bending transducer structure (12). The mechanical system according to one of the Claims 3 until 10 , wherein a groove structure (58) and an opposite spring structure (62) are arranged in an intermediate space (38) between the one bending element (26 ₁ ) and a second bending element (26 ₂ ); wherein the groove structure and the spring structure form a mechanical contact in a deflected state of the mechanical system and a relative movement of the Prevent spring structure (62) and the groove structure relative to each other along a direction perpendicular to a bending direction (14) of the bending transducer structure (12). The mechanical system according to Claim 11 , wherein the adaptation structure (18) has connecting elements (64) between adjacent groove structures (58) which have a conductive or insulating material. The mechanical system according to one of the preceding claims, wherein the adaptation structure (18) is at least partially arranged between a first section of the bending transducer structure (12) and a second section of the bending transducer structure (12) along a bending direction (14) of the bending transducer structure. The mechanical system according to Claim 13 , wherein the bending transducer structure (12) has at least two bending elements (26 ₁ , 26 ₂ ), which are mechanically coupled in parallel and form an intermediate space (38) with an adjacent bending element of the bending transducer structure (12), at least part of the adaptation structure (18) is arranged in the intermediate space (38) and is mechanically coupled in parallel to the adjacent bending elements via the mechanical contact; wherein bending of the bending transducer structure causes mechanical contact between the conforming structure (18) and at least one of the adjacent bending elements in the gap. The mechanical system according to Claim 14 , comprising at least three flexure elements mechanically coupled in parallel to form at least a first gap between a first flexure element and a second flexure element and to form a second gap between the second flexure element and a third flexure element; wherein a first part of the matching structure (18) is arranged in the first gap to form a first contact, and a second part of the matching structure (18) is arranged in the second gap to form a second contact. The mechanical system according to any one of the preceding claims, wherein the flexural transducer structure (12) comprises a first transducer section and a second opposed transducer section, the first transducer section and the second transducer section being formed convexly with respect to a central region between the first transducer section and the second transducer section , wherein the adjustment structure (18) comprises a bending beam structure that is mechanically coupled in parallel to the first transducer section and the second transducer section and is coupled between the first transducer section and the second transducer section. The mechanical system according to Claim 16 , wherein the bending beam structure of the adaptation structure (18) has a local stiffening in a central region of the bending beam structure. The mechanical system according to Claim 16 or 17 , wherein the matching structure (18) comprises an electrode structure having a first electrode, a second electrode and an insulating material therebetween, the electrode structure forming at least a part of the flexural beam structure; wherein the conforming deformation results in deformation of the electrode structure; wherein the mechanical system is adapted to provide an electrical signal (16) corresponding to the adaptation deformation. The mechanical system according to one of the Claims 16 until 18 , wherein the first transducer section (12a) and the second transducer section (12b) are arranged symmetrically or asymmetrically with respect to one another. The mechanical system according to any preceding claim, wherein the adjustment structure (18) is located at least partially outside a volume (24) enclosed by outer sides of the flexural transducer structure (12). The mechanical system according to Claim 20 , wherein the adjustment structure (18) comprises a first bending beam structure (84 ₁ ) and a second adjacent bending beam structure (84 ₂ ), both ends (86) thereof being connected to the bending transducer structure; wherein the adjustment structure (18) is configured to provide adjustment formation as a bend of the first bending beam structure (84 ₁ ) and the second bending beam structure (84 ₂ ), wherein during bending of the bending transducer structure (12), the adjustment structure (18) is configured to form a Contact between the first bending beam structure (84 ₁ ) and the second bending beam structure (84 ₂ ) in a contact surface (22), which increases with an increase in a bending amplitude of the bending transducer structure (12). The mechanical system according to Claim 20 or 21 , wherein the adjustment structure (18) comprises a first bending beam structure (84 ₁ ), a second bending beam structure arranged in series with the first bending beam structure (84 ₁ ), and a spring structure arranged between the first bending beam structure (84 ₁ ) and the second Bending beam structure is arranged, wherein the spring structure (96; 102) is adapted to be at a distance from the bending transducer structure (12) in a non-deflected manner to locally reduce the state of the mechanical system; wherein the spring structure (96; 102) has a linearized spring characteristic and is arranged to form mechanical contact with the bending transducer structure (12) or with another bending beam structure of the adjustment structure (18) to provide for the second nonlinear mechanical stiffness contribution care for. The mechanical system according to Claim 22 , wherein the spring structure (96; 102) has two flexural elements which face one another and are connected to one another at a connecting portion; wherein the spring structure is configured to increase a contact area between the two flexure elements with an increase in deflection of the flexure transducer structure (12). The mechanical system according to one of the Claims 20 until 23 , wherein the adjustment structure (18) comprises a spring structure (96; 102) that is mechanically attached to the bending transducer structure (12) and is supported on a substrate that supports the bending transducer structure (12). The mechanical system according to Claim 24 , wherein the spring structure (96; 102) has a plurality of layered bending beam structures. The mechanical system according to one of the Claims 20 until 23 , wherein the adjustment structure (18) comprises a spring structure (96; 102) which is mechanically attached to the bending transducer structure (12) and is supported by a bending beam structure which bends in concert with the bending transducer structure (12). The mechanical system according to one of the Claims 20 until 26 , wherein the bending transducer structure comprises a conductive material, and wherein the adaptation structure (18) comprises the conductive material. The mechanical system according to one of the Claims 20 until 27 , wherein the adaptation structure (18) has a bending beam structure which is coupled in parallel to a bending beam structure of the bending transducer structure (12). The mechanical system according to Claim 28 , wherein the bending beam structure has at least one local stiffening or a local weakening between a first end and a second end of the bending beam structure. The mechanical system according to Claim 28 or 29 , wherein the bending transducer structure (12) comprises a first bending element and a second bending element (26 ₂ ) coupled in parallel to the first bending element (26 ₁ ); wherein the adjustment structure (18) has at least a first adjustment element (18 ₁ ) mechanically connected in parallel to the first bending element (18 ₁ ) while forming a first gap; and at least a second adjustment element (18 ₂ ) mechanically connected in parallel to the second flexure element while forming a second gap (92 ₂ ). The mechanical system according to one of the claims, wherein the second non-linear contribution at least partially counteracts the first non-linear contribution, the combination of the first non-linear mechanical stiffness contribution and the second non-linear mechanical stiffness contribution compared to the first non-linear mechanical stiffness -Contribution has a higher linearity. The mechanical system according to any one of the preceding claims, wherein the bending transducer structure (12) comprises a first bending element (26 ₁ ) and a second bending element (26 ₂ ) secured to one another at discrete positions (118) along a bending direction (14 ), along which the bending transducer structure (12) is configured to provide the bending, a stiffness of the first bending element (26 ₁ ) differs compared to the second bending element (26 ₂ ). The mechanical system according to any one of the preceding claims, wherein in a non-deflected state of the mechanical system, a flexural element of the flexural transducer structure (12) has a curved or angular path between a first end and a second end of the flexural element to define a direction of bending . The mechanical system according to any one of claims, wherein the flexural transducer structure (12) comprises at least: • an electrostatic or electrodynamic configuration; • a piezoelectric configuration; • an electrothermal configuration; and or • an electroactive polymer configuration. The mechanical system of any preceding claim, wherein the bending transducer structure (12) is configured to bend in response to the applied electrical signal (16); wherein the mechanical system includes a control unit configured to provide the electrical signal (16). The mechanical system according to any preceding claim, wherein the flexural transducer structure (12) is configured to provide the electrical signal (16) in response to the specified applied external force (F) causing the bend; wherein the mechanical system has a readout circuit configured to provide the electrical signal (16). The mechanical system according to any one of claims, wherein the mechanical system is a micromechanical system. The mechanical system according to one of the Claims 1 until 37 , wherein the bending transducer structure (12) is adapted to provide the bending in a planar manner with respect to a layer arrangement comprising the mechanical system. The mechanical system according to the Claims 1 until 37 , wherein the bending transducer structure (12) is adapted to provide the bending in an out-of-planar manner with respect to a layer arrangement comprising the mechanical system. A mechanical system arrangement having a plurality of cells arranged mechanically in series with one another, each cell being configured according to any one of the preceding claims. A mechanical system that has the following features: a bending transducer structure (12) configured to non-linearly deform based on bending in response to an applied electrical signal (16) and/or to non-linearly provide an electrical signal (16) in response to an applied external force (F) which is the bending causes an adjustment structure (18) mechanically coupled to the bending transducer structure (12); wherein the bending and a deformation of the adaptation structure (18) are causally correlated, the deformation of the adaptation structure (18) providing a nonlinear force for the bending transducer structure (12) that reduces the magnitude of a nonlinearity in an overall response of the mechanical system. Method for providing a mechanical system, the method comprising the following steps: Providing a bending transducer structure (12) such that it is configured to provide a bend in response to an applied electrical signal (16) and/or to provide an electrical signal (16) in response to an applied external force (F) causing the bend , such that a structural stiffness (52) of the bending transducer structure provides a first nonlinear mechanical stiffness contribution of the bend; mechanically coupling an accommodating structure (18) to the bending transducer structure (12) to provide accommodating deformation along with the bending, such that a structural stiffness (52) of the accommodating structure (18) provides a second nonlinear mechanical stiffness contribution to the Bending based on mechanical coupling when deformed. Method for providing a mechanical system, the method comprising the following steps: Providing a bending transducer structure (12) such that it is configured to non-linearly deform based on a bend in response to an applied electrical signal (16) and/or to non-linearly provide an electrical signal (16) in response to an applied external force (F) , which causes the bend, mechanically coupling an adaptation structure (18) to the bending transducer structure (12); so that the bending and a deformation of the adaptation structure (18) are causally correlated, so that the deformation of the adaptation structure (18) provides a nonlinear force for the bending transducer structure (12), which reduces the magnitude of a nonlinearity in the overall response of the mechanical system.

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