Three-Dimensional Topologies of Compliant Flapping Mechanisms

Design of a variable-diameter wheel with a novel distributed compliant mechanism

Compliant mechanisms are single-piece flexible structures that deliver the desired motion by undergoing elastic deformation as opposed to jointed rigid body motions of conventional mechanisms. Compliance in design leads to jointless, no-assembly (Fig. 1), monolithic mechanical devices and is particularly suited for applications with small range of motions. The compliant windshield wiper shown in Fig. 1 illustrates this paradigm of no-assembly. Conventional flexural mechanisms employ flexural joints that connect relatively rigid links as depicted in Fig. 2. Reduced fatigue life, high stress concentration and difficulty in fabrication are some of the drawbacks of flexural joints. Our focus is on designing compliant mechanisms with distributed compliance which employs flexural links (see Fig. 3) and have no joints (neither pin nor flexural joints) for improved reliability, performance, and ease of manufacture. Distributed compliant mechanisms derive their flexibility due to topology and shape of the material continuum rather than concentrated flexion at few regions. This paper focuses on the unique methodology employed to design jointless mechanisms with distributed compliance. The paper also illustrates a compliant stroke amplification mechanism that was recently designed, fabricated and tested for MEMS application.

Random variable of thermo-mechanical coupling (TMC) structure is analyzed first, then the topology optimization model of TMC compliant mechanism is established. According to the uncertainty factors such as temperature, load, volume ratio and thermal expansion coefficient in the process of topology optimization, the robust reliability optimal design method is introduced into the topology optimization process. The various factors on the sensitivity of topology optimization process is analyzed, the best match between various factors is find out, which make the product has robust reliability for the change of the uncertainty. The residual analysis for the most sensitive factors is carried out. Finally the correctness and validity of the method is verified with an example. Introduction When we study the compliant mechanisms by adopting topological optimization method, we only need to give design domain and allocate input and output position, no need from the perspective of a known rigidity. The mechanism come from this method have a input and output relationship of optimized “force—displacement”, thus it attracts people’s attention. Topology optimization research is developing from certain topology optimization direction to reliable topology optimization direction. Jinqing Zhan proposed a reliable topology optimization method of compliant mechanism based on infrastructure method. KHARMANDA proposed a reliable topology optimization method. Zhaokun Li proposed a geometric nonlinear topology optimization research method based on reliable compliant mechanism. Their research turned out that the mechanism based on reliable topology optimization is more reasonable than the mechanism based on certain topology optimization. Yongcong Kuang build a level set function to design variable, stiffness minimization, and proposed corresponding optimization algorithm. Mingtao Cui established a monolithic compliant mechanism multi-target reliable topology optimization design dual mathematical model. This paper combines topology optimization process of compliant mechanism and robust reliability optimal design, analyzes the sensitivity of uncertainty random variables such as design domain’s size, external load and temperature in topology optimization process. Then get the best combination among these random variables. Random Variable Coupling Field Analysis Hot objects will produce thermal expansion, thus caused by the thermal deformation and displacement of combined action of mechanical load and temperature load structure called a hot solid coupling structure, the finite element balance equation :

A bioinspired tethered MAV model is designed, constructed and studied for structural dynamic characteristics using novel materials and methods. The model consists of two flapping wings, a compliant flapping mechanism, and a supporting chassis. Large size insects such as dragonfly and cicada are considered as inspiration for the designing purposes. The wings and mechanism designed in this study are a simplified form of the natural counterparts. These idealized bioinspired structures are first studied for structural dynamic characteristics using finite element methods. Carbon nanotubes/polypropylene (CNTs/PP) nanocomposite stiffeners and a thin LDPE membrane are used to realize the designed wing model. The use of this novel material composition resulted in a lightweight, thin, and flexible wing capable of large amplitude passive bending-twisting motion. For constructing the flapping mechanism, a novel compliant mechanism is fabricated and attached with a piezoelectric actuator of cantilever form. The compliant mechanism is designed with CNTs/PP nanocomposite flexure joints supported using rigid carbon fiber/epoxy composite linkages. The fabrication of wing stiffeners and mechanism flexures from lab developed CNTs/PP nanocomposite materials is carried out using laser micromachining based manufacturing technique. The complete MAV model is constructed by assembling the wings and mechanism with a carbon fiber/epoxy composite chassis. The final assemblage is a two-winged MAV model of a total mass, body length, and wingspan of 0.6 1g, 60.46 mm, and 90.14 mm, respectively. An external customized power supply is developed and used with a microcontroller to actuate the flapping mechanism and wings during experiments. The computational structural analysis showed that no resonance occurs at the mechanism, all the first four fundamental modes are at the wings. This is advantageous for accurate and efficient motion transmission to the wings. The model generates large-amplitude wing deflections with a very small amplitude input excitation from the actuator - useful for higher aerodynamic performance. Experimentally, the structural dynamic analysis of the MAV model is carried out using an in-house high-speed 3D digital image correlation (DIC) technique, which reveals that the wings generate bending dominated deforming shape with marginal twisting and positive camber (during downstroke). Structural dynamic results from computations are in good agreement with the experiments that validates both of the approaches for further advancements in the developed MAV model. Overall outcome of the current work is a simplified biomimetic MAV design, a potential candidate for developing mechanically efficient MAV models.

Compliant mechanisms have been defined as mechanical systems that derive some or all of their mobility from the flexibility of one or more of their members. In general, due to the large-deflection nature of the compliant members, analysis and synthesis of compliant mechanisms have typically required a numerical iterative solution method. Recently, analytical loop-closure synthesis techniques have been extended to the design of compliant mechanisms, by utilizing the concept of an equivalent pseudo-rigid-body model for a compliant mechanism. These developments have greatly simplified the synthesis of compliant mechanisms. These mechanisms have been synthesized for three precision points using analytical and graphical methods. In rigid-link mechanism design, additional precision points may be incorporated by using Burmester theory. With this enhancement as the motivation, this paper presents the first use of Burmester theory to design compliant mechanisms for four and five precision points. This is facilitated by use of the concept of an equivalent pseudo-rigid-body model. Burmester theory yields a linear set of kinematic equations, allowing for their easy utilization herein. Also for some design problems, this theory can provide a graphical representation of all possible solutions for compliant mechanisms. In addition to the specification of precision points for compliant mechanisms, input torque and/or potential energy values may also be prescribed.

Compliant mechanisms utilize the elastic deformation of their constituent members to transfer forces or displacements. Compliant mechanisms are advantageous in robotic applications because of their simplified manufacturing, monolithic structure, high precision, low wear and backlash, and flexibility to accommodate a wide range of actuation schemes. Despite these significant advantages, modeling these mechanisms is challenging because of their complex and large nonlinear deformations. Currently, most modeling methods for compliant mechanisms are either kinematic or kinetostatic, such as the pseudo-rigid body method (PRBM), beam constraint model (BCM), and load-flow-based method. These methods are mostly limited to bending deformation and do not consider shear or stretch strain. Furthermore, they are not conducive to modeling compliant mechanisms with embedded actuators in the geometry of the mechanism. To overcome these limitations, here we adopt Cosserat rod modeling, which captures the generalized deformations of the constituent members of compliant mechanisms. Furthermore, it allows the modeling of compliant mechanisms with actuation members. Several compliant mechanism experimental prototypes, including compliant inverters and a compliant gripper, were presented to validate and depict the effectiveness of the Cosserat rod modeling. This modeling approach enables large-scale and efficient modeling of the complaint mechanisms with actuators and sensors.

Bistable mechanical devices remain stable in two distinct positions without power input. They find application in valves, switches, closures, and clasps. Mechanically bistable behavior results from the storage and release of energy, typically in springs, with stable positions occurring at local minima of stored energy. Compliant mechanisms offer an elegant way to achieve this behavior by incorporating both motion and energy storage into the same flexible element. Interest in compliant bistable mechanisms has also recently increased because of the advantages of bistable behavior in many micro-electro-mechanical systems (MEMS). Design of compliant or rigid-body bistable mechanisms typically requires simultaneous consideration of both energy storage and motion requirements. This paper simplifies this process by developing theory that provides prior knowledge of mechanism configurations that guarantee bistable behavior. Configurations which include one or more translational, or slider, joints are studied in this work. Several different mechanism types are analyzed to determine compliant segment placement that will ensure bistable mechanism operation. Examples demonstrate the power of the theory in design.

This paper proposes a new compliant mechanism for the stroke amplification of piezoelectric actuators. Compared with the existing ones, this compliant stroke amplification mechanism (CSAM) has several advantages including lightweight, less stress concentration, large motion range, as well as ease of manufacture in macro- and micro-scales, mainly due to the completely distributed compliance and largely reduced moving mass. Kinetostatic models of the CSAM, with consideration of the payloads applied on the output stage, are derived for quick and insightful determinate analysis, which enables optimization of the associated parameters to achieve different objectives. The results obtained from the kinetostatic models are in reasonable agreement with the FEA simulation results, with less than 3.8% difference when the input displacement is less than 10 µm. An optimization method, based on the analytical models, is introduced and employed to increase the amplification ratio of the CSAM by up to 240%. The optimized CSAM is an excellent candidate for the stroke amplification of piezoelectric actuators, which is fabricated and experimentally tested. The optimization method is able to be extended to design other compliant mechanisms with optimized size, shape and topology configuration simultaneously.

Compliant mechanisms gain at least some of their mobility from the deflection of flexible members rather than from movable joints only. Dynamic effects are very important to improving the design of compliant mechanisms. An investigation on the dynamics and synthesis of the compliant mechanisms is presented. The dynamic model of compliant mechanisms is developed at first. The natural frequency and sensitivity are then studied based on the dynamic model. Finally, optimal design of compliant mechanism is investigated. The experimental study of natural frequency is performed. The comparison between the experiment results and the theoretical results verifies the validity of the experiment system and theoretical model.

This paper proposes an alternative topology optimization approach for the design of the large displacement compliant mechanisms with geometrical non-linearity by using the Element-free Galerkin (EFG) Method. In this study, because of its non-negative and range-bounded properties, Shepard function method, as a density filter, is used to generate a non-local nodal density field with enriched smoothness over the design domain. Besides, the Shepard function method is employed to build a point-wise density interpolation, the numerical implementation to calculate the artificial densities at all Gauss points. The moving least squares (MLS) method is then used to construct shape functions with compactly supported weight functions, to assemble the meshless approximations of system state equations. A typical large deformation compliant mechanism is presented to demonstrate the effectiveness of the proposed method.

Inspired by nature’s multi-material compliant designs and the capability of modern manufacturing methods to make multi-material components without assembly, and motivated by the versatility and enhanced functionality with multi-material designs, we formalize the notion and the design of heterogeneous compliant mechanisms. In the topology optimization of compliant mechanisms, a fictitious density function is often used for material interpolation to overcome the computational difficulties encountered in the large “0-1” type integer programming problem. In this paper, we illustrate that a gradually formed continuous peak function can be used for material interpolation. One of the advantages of introducing the peak function is that multiple materials can easily be incorporated into the topology optimization without increasing the number of design variables. By using the peak function and the optimality criteria method, we synthesize compliant mechanisms with multiple materials with and without the material resource constraint. The numerical examples include the two, three, and four material designs where void is treated as one material. This new design method enables us to optimally juxtapose stiff and flexible materials in heterogeneous compliant mechanisms that can be built using a variety of modern manufacturing methods.

The design of compliant mechanisms has been aided by the development of pseudo-rigid-body models to predict the motion of flexible members undergoing large displacements. Many of these models are based on the fact that the end of a cantilever beam follows a near-circular path when planar loads are applied. This paper shows that the application of 3-dimensional end-loading causes a beam to follow a near-spherical path, even for beams with non-circular cross-sections. A 3D pseudo-rigid-body model is presented that allows the motion of an end-loaded rectangular beam to be predicted using a rigid link and a spherical joint. Two sets of deflection limits for 0.5% error are presented and shown to be dependent upon the aspect ratio of the cross-section of the beam. The model has the potential for aiding in the design of spatial compliant mechanisms and analysis of planar compliant mechanisms undergoing large out-of-plane motions.

Morphing is a technology with high potential to reduce emissions in aviation, since it enables wings to adapt their shape to operate at a higher efficiency over the full range of flight conditions. This paper is presenting a concept to adapt camber by drooping the nose. The scope is the setup and bench top testing of a full scale wing tip leading edge wind tunnel model with a morphing droop nose. The complete model features a span of 1.3 m and a strong taper from the root to the tip. For completeness, the design approach is covered as well. The design comprises a GFRP skin to be drooped by two compliant mechanisms, which are driven by linear motors. The compliant morphing devices are “designed-through-optimization”, with the optimization algorithms including Simplex optimization for composite compliant skin design, continuum-based and load path representation topology optimization methods for compliant internal substructure design. The compliant mechanism is manufactured by nickel-titanium alloy to allow high strains in the order of several percent, which is shown to be critical in the design of such compliant mechanisms. In order to validate the models, strains within the mechanisms are measured while drooping the nose in the bench top test. This is done after installing the mechanisms into the leading edge skin. It can be shown, that the simulation for the inboard mechanism is close to the experimental results. The comparison of strain levels in the skin and in the mechanism during droop reveals that the stiffness distribution between these two components is quite different. As a result this ratio can be taken into account in future design processes in order to distribute strains more evenly. Moreover the 3D shapes of the morphed and clean skin are measured and their comparison with the target shapes is presented as well. Finally, the bench top tests are a proof of concept for the overall concept and design which resultes in a “go” for the following low speed subsonic wind tunnel tests.

The formulation of design procedures for rigid-body mechanisms has benefited from the application of type-synthesis techniques. Therefore, with modifications to allow for inclusions of compliance, type synthesis is seen as a useful tool in the design of compliant mechanisms. Previous efforts have developed methods that result in a large number of possible design solutions to a given problem. This paper deals primarily with the development of a simplified compliant-mechanism type-synthesis methodology that limits the number of design solutions considered. The techniques are derived by modifying existing compliant mechanism type-synthesis techniques to yield a simpler model with greater pragmatic value.

Energy based topology optimization method has been used in the design of compliant mechanisms for many years. Although many successful examples from the energy based topology optimization have been presented, optimized configurations of these designs are often very similar to their rigid linkage counterparts except using compliant joints in place of rigid links. It is obvious that these complaint joints will endure large deformations under the applied forces in order to perform the specified motions and the large deformation will produce high stress which is very undesirable in compliant mechanism design. In this paper, a strain based topology optimization method is proposed to avoid localized high deformation design which is one of the drawbacks using strain energy formulation. Therefore, instead of minimizing the strain energy for structural rigidity, a global effective strain functional is minimized in order to distribute the deformation within the entire mechanism while maximizing the structural rigidity. Furthermore, the physical programming method is adopted to accommodate both flexibility and rigidity design objectives. Comparisons of design examples from both the strain energy based topology optimization and the strain based method are presented and discussed.