Analytical modeling and computational optimization for a 1-DOF 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.

This paper presents a novel piezoelectric XY micro-displacement scanning stage (MDSS), which features a parallel structure based on compliant mechanisms and has a compact configuration. Since the coupling problem between two motion axes, an innovative elliptical compliant restraint mechanism (ECRM) with a compact layout is proposed and utilized in XY MDSS to obtain high motion accuracy. And the XY MDSS can realize compact structure and lower input stiffness for a large workspace owing to the ECRM simultaneously. Due to the limited displacement of the piezoelectric stack actuator, compliant amplification mechanism is applied to achieve a large stroke. In order to estimate the static and dynamic characteristics theoretically, Castigliano’s second theorem and Lagrange’s method are utilized to establish the analytical models of the newfangled ECRM, compliant amplification mechanism, and XY MDSS. The finite element analysis and experimental tests are carried out to evaluate the performances of XY XDSS, and the results are all in correspondence with analytic solutions, which further validate the correctness of the analytical modeling methodologies. Experimental results show that the XY MDSS can realize a workspace of 58.8 μm × 51.5 μm with a resonance frequency of 576.5 Hz and nanometer-level resolution. The effectiveness of the designed ECRM is also proved simultaneously, which could well limit the coupling motion. The theoretical studies, finite element analysis, and experimental testing all demonstrate that the designed XY MDSS with ECRM has good performance while having a compact structure.

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

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.

While nonlinear-elastic materials demonstrate potential in enhancing the performance of compliant mechanisms, their behavior still needs to be captured in a generalized mechanical model. To inform new designs and functionality of compliant mechanisms, a better understanding of nonlinear-elastic materials is necessary and, in particular, their mechanical properties that often differ in tension and compression. In the current work, a beam-based analytical model incorporating nonlinear-elastic material behavior is defined for a folding compliant mechanism geometry. Exact equations are derived capturing the nonlinear curvature profile and shift in the neutral axis due to the material asymmetry. The deflection and curvature profile are compared with finite element analysis along with stress distribution across the beam thickness. The analytical model is shown to be a good approximation of the behavior of nonlinear-elastic materials with tension–compression asymmetry under the assumptions of the von Kármán strain theory. Through a segmentation approach, the geometries of a semicircular arc and folding compliant mechanism design are defined. The deflection of the folding compliant mechanism due to an applied tip load is then evaluated against finite element analysis and experimental results. The generalized methods presented highlight the utility of the model for designing and predicting the behavior of other compliant mechanism geometries and different nonlinear-elastic materials.

Kinetostatic modeling of complex compliant mechanisms with serial-parallel substructures: A semi-analytical matrix displacement method

The design of the canopy utilizes the conventional rigid body mechanisms which is vulnerable to the presence of backlash, friction of joints or wearing of mechanical parts which lead to short product life. Compliant mechanisms are employed to reduce these mechanical problems, owing to their zero-joint and monolithic structure. A reference design for the conventional canopy was chosen and modified through reviewing different patent designs. Six different configurations of the pseudo-rigid-body model (PRBM) were constructed, and the best configuration was selected. Kinematic synthesis with function generation was performed for the chosen PRBM using MATLAB. The obtained results from the kinematic synthesis were then used to calculate the dimensions and stresses of the flexural pivots for the compliant stretcher mechanism. Finite Element Analysis (FEA) simulation was then performed on each of the models and the obtained flexural pivot stresses were compared with that of the PRBM. This research successfully replaces all the rigid joints and links of the stretcher mechanism of the conventional canopy to form a monolithic structure of compliant stretcher mechanism.

Compliant mechanism is a kind of new type mechanism and its analysis is very complex because flexible links often under large deflections which introduce geometry nonlinearities. A new model (2R PRBM) can simulate accurately both the deflection path and angle of the flexible link. A new dynamic model of compliant mechanism is developed using the 2R PRBM. The dynamic equation of planar compliant mechanism is derived. The dynamic analysis on the natural frequency of compliant mechanism is obtained in the example of a planar compliant parallel-guiding mechanism. The numerical results show the advantage of the proposed method for the dynamic analysis of compliant mechanisms.

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.

This work introduces an interior contact-aided rolling element (I-CORE) compliant mechanism that draws upon the concepts used for the contact-aided rolling element, cross-axis flexural pivot, and pre-curved flexible beam. The I-CORE incorporates a bilinear compressive stiffness response with an initial tailorable stiffness governed by the flexural geometry, followed by a stiffness curve governed by the material stiffness at the contact point. The I-CORE mechanism can achieve one or two degrees of rotational freedom as well as a single degree of translational freedom. The purpose of the present work was to introduce the I-CORE mechanism, as well as a pseudo-rigid-body replacement model (PRBM) of the I-CORE mechanism which was subsequently validated using both finite element analysis and benchtop mechanical testing. A pseudo-rigid body model was created for the I-CORE to simplify the rapid adaptation of this mechanism to different design applications. This model was validated using both finite element analysis and benchtop mechanical testing under both compression and rotation loading conditions. Additionally, multiple configurations of the device were created and evaluated in order to test its sensitivity to certain design features including the flexure width, flexure thickness, and the radius of the rounded contact surfaces. It was found that the model is sensitive to the thickness of the flexures and that despite some limitations, the pseudo-rigid body model is sufficiently accurate for initial design work. Some possible applications of the mechanism are proposed.

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.

Topology optimization of compliant mechanism and its support through a level set method

A novel compliant mechanism with three degree of freedom (DOF) is proposed, based on the method of Freedom and Constraint Topology (FACT). One movement and two rotations are obtained in Case 3, Type 2 freedom space. A redundant constraint is added to improve the symmetry. The finite element modal (FEM) is established and static force analysis is conducted. Results demonstrate that the compliant mechanism is decoupled. Modal analysis is carried out with the finite element method. And four orders natural frequency and main vibration mode are obtained.

Parasitic motion is undesired in precision mechanisms, it causes unwanted kinematics. These erroneous motions are especially apparent in compliant mechanisms. Usually an analysis of parasitic motion is only valid for one type of mechanism. Kinematic information is imbedded in the compliance matrix of any mechanism; an eigenscrew decomposition expresses this kinematic information as screws. It uses screw theory to identify the lines along which a force yields a parallel translation and a rotation yields a parallel moment. These lines are called eigenwrenches and eigentwists. Any other load on the compliant mechanism will lead to parasitic motion. This article introduces two parasitic motion metrics using eigenscrew decomposition: the parasitic resultant from an applied screw and the deviation of an actual degree of freedom from a desired degree of freedom. These metrics are applicable to all compliant mechanism and allow comparison between two compliant mechanisms. These metrics are applied to some common compliant mechanisms as an example.

This paper focuses on experiments and finite element modelling of flexible plug expansion joints (Asphaltic Plug Joints, APJ) subject to thermally induced horizontal movements. Five geometric and structural key parameters that influence (APJs) responses under thermal movements are studied: (1) joint length; (2) joint thickness; (3) joint width; (4) anti-bonding mat; (5) movement-aid spring. The viscoelastic computational finite element models are based on properties determined with a special cyclic coaxial shear test (CAST) and validated by an integrated approach incorporating cold temperature repeated movement capacity tests with a special Joint Movement Simulator (JMS) and a 3-Dimensional Digital Image Correlation system (3D DIC). It was found that the increase of joint width significantly reduces the stress at the interface between the mastic asphalt and APJ. The results also showed, that thin joints generate lower stress levels in APJ under thermal condition. Moreover, peak stresses in APJ appeared controlled mainly by the total size of the debonded region and the horizontal movement applied. The main findings are considered valuable for superior structural design, geometry selection and construction guidelines for APJ.