Shape design of pin-jointed multistable compliant mechanisms using snapthrough behavior

A general approach is presented for generating pin-jointed multistable compliant mechanisms using snapthrough behavior. An optimization problem is formulated for minimizing the total structural volume under constraints on the displacements at the specified nodes, stiffnesses at initial and final states, and load factors to lead to snapthrough behavior. The design variables are cross-sectional areas and the nodal coordinates. It is shown in the numerical examples that several mechanisms can be naturally found as a result of optimization starting from randomly selected initial solutions. It is also shown that no local bifurcation point exists along the equilibrium path, and the obtained mechanism is not sensitive to initial imperfections.     

Topology optimization of structures with integral compliant mechanisms for mid-frequency response

The purpose of this paper is to present a method for developing new truss-like sandwich structures that exhibit desirable mid-frequency vibratory characteristics. Specifically, a genetic algorithm optimization routine is used to determine candidate small scale structural topologies, i.e. unit cells, that may be used in the design of larger scale periodic sandwich structures. This multi-scale procedure is demonstrated starting with several unit cell topology optimization examples. From these examples a specific optimal unit cell is selected for further investigation and integration into a periodic sandwich beam. Computational results indicate that the proposed optimization approach is effective when used to design new structures for reduced mid-frequency vibratory response.     

Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms

The paper formulates an analytical method for displacement and stiffness calculations of planar compliant mechanisms with single-axis flexure hinges. The procedure is based on the strain energy and Castigliano’s displacement theorem and produces closed-form equations that incorporate the compliances characterizing any analytically-defined hinge, together with the other geometric and material properties of the compliant mechanism. Displacement amplification, input stiffness and output stiffness calculations can simply be performed for any serial compliant mechanism. The class of amplifying compliant mechanisms that contain symmetric corner-filleted or circular flexure hinges is specifically addressed here. A parametric study of the mechanism performance is performed, based on the mathematical model, and an optimization procedure is proposed, based on Lagrange’s multipliers and Kuhn-Tucker conditions, which identifies the design vector that maximizes the performance of these flexure-based compliant mechanisms. Independent finite element simulation confirms the analytical model predictions.     

Complex-shaped beam element and graph-based optimization of compliant mechanisms

Compliant mechanisms are designed to be intentionally flexible, providing hingeless mechanisms. This work contributes a complex-shaped beam element formulation in conjunction with the ground structure approach. We identify compliant mechanism design solutions by using evolutionary topology optimization and increase flexibility by using a parametrization concept based on graph theory. The new operators for evolutionary optimization are also explained and sample problems are used to address the question of how our contribution increases design solutions space.     

Topology design of large displacement compliant mechanisms with multiple materials and multiple output ports

Topology optimization of compliant mechanisms is presented in this paper wherein the layout design problem is addressed in its original binary or discrete (0-1) form. Design variables are modeled as discrete variables and allowed to assume values pertaining only to their void (0) or solid (1) states. Due to this discrete nature, a genetic algorithm is employed as an optimization routine. Using the barrier assignment approach, the search algorithm is extended to use with multiple materials. The layout design of compliant mechanisms is performed wherein displacements at multiple points (ports) in the design region are maximized along the respective prescribed directions. With multiple output ports and multiple materials, additional freedom in motion and force transduction can be achieved with compliant mechanisms. Geometrically large deformation analysis is employed to compute the displacement-based multiple objectives that are extremized using Nondominated Sorting in Genetic Algorithms (or NSGA). With genetic algorithms, buckling or snap through like issues with nonconvergent solutions in the population when computing nonlinear deformations can be implicitly circumvented.     

Topology synthesis of Multi-Input–Multi-Output compliant mechanisms

A generalized formulation to design Multi-Input–Multi-Output (MIMO) compliant mechanisms is presented in this work. This formulation also covers the simplified cases of the design of Multi-Input and Multi-Output compliant mechanisms, more commonly used in the literature. A Sequential Element Rejection and Admission (SERA) method is used to obtain the optimum design that converts one or more input works into one or more output displacements in predefined directions. The SERA procedure allows material to flow between two different material models: ‘real’ and ‘virtual’. The method works with two separate criteria for the rejection and admission of elements to efficiently achieve the optimum design. Examples of Multi-Input, Multi-Output and MIMO compliant mechanisms are presented to demonstrate the validity of the proposed procedure to design complex complaint mechanisms.     

Six-DOF micro-manipulator based on compliant parallel mechanism with integrated force sensor

This paper describes the design of a micro-scale manipulator based on a six-DOF compliant parallel mechanism (CPM), which is featured by piezo-driven actuators and integrated force sensor capable of delivering six-DOF motions with high precision and providing real-time force information for feedback control. Particularly, the position and screw-based Jacobian analyses of the CPM are presented. Then, the compliance model and the workspace evaluation of the CPM are proposed in order to account for the compliance and obtain design guidelines. Finally, the integrated sensor is introduced. The static features of such a mechanism include high positioning accuracy, structural compactness and smooth and continuous displacements.     

Topology optimization of compliant mechanisms using element-free Galerkin method

This paper will propose a topology optimization approach for the design of large displacement compliant mechanisms with geometrical non-linearity by using the element-free Galerkin (EFG) method. In this method, the Shepard function is applied to construct a physically meaningful density approximant, to account for its non-negative and range-bounded property. Firstly, in terms of the original nodal density field, the Shepard function method functionally similar to a density filter is used to generate a non-local nodal density field with enriched smoothness over the design domain. The density of any node can be evaluated according to the nodal density variables located inside the influence domain of the interested node. Secondly, in the numerical implementation the Shepard function method is again employed to construct a point-wise density interpolant. Gauss quadrature is used to calculate the integration of background cells numerically, and the artificial densities over all Gauss points can be determined by the surrounding nodal densities within the influence domain of the concerned computational point. Finally, the moving least squares (MLS) method is applied to construct the shape functions using the weight functions with compact support for assembling the meshless approximations of state equations. Since MLS shape functions are lack of the Kronecker delta function property, the penalty method is applied to enforce the essential boundary conditions. A typical large-deformation compliant mechanism is used as the numerical example to demonstrate the effectiveness of the proposed method.     

A new level set method for systematic design of hinge-free compliant mechanisms

This paper presents a new level set-based method to realize shape and topology optimization of hinge-free compliant mechanisms. A quadratic energy functional used in image processing applications is introduced in the level set method to control the geometric width of structural components in the created mechanism. A semi-implicit scheme with an additive operator splitting (AOS) algorithm is employed to solve the Hamilton-Jacobi partial differential equation (PDE) in the level set method. The design of compliant mechanisms is mathematically represented as a general non-linear programming with a new objective function augmented by the high-order energy term. The structural optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints. In doing so, it is expected that numerical difficulties such as the Courant-Friedrichs-Lewy (CFL) condition and periodically applied re-initialization procedures in most conventional level set methods can be eliminated. In addition, new holes can be created inside the design domain. The final mechanism configurations consist of strip-like members suitable for generating distributed compliance, and solving the de-facto hinge problem in the design of compliant mechanisms. Two widely studied numerical examples are studied to demonstrate the effectiveness of the proposed method in the context of designing distributed compliant mechanisms.     

Hybrid Taguchi-cuckoo search algorithm for optimization of a compliant focus positioning platform

A long positioning range and a high first natural frequency are the two most important quality responses of a compliant focus positioning platform (CFPP). This paper aims to develop a hybrid Taguchi-cuckoo search (HTCS) algorithm to optimize overall the quality responses, simultaneously. The CFPP is designed via using flexure hinges. The length, width, and thickness of flexure hinges are considered as design variables. The Taguchi’s L₁₆ orthogonal array is used to establish the experimental layout and the S/N ratios of each response are computed. The analysis of variance (ANOVA) is computed to investigate the effect of design parameters on the quality responses. Results of ANOVA are then utilized to limit the search space of design parameters that serves as initial population for the cuckoo search meta-heurist algorithm. The results showed that the HTCS algorithm is more effective than DE, GA, PSO, AEDE, and PSOGSA. The CFPP enables a long positioning range of 188.36 μm and a high frequency response of 284.06 Hz. The proposed HTCS approach can effectively optimize the multiple objectives for the CFPP and would be useful technique for related optimization problems.     

Adaptive neuro-fuzzy prediction of grasping object weight for passively compliant gripper

The development of universal grippers able to pick up unfamiliar objects of widely varying shapes and surfaces is a very challenging task. Passively compliant underactuated mechanisms are one way to obtain the gripper which could accommodate to any irregular and sensitive grasping objects. The purpose of the underactuation is to use the power of one actuator to drive the open and close motion of the gripper. The fully compliant mechanism has multiple degrees of freedom and can be considered as an underactuated mechanism. This paper presents a new design of the adaptive underactuated compliant gripper with distributed compliance. The optimal topology of the gripper structure was obtained by iterative finite element method (FEM) optimization procedure. The main points of this paper are in explanation of a new sensing capability of the gripper for grasping and lifting up the gripping objects. Since the sensor stress depends on weight of the grasping object it is appropriate to establish a prediction model for estimation of the grasping object weight in relation to sensor stress. A soft computing based prediction model was developed. In this study an adaptive neuro-fuzzy inference system (ANFIS) was used as soft computing methodology to conduct prediction of the grasping objects weight. The training and checking data for the ANFIS network were obtained by FEM simulations.     

Design,kinematic modeling and sliding mode control with sliding mode observer of a novel 3-PRR compliant mechanism

Compliant mechanisms have great advantages to be used as micropositioning stages for high-precision applications but they are very sensitive to manufacturing tolerances and assembling errors. In this work, a novel compliant stage having 3-PRR kinematic structure and actuated by piezoelectric actuators is introduced. A kinematic modeling based on compliance of the flexible elements and finite element analysis based model have been extracted. It is found out that the experimental results are not compatible with the theoretical results due to the manufacturing, actuator assembly errors. The position control of the mechanism has been achieved using sliding mode control which is a great method for unpredictable varying parameters in the system. Sliding mode observer has also been used for the hysteresis and nonlinearities of the piezoelectric actuators. Experimental models for each actuation axis have been used as the nominal models for the sliding mode observer. In order to see the advantage of the control method simple PID control has also been implemented. It is seen that sliding mode control with sliding mode observer using experimental models reduces the position tracking errors to the range of the accuracy of our available measurement.     

Proxy-based position control of manipulators with passive compliant actuators: Stability analysis and experiments

In this work we introduce a position control scheme which is targeted at the enhancement of the safety of compliant joint robots. In addition to the necessity for accuracy and robustness that both serve as prerequisites for the successful performance of various tasks, the ability to safely handle unexpected events, such as communication failures or unintended interactions which may endanger the robot/human safety, is a paramount requirement. To achieve a smooth motion behaviour of compliant systems under different circumstances, damping control actions are essential. To this end, a novel proxy-based approach for compliant joint robots, integrated into a passivity-guaranteed controller, is proposed. The stability analysis of the proposed scheme is presented and the global asymptotic convergence, as well as the passivity of the control scheme, are analytically proven. The performance of the proposed approach is practically evaluated by means of experiments on a spatial robotic arm with passive compliant actuators, and is compared with that of a classical PD approach. Experimental results validate the ability of the proposed approach to inject damping in order to provide smooth and damped recovery when an interruption in task execution occurs.     

Design of distributed compliant micromechanisms with an implicit free boundary representation

In this paper, a parameterization approach is presented for structural shape and topology optimization of compliant mechanisms using a moving boundary representation. A level set model is developed to implicitly describe the structural boundary by embedding into a scalar function of higher dimension as zero level set. The compactly supported radial basis function of favorable smoothness and accuracy is used to interpolate the level set function. Thus, the temporal and spatial initial value problem is now converted into a time-separable parameterization problem. Accordingly, the more difficult shape and topology optimization of the Hamilton–Jacobi equation is then transferred into a relatively easy size optimization with the expansion coefficients as design variables. The design boundary is therefore advanced by applying the optimality criteria method to iteratively evaluate the size optimization so as to update the level set function in accordance with expansion coefficients of the interpolation. The optimization problem of the compliant mechanism is established by including both the mechanical efficiency as the objective function and the prescribed material usage as the constraint. The design sensitivity analysis is performed by utilizing the shape derivative. It is noted that the present method is not only capable of simultaneously addressing shape fidelity and topology changes with a smooth structural boundary but also able to avoid some of the unfavorable numerical issues such as the Courant–Friedrich–Levy condition, the velocity extension algorithm, and the reinitialization procedure in the conventional level set method. In particular, the present method can generate new holes inside the material domain, which makes the final design less insensitive to the initial guess. The compliant inverter is applied to demonstrate the availability of the present method in the framework of the implicit free boundary representation.     

An optimization method for dynamics of structures with repetitive component patterns

The design obtained from a topology optimization problem can be sensitive to the type and details of the ground structure used. A new type of ground structure containing hinged beam elements is described that increases the types of elements in the ground structure available to the optimizer. In addition to the pin-ended truss and rigidly-connected beam elements that have traditionally been used, two new types of elements are introduced: (1) a beam with a hinge on one end and a solid connection on the other end, (2) a beam with hinges on both ends. These elements have different deflection characteristics than those of the typical truss or beam elements, and can be used in ground structure-based compliant mechanism design. Given a reduced ground structure, these new elements effectively increase the design space. Pin-ended members with lengths larger than those of the ground structure cell size are permitted to develop, reducing the sensitivity of solutions to the cell density of the reduced ground structure. Furthermore, because these longer members do not require intermediate lateral support to provide stability, as series connections of shorter pin-ended members do, fewer ancillary members are required. Two compliant mechanism problems are solved to demonstrate the effectiveness of these new elements.     

Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace

In recent years, nanotechnology has been developing rapidly due to its potential applications in various fields that new materials and products are produced. In this paper, a novel macro/micro 3-DOF parallel platform is proposed for micro positioning applications. The kinematics model of the dual parallel mechanism system is established by the stiffness model with individual wide-range flexure hinge and the vector-loop equation. The inverse solutions and parasitic rotations of the moving platform are obtained and analyzed, which are based on a parallel mechanism with real parameters. The reachable and usable workspace of the macro motion and micro motion of the mechanism are plotted and analyzed. Finally, based on the analysis of parasitic rotations and usable workspace of micro motion, an optimization for the parallel manipulator is presented. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for the dual parallel mechanism in order to achieve the features of both larger workspace and higher motion precision.     

Genetic algorithm with advanced mechanisms applied to the protein structure prediction in a hydrophobic-polar model and cubic lattice

This paper presents a genetic algorithm applied to the protein structure prediction in a hydrophobic-polar model on a cubic lattice. The proposed genetic algorithm is extended with crowding, clustering, repair, local search and opposition-based mechanisms. The crowding is responsible for maintaining the good solutions to the end of the evolutionary process while the clustering is used to divide a whole population into a number of subpopulations that can locate different good solutions. The repair mechanism transforms infeasible solutions to feasible solutions that do not occupy the lattice point for more than one monomer. In order to improve convergence speed the algorithm uses local search. This mechanism improves the quality of conformations with the local movement of one or two consecutive monomers through the entire conformation. The opposition-based mechanism is introduced to transform conformations to the opposite direction. In this way the algorithm easily improves good solutions on both sides of the sequence. The proposed algorithm was tested on a number of well-known hydrophobic-polar sequences. The obtained results show that the mechanisms employed improve the algorithm's performance and that our algorithm is superior to other state-of-the-art evolutionary and swarm algorithms.     

Design and robust optimal control of smart beams with application on vibrations suppression

This paper presents the design of a vibration control mechanism for a beam with bonded piezoelectric sensors and actuators and an application of the arising smart structure for vibrations suppression. The mechanical modeling of the structure and the subsequent finite element approximation are based on Hamilton's principle and classical engineering theory for bending of beams in connection with simplified modeling of piezoelectric sensors and actuators. Two control schemes LQR and H₂ are considered. The latter robust controller takes into account uncertainties of the dynamical system and moreover incompleteness of the measured information, it therefore leads to applicable design of smart structures. The numerical simulation shows that sufficient vibration suppression can be achieved by means of the proposed general methods.