Optimization Of Compliant Mechanisms Research Articles

Towards Design Optimization of Compliant Mechanisms: A Hybrid Pseudo-Rigid-Body Model-Finite Element Method Approach and an Accurate Empirical Compliance Equation for Circular Flexure Hinges.

Innovative designs such as morphing wings and terrain adaptive landing systems are examples of biomimicry and innovations inspired by nature, which are actively being investigated by aerospace designers. Morphing wing designs based on Variable Geometry Truss Manipulators (VGTMs) and articulated helicopter robotic landing gear (RLG) have drawn a great deal of attention from industry. Compliant mechanisms have become increasingly popular due to their advantages over conventional rigid-body systems, and the research team led by the second author at Toronto Metropolitan University (TMU) has set their long-term goal to be exploiting these systems in the above aerospace applications. To gain a deeper insight into the design and optimization of compliant mechanisms and their potential application as alternatives to VGTM and RLG systems, this study conducted a thorough analysis of the design of flexible hinges, and single-, four-, and multi-bar configurations as a part of more complex, flexible mechanisms. The investigation highlighted the flexibility and compliance of mechanisms incorporating circular flexure hinges (CFHs), showcasing their capacity to withstand forces and moments. Despite a discrepancy between the results obtained from previously published Pseudo-Rigid-Body Model (PRBM) equations and FEM-based analyses, the mechanisms exhibited predictable linear behavior and acceptable fatigue testing results, affirming their suitability for diverse applications. While including additional linkages perpendicular to the applied force direction in a compliant mechanism with N vertical linkages led to improved factors of safety, the associated increase in system weight necessitates careful consideration. It is shown herein that, in this case, adding one vertical bar increased the safety factor by 100N percent. The present study also addressed solutions for the precise modeling of CFHs through the derivation of an empirical polynomial torsional stiffness/compliance equation related to geometric dimensions and material properties. The effectiveness of the presented empirical polynomial compliance equation was validated against FEA results, revealing a generally accurate prediction with an average error of 1.74%. It is expected that the present investigation will open new avenues to higher precision in the design of CFHs, ensuring reliability and efficiency in various practical applications, and enhancing the optimization design of compliant mechanisms comprised of such hinges. A specific focus was put on ABS plastic and aluminum alloy 7075, as they are the materials of choice for non-load-bearing and load-bearing structural components, respectively.

A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization

To overcome a significant challenge in traditional parameterized level set methods based on globally supported radial basis functions, we propose employing a local differentiation construction of radial basis functions using finite difference, a technique previously applied to solving partial differential equations but novel in the context of topology optimization. We present a novel parameterized level set method for structural topology optimization of compliance minimization and compliant mechanism, with the main aim of reducing computational costs associated with fully dense matrices when approximating systems with a large number of collocation points. The new scheme implemented with rectangular mesh elements and polygonal mesh generation accommodates both rectangular and complex design domains. Numerical results are provided to demonstrate the algorithm's effectiveness.

Topology and orientation optimization of multi-material hinge-free composite compliant mechanisms under multiple design-dependent loadings

Compliant mechanisms with multiple input loads and output ports are commonly applied in micro-electromechanical systems (MEMS), while compliant mechanisms under design-dependent pressure loadings (such as pneumatic or hydraulic) can generate smooth and compatible deformations. Combining these two types of problems, we propose the design problem of compliant mechanisms under multiple design-dependent loadings. To potentially improve the structural performances, fiber-reinforced composite materials are introduced, and multi-material topology optimization and material orientation optimization are considered simultaneously, which enables the materials to be anisotropic and heterogeneous. Since compliant mechanisms utilize elastic deformation to transmit input forces or displacements to output forces or displacements, anisotropic and heterogeneous material can increase the freedoms in displacement and force transmissions compared to conventional homogeneous isotropic material. The topology optimization is implemented via an extended moving iso-surface threshold (MIST) method for multi-material, in which a novel element-based searching scheme is employed for tracking multiple fluid–structure interfaces. The orientation optimization is achieved via an analytical solution derived for fully anisotropic materials and multi-input-multi-output compliant mechanisms. Numerical examples are presented to show the validity of the present MIST method to design multi-material hinge-free compliant mechanisms under multiple design-dependent loadings.

Topology optimization of compliant mechanisms including links, supports and material distribution

This paper proposes a novel topology optimization method integrating the layout of the supports, links and material distribution to design partially compliant mechanisms. The potential supports and links are distributed in the design domain in initialization, each with an active or inactive state. The nonlinear spring model is implemented for the unified modeling of potential supports and links. The mechanical properties of springs are associated with the states of supports and links. Within the traditional density-based framework, a new group of design variables representing the states of supports and links is introduced into the topology optimization model. For obtaining a physically realizable mechanism, the design variables representing the element density of the structure and the states of supports or links are uniformly penalized for avoiding intermediate values. Sensitivity analysis is conducted by implementing the adjoint equation method. The versatility and flexibility of the proposed method are demonstrated via numerical examples and the accuracy of the nonlinear spring model is verified by comparison of results.

Topology Optimization of Compliant Mechanisms Considering Manufacturing Uncertainty, Fatigue, and Static Failure Constraints

This study presents a new robust formulation for the topology optimization of compliant mechanisms, addressing the design challenges while considering manufacturability, static strength, and fatigue failure. A three-field density projection is implemented to control the minimum size of both real-phase and null-phase material structures to meet the manufacturing process requirements. The static strength is evaluated via the sum of the amplitude and the mean absolute value of the signed von Mises stress. The fatigue failure is solved via the modified Goodman criterion. The real output displacement is optimized by adding artificial springs to the prescribed value. This approach is implemented based on an improved solid isotropic material with penalization (SIMP) interpolation method to describe and solve the optimization model and derive the shape sensitivity of the optimization problem. Finally, two numerical examples are applied to illustrate the effectiveness of the presented method.

Topology optimization of compliant mechanisms under transient thermal conditions

This work considers multi-material topology optimization of compliant mechanisms under transient thermal and quasi-static mechanical conditions wherein thermally actuated devices are optimized for different operating conditions. The materials are modeled using finite strain thermo-hyperelasticity and a two way coupling between the energy balance and equilibrium equations is investigated. The design updates are generated from the gradient-based method of moving asymptotes optimizer and the sensitivities are computed using the time dependent adjoint sensitivity analysis. Results show the impact of designing for short versus long actuation times.

Buckling-induced instability in topology optimization of compliant constant-force mechanisms

Compliant constant-force mechanisms are compliant mechanisms that provide a nearly constant force over a prescribed deflection range. Topology optimization is an effective method for compliant constant-force mechanism design. However, instabilities caused by buckling often cause the optimization algorithm to fail to converge. This study analyzes the causes of buckling-induced instability and proposes methods to avoid this instability. A mechanism with three torsional springs is proposed, and its three force–displacement curves are analyzed. These bifurcated force–displacement curves cause the optimization algorithm to be unstable. Several topology optimization models with buckling constraints are proposed for designing compliant constant-force mechanisms. Their effects are tested and analyzed in numerical examples with different target constant forces and constant-force strokes. Almost all optimization results have three hinges, corresponding to a proposed mechanism with three torsion springs. A slight change in their initial design causes a large change in the force–displacement curve, which eventually leads to buckling-induced instability. This instability can be avoided by constraining the buckling load calculated at the configuration near the start of the constant-force stroke.

HMPS法とCA-IESO法を用いたコンプライアントメカニズムの形態創生

In this paper, a topology optimization method of compliant mechanisms considering geometrical nonlinearity is proposed. In the method, the HMPS method, which is one of particle methods, is used for the analysis considering geometrical nonlinearity. The CA-IESO (Cellular Automaton - Improved Evolutionary Structural Optimization) method is used for the topology optimization. In the formulations, we show the objective function and the sensitivity those are adapted to the topology optimization of compliant mechanism using the CA-IESO method. Several numerical examples are provided to demonstrate the effectiveness of the proposed method for the topology optimization of compliant mechanisms.

Design Optimization of Compliant Mechanisms for Vibration- Assisted Machining Applications Using a Hybrid Six Sigma, RSM-FEM, and NSGA-II Approach

Design Optimization of Compliant Mechanisms for Vibration- Assisted Machining Applications Using a Hybrid Six Sigma, RSM-FEM, and NSGA-II Approach

Topology Optimization of Compliant Mechanisms Based on Rotation Constraint Strategy

Topology Optimization of Compliant Mechanisms Based on Rotation Constraint Strategy

Topology optimization of compliant mechanisms with distributed compliance (hinge-free compliant mechanisms) by using stiffness and adaptive volume constraints instead of stress constraints

Many approaches have been developed for the synthesis of compliant mechanisms via topology optimization. Most of these approaches produce mechanisms with lumped compliance if not extended appropriately, such as with stress constraints. With mechanisms with lumped compliance, the deformation is concentrated in regions of small dimensions (referred to as “de facto hinges” or “one-node connected hinges”) causing notch overstresses. Some extensions to these approaches overcome this by forcing mechanisms with distributed compliance (also referred to as “hinge-free compliant mechanisms”). However, the currently known extensions have a number of drawbacks. Stress constraints, for example, make the optimization formulation highly nonlinear and non-convex. In this paper, a new extension is presented that permits the synthesis of mechanisms with distributed compliance by combining a constraint for the allowed structural stiffness with an adaptive volume constraint. The presented optimization approach can be easily solved using linear optimization. The basis for the extension presented in this paper is the modal synthesis approach, which permits the synthesis of transverse-load-insensitive compliant mechanisms. The methodology developed is tested on suitable design examples.

A novel large stepping-stroke actuator based on the bridge-type mechanism with asymmetric stiffness

This paper presents the design, analysis, and experiments of a novel stick–slip actuator with large working stroke and high resolution based on parasitic motion. To meet the requirement on large stepping-stroke in the fields of nanofabrication and nano-characterization, the bridge-type mechanism with asymmetric stiffness which changes the distribution of piezoelectric actuator elongation at two input points is proposed. A chain-based compliance matrix model is established for the static performance characterization and parameter optimization of the dual-input closed-loop compliant mechanism, and the performance is further studied by finite element method. The prototype of the proposed actuator is manufactured and experimental tests are conducted to investigate its characteristics. The results indicate that the maximum motion speed is 23.53 mm/s with the driving frequency of 350 Hz. The stepping-stroke is 102 μm, and the resolution is measured to be 12 nm. It is confirmed that the proposed actuator is feasible to enlarge the stepping-stroke and work stably.

Design of compliant mechanisms: An explicit topology optimization method using end-constrained spline curves with variable width

In this study, an approach using moving end-constrained spline (ECS) curves with variable widths is presented for the explicit topology optimization of compliant mechanisms. The proposed approach uses a series of spline curves to represent the topology of the compliant mechanism. Instead of using a fixed width, we let the width of such spline curves vary along the curve. The optimized design is obtained by optimizing the width of the spline curves and the position of the control points. To avoid infeasible solutions in the design process, the end points of several specific spline curves are constrained according to the design region. The validity of the proposed method is demonstrated using different types of splines, such as the Bézier curve and B-spline curve, for the design of a force inverter, a compliant gripper and a compliant orthogonal displacement amplification mechanism.

Multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition

Multi-material compliant mechanisms design enables potential design possibilities by exploiting the advantages of different materials. To satisfy mechanical/thermal impedance matching requirements, a method for multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition is presented in this study. In the optimization model, the element stacking method is employed to describe the material distribution and handle material-dependent boundary condition. The maximization of the output displacement of the compliant mechanism is developed as the objective function and the structural volume of each material is the constraint. Fictitious domain approach is applied to circumvent the numerical instabilities in topology optimization problem with geometrical nonlinearities. The method of moving asymptotes is applied to solve the optimization problem. Several numerical examples are presented to demonstrate the validity of the proposed method. The optimal topologies of the compliant mechanisms obtained by the proposed method can satisfy the specified material-dependent boundary condition.

Topology Optimization of Multi-Materials Compliant Mechanisms

In this article, a design method of multi-material compliant mechanism is studied. Material distribution with different elastic modulus is used to meet the rigid and flexible requirements of compliant mechanism at the same time. The solid isotropic material with penalization (SIMP) model is used to parameterize the design domain. The expressions for the stiffness matrix and equivalent elastic modulus under multi-material conditions are proposed. The least square error (LSE) between the deformed and target displacement of the control points is defined as the objective function, and the topology optimization design model of multi-material compliant mechanism is established. The oversaturation problem in the volume constraint is solved by pre-setting the priority of each material, and the globally convergent method of moving asymptotes (GCMMA) is used to solve the problem. Widely studied numerical examples are conducted, which demonstrate the effectiveness of the proposed method.

Topology optimization of compliant mechanisms and structures subjected to design-dependent pressure loadings

This article presents an extended algorithm for topology optimization of compliant mechanisms and structures with design-dependent pressure loadings using the moving iso-surface threshold (MIST) method. In this algorithm, the fluid-structure interface is modeled using the finite element method via considering equivalent virtual strain energy and work and is tracked by an element-based searching scheme. Design-dependent pressure loads are directly applied on interface boundary and are calculated as virtual work equivalent nodal forces in the interface elements based on the finite element formulation. Several numerical examples are presented for topology optimization of mean compliance and compliant mechanisms. The present algorithm is validated through benchmarking with the results in literature and/or full finite element analysis (FEA) results of the optimum compliant mechanism and structure designs.

Topology Optimization of Multi-material Compliant Mechanisms Using Node-density Interpolation Scheme

Topology Optimization of Multi-material Compliant Mechanisms Using Node-density Interpolation Scheme

Dynamic Modeling and Error Analysis of a Cable-Linkage Serial-Parallel Palletizing Robot

The efficiency and accuracy for parallel robot play a significant role in the industrial production process. In order to further improve the motion performance of parallel robot, this paper focuses on the study of mechanism design, dynamic modeling and error analysis of a cable-linkage serial-parallel palletizing robot (CSPR). Firstly, the CSPR is designed as a series-parallel hybrid mechanism driven by flexible cables, which can effectively reduce the inertia and improve the dynamic response. As is known that kinematic design optimization of compliant mechanisms requires accurate yet efficient mathematical models, the kinematics and dynamic models are established by the homogeneous coordinate transformation method and Lagrange equation. Based on the dynamic mathematical model of the robot, a variety of sensors are chosen to construct the hardware control system and the sliding mode variable structure control strategy is also designed based on motion errors. Then, the motion performance and load carrying capacity of the CSPR were analyzed and compared in different operating conditions respectively, and the results verify the validity and efficiency of the mechanism.

Topology optimization and 3D printing of large deformation compliant mechanisms for straining biological tissues

This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical nonlinearity together with a suitably chosen hypereleastic material model, wherein the mechanical equilibrium equations are solved using the total Lagrangian finite element formulation. An objective based on least-square error with respect to target strains is formulated and minimized with the given set of constraints and the appropriate surroundings of the tissues. To circumvent numerical instabilities arising due to large deformation in low stiffness design regions during topology optimization, a strain-energy based interpolation scheme is employed. The approach uses an extended robust formulation i.e. the eroded, intermediate and dilated projections for the design description as well as variation in tissue stiffness. Efficacy of the synthesis approach is demonstrated by designing various compliant mechanisms for providing different target strains in biological tissue constructs. Optimized compliant mechanisms are 3D-printed and their performances are recorded in a simplified experiment and compared with simulation results obtained by a commercial software.

Multi-material topology optimization of compliant mechanisms using regularized projected gradient approach

In this article, the identification of optimal topologies for multi-material compliant mechanisms based on the regularized projected gradient approach is presented and analyzed. The monolithic structure of compliant mechanisms makes them suitable to be used in microelectromechanical systems to transfer load and force. The use of additive manufacturing technologies makes it possible to build multi-material structures. However, a proper design optimization approach must be considered to design multi-material mechanisms as well. In this article, the solid isotropic material with a penalization (SIMP) material interpolation scheme is used to parameterize the continuum design domain. The perimeter penalization approach is utilized to remove the checkerboard patterns and scatters in optimal designs. To handle the volume equality constraint, the regularized constraint projection strategy is utilized. Some benchmark problems are considered to analyze the performance of the method.