Synthesis Of Compliant Mechanisms Research Articles

Type Synthesis of Three-Degree-of-Freedom Translational Compliant Parallel Mechanisms

In this paper, we apply screw theory to type synthesis of compliant parallel mechanisms (PMs) with translational degree-of-freedom (DOF). Compliant PMs are formed by a moving platform supported by three or more limbs each of which is a serial chain of flexure joints and rigid bodies. They achieve movement through the deformation of flexure joints and have been widely used in precision machinery. As an important task in the conceptual design stage, the goal of type synthesis is to determine the chain of each limb as well as their relationship when they are assembled in parallel for a prescribed motion pattern. In our approach, we study a category of commonly used flexure primitives and flexure elements whose freedom and constraint spaces are characterized by twists and wrenches in screw theory. Following the well-studied synthesis procedure for rigid body PMs, we propose a synthesis procedure for compliant PMs via screw theory. As an example, we demonstrate the procedure for synthesizing compliant PMs with three translational DOF. Tables of limbs, types, and geometric conditions for the assemblies of these limbs are presented. The paper provides a catalog of 3DOF translational compliant PM designs. At last, we developed finite element simulation to validate one of the synthesized designs.

Design of progressively folding thin-walled tubular components using compliant mechanism synthesis

This work introduces a design method for the progressive collapse of thin-walled tubular components under axial and oblique impacts. The proposed design method follows the principles of topometry optimization for compliant mechanism design in which the output port location and direction determine the folding (collapse) mode. In this work, the output ports are located near the impact end with a direction that is perpendicular to the component's longitudinal axis. The topometry optimization is achieved with the use of hybrid cellular automata for thin-wall structures. The result is a complex enforced buckle zone design that acts as a triggering mechanism to (a) initiate a specific collapse mode from the impact end, (b) stabilize the collapse process, and (c) reduce the peak force. The enforced buckle zone in the end portion of the tube also helps to avoid or delay the onset of global bending during an oblique impact with load angles higher than a critical value, which otherwise adversely affects the structure's capacity for load-carrying and energy absorption. The proposed design method has the potential to dramatically improve thin-walled component crashworthiness.

Compliant mechanism synthesis by using elastic similitude

Compliant mechanisms have several advantages, especially smaller number of elements and therefore less movable joints. The flexural members furthermore allow an integration of special functions like balancing or locking. Especially fiber reinforced materials exhibit a wide range of function integration considering their compliance in passive as well active applications. To take advantage of compliant elements in applications a robust synthesis tool is needed. The synthesis based on topology optimization method or the pseudo rigid body approach leads to complex structures. Considering the use of fiber reinforced material a synthesis approach which leads to less complex structures is more suitable. For building up simple structures, with only one cantilever beam as compliant element(B) a graphical approach using the elastic similitude is the most efficient method. A step-by-step synthesis procedure is presented to synthesize compliant mechanisms with rotatory joints(R) and prismatic joints(P) to develop RRB/PRB- and RPB-linkages. Using the elastic similitude to implement these results into a graphical synthesis algorithm is the innovation part of this paper. It can be shown that this approach leads to a comfortable handling of beam elements during the synthesis, where the two free parameters can be directly coupled to scale and fix the orientation of the beam element. This advantage inherently shortens the development process. In giving an example the focus lies of the experimental approach, which also shows that the simple BERNOULLI beam model is valid and so the synthesis by using the elastic similitude. The method is presented and discussed by using an application for a cup holder mechanism made of fiber reinforced material.

Development of a new adaptive shape morphing compliant structure with embedded actuators

By embedding actuators within a compliant structure (compliant mechanism), it is possible to develop adaptive system, that is, a shape morphing structure that is capable of producing many different shapes of its output surface. Such structures are of interest for a number of applications. This article presents the new solution of adaptive shape morphing compliant structure with embedded actuators that is capable of changing its shape on demand to meet various performance requirements; the physical prototype of this structure is manufactured. Upgraded approach to the synthesis of compliant mechanisms with embedded actuators is also presented. The existing design methodology for simultaneous synthesis of compliant mechanism and actuator placement often produces compliant system with intersecting structural elements as well as actuators which is very difficult to manufacture. Thus, the design methodology is improved so that compliant systems are obtained without intersecting elements. The scalability of the shape morphing compliant structure is investigated as well. Two possible applications of the novel developed shape morphing structure are presented, for adaptive compliant gripper and shape morphing wing that resembles the profile of a bird wing.

Shape control of a beam consisting of triangular meso-structure segments with multiple V-shaped flexure springs

This paper presents a direct displacement synthesis method for the design of shape control of meso-structure beams with multiple V-shaped flexure springs. The objective is to design a beam that will deform to a desired final shape when under a specific load. The method uses a ground structure geometry which can facilitate variable bending stiffness along the length of the beam using compliant spring members. The synthesis procedure involves the use of direct displacement to determine how the bending stiffness of the beam must vary to produce the desired shape change. The direct displacement synthesis method differs from other compliant mechanism synthesis methods found in literature, such as pseudo-rigid-body and continuum structure optimisation, in the approach taken to solve for the unknown variables in the system. By using direct displacement to determine how the structure must respond to a specific load to achieve the desired shape change, the unknown variables within the system can be extracted directly without the use of optimisation techniques. The method is detailed and sensitivities explored. With this method and no iterations, the spring configuration values can be determined such that the resulting shape is within 1% of the target shape.

Structural topology and shape optimization using a level set method with distance-suppression scheme

In level set methods for structural topology and shape optimization, the level set function gradients at the design interface need to be controlled in order to ensure stability of the optimization process. One popular way to do this is to enforce the level set function to be a signed distance function by periodically using initialization schemes, which is commonly known as re-initialization. However, such re-initialization schemes are time-consuming, as additional partial differential equations need to be solved in every iteration step. Furthermore, the use of re-initialization brings some undesirable problems; for example, it may move the zero level set away from the expected position. This paper presents a level set method with distance-suppression scheme for structural topology and shape optimization. An energy functional is introduced into the level set equation to maintain the level set function to close to a signed distance function near the structural boundaries, meanwhile forcing the level set function to be a constant at locations far away from the structural boundaries. As a result, the present method not only can avoid the need for re-initialization but also can simplify the setting of the initial level set function. The validity of the proposed method is tested on the mean compliance minimization problem and the compliant mechanisms synthesis problem. Different aspects of the proposed method are demonstrated on a number of benchmarks from the literature of structural optimization.

An efficient 3D topology optimization code written in Matlab

This paper presents an efficient and compact Matlab code to solve three-dimensional topology optimization problems. The 169 lines comprising this code include finite element analysis, sensitivity analysis, density filter, optimality criterion optimizer, and display of results. The basic code solves minimum compliance problems. A systematic approach is presented to easily modify the definition of supports and external loads. The paper also includes instructions to define multiple load cases, active and passive elements, continuation strategy, synthesis of compliant mechanisms, and heat conduction problems, as well as the theoretical and numerical elements to implement general non-linear programming strategies such as SQP and MMA. The code is intended for students and newcomers in the topology optimization. The complete code is provided in Appendix C and it can be downloaded from http://top3dapp.com .

A Velocity Predictor–Corrector Scheme in Level Set-Based Topology Optimization to Improve Computational Efficiency

This paper presents an optimization method for solving level set-based topology optimization problems. A predictor–corrector scheme for constructing the velocity field is developed. In this method, after the velocity fields in the first two iterations are calculated using the shape sensitivity analysis, the subsequent velocity fields are constructed based on those obtained from the first two iterations. To ensure stability, the velocity field is renewed based on the shape sensitivity analysis after a certain number of iterations. The validity of the proposed method is tested on the mean compliance minimization problem and the compliant mechanisms synthesis problem. This method is quantitatively compared with other methods, such as the standard level set method, the solid isotropic microstructure with penalization (SIMP) method, and the discrete level set method.

Topology synthesis of multi-material compliant mechanisms with a Sequential Element Rejection and Admission method

The design of multi-material compliant mechanisms by means of a multi Sequential Element Rejection and Admission (SERA) method is presented in this work. The SERA procedure was successfully applied to the design of single-material compliant mechanisms. The main feature is that the method allows material to flow between different material models. Separate criteria for the rejection and admission of elements allow material to redistribute between the predefined material models and efficiently achieve the optimum design. These features differentiate it to other bi-directional discrete methods, making the SERA method very suitable for the design of multi-material compliant mechanisms. Numerous examples are presented to show the validity of the multi SERA procedure to design multi-material compliant mechanisms.

A numerical method for static analysis of pseudo-rigid-body model of compliant mechanisms

This paper presents a numerical method for analyzing the pseudo-rigid-body model of compliant mechanisms based on finite elements and the principle of minimum potential energy. The proposed method represents the links of pseudo-rigid-body model with truss elements. As a result, the pseudo-rigid-body model is modeled into a compliant system that consists of finite elements and springs. The static equilibrium position of the pseudo-rigid-body model can be obtained by minimizing the potential energy function of this compliant system. A comparison between the proposed method and the MinPE method is presented. Lastly, a case study is provided to demonstrate the application of this method in the automated analysis of pseudo-rigid-body models. This numerical method paves the way for introducing the topology optimization techniques into the synthesis of flexure-based compliant mechanisms.

A multi-objective method of hinge-free compliant mechanism optimization

A new multi-objective formulation for topology synthesis of hinge-free compliant mechanisms is presented based on the SIMP method. A weighted sum formed objective function is developed by taking into consideration the input and output mean compliances. The weighting factors are set based on the information that is obtained from the previous iteration and automatically updated with each optimization iteration step. Shape sensitivity analysis is addressed. Some numerical examples are presented to illustrate the validity of the proposed method.

Reverse kinetostatic analysis and stiffness synthesis of a spatial tensegrity-based compliant mechanism

This paper presents an analysis of a spatial tensegrity-based mechanism. In this study, a moving body in space is joined to ground by seven compliant leg connectors. Each leg connector is comprised of a spring in series with an adjustable piston. The mechanism is said to be ‘tensegrity-based’ in that it is prestressed when at equilibrium due to compliant linear elements. Two problems are solved in this paper; the reverse kinetostatic analysis and stiffness synthesis problems. In the first problem, the values of the seven spring constants and free lengths are given and the lengths of the seven pistons are determined such that: (1) the top body is given at a desired pose; (2) the top body is at equilibrium while a specified external wrench is applied; and (3) the total potential energy stored in the seven springs equals some desired value. In the second problem, the seven spring constants and the lengths of the seven pistons are determined such that conditions (1) and (2) are met and also the instantaneous stiffness matrix of the top body equals a specified set of matrix values. The paper formulates the solutions of these problems. Numerical examples are also presented.

Design of Crashworthy Structures With Controlled Energy Absorption in the Hybrid Cellular Automaton Framework

This work presents a novel method for designing crashworthy structures with controlled energy absorption based on the use of compliant mechanisms. This method helps in introducing flexibility at desired locations within the structure, which in turn reduces the peak force at the expense of a reasonable increase in intrusion. For this purpose, the given design domain is divided into two subdomains: flexible (FSD) and stiff (SSD) subdomains. The design in the flexible subdomain is governed by the compliant mechanism synthesis approach for which output ports are defined at the interface between the two subdomains. These output ports aid in defining potential load paths and help the user make better use of a given design space. The design in the stiff subdomain is governed by the principle of a fully stressed design for which material is distributed to achieve uniform energy distribution within the design space. Together, FSD and SSD provide for a combination of flexibility and stiffness in the structure, which is desirable for most crash applications.

A Kinetostatic Formulation for Load-Flow Visualization in Compliant Mechanisms

Load flow visualization, which is an important step in structural and machine assembly design may aid in the analysis and eventual synthesis of compliant mechanisms. In this paper, we present a kineto-static formulation to visualize load flow in compliant mechanisms. This formulation uses the concept of transferred forces to quantify load flow from input to the output of a compliant mechanism. The magnitude and direction of load flow in the constituent members enables functional decomposition of the compliant mechanism into (i) Constraints (C): members that are constrained to deform in a particular direction and (ii) Transmitters (T): members that transmit load to the output. Furthermore, it is shown that a constraint member and an adjacent transmitter member can be grouped together to constitute a fundamental building block known as an CT set whose load flow behavior is maximally decoupled from the rest of the mechanism. We can thereby explain the deformation behavior of a number of compliant mechanisms from literature by visualizing load flow, and identifying building blocks.

Incorporation of flexural hinge fatigue-life cycle criteria into the topological design of compliant small-scale devices

The design synthesis of compliant mechanisms yields optimized topologies that combine several stiff parts with highly elastic flexural hinges. The hinges are often represented in a finite element analysis by a single node (one-node hinge), which leaves the actual physical meaning of the hinge (to be fabricated) ambiguous. In order to circumvent this problem, in this work, one-noded hinges have the fatigue-life incorporated into them during the design synthesis by embedding analytical expressions accounting for stress concentration, surface finish, non-zero mean stresses and superposed multiple loading conditions into the formulation. Various flexural hinges with rectangular, circular and parabolic profile geometries are investigated. By incorporating the hinge geometry and fatigue behavior into the design process, unclear interpretation issues that would be encountered during any later manufacturing stage of a compliant mechanism design are removed. Examples are provided to illustrate the overall process.

The Analysis of a Simplified 2R Pseudo-Rigid-Body Model with Moment Load

Pseudo-rigid-body model (PRBM) method, which simplifies the geometrical nonlinear analysis, has become an important tool for the analysis and synthesis of compliant mechanisms. In this paper, a simplified 2R PRBM with two rigid links and two torsion springs is proposed. The characteristic radius factor and stiffness coefficients are selected as the design variables; in order to be better to simulate the tip point and tip slope, a three-dimensional objective function is formulated to optimize the new pseudo-rigid-body model. It is revealed in this paper that the precision of the tip point simulation can be improved when the coefficient of the tip slope error in the objective function is reduced.

A building block synthesis approach for precision flexure systems with integrated, strain-based position sensing

Abstract Early stage design of precision flexure systems that utilize strain-based displacement sensing is difficult due to the strong coupling between the mechanical and sensing subsystems. Traditional tools for flexure system and compliant mechanism synthesis are not capable of simultaneously optimizing the mechanical and sensing subsystems. The building block synthesis approach developed in this work is the only tool capable of designing compliant mechanisms with integrated strain based sensing. Building block modeling allows for rapid synthesis and vetting of concepts. This approach also allows the designer to determine concept feasibility, identify performance limits and tradeoffs, and obtain 1st order estimates of flexure geometry. In short, this method enables one to find an optimal design and set first order design parameters. The utility of the building block approach is detailed in a case study detailing the synthesis and modeling of three different one degree-of-freedom translational stages that are all derived from the series and parallel addition of fixed-guided cantilever beam building blocks.

Systematic Synthesis of Large Displacement Contact-Aided Monolithic Compliant Mechanisms

A single-piece contact-aided compliant mechanism (CCM) deforms to use one or many contact interactions to deliver the prescribed intricate input–output functionality. We present an automated synthesis procedure to design CCMs to trace large, non-smooth paths. Such paths can be traced by rigid-body or partially compliant mechanisms as well but the complexity, bulkiness and the presence of hinges is a disadvantage in terms of increased friction, backlash, need for lubrication, noise, and vibrations. In designing CCMs, both curved frame and two-dimensional finite elements are employed to represent the continuum and simulate the formation of contact sites. A contact site is one that allows relative rotation/sliding of a deforming member with respect to the neighboring one it is in contact with. The proposed design algorithm uses commercial software for large displacement contact analysis. The overall procedure automatically determines the CCM topology, feature shapes and sizes, and therefore the number (e.g., single or multiple) and nature (e.g., stiction or sliding) of contact sites. It systematically favors the continuum designs with lower function values when the synthesis problem is posed using a minimization objective. Synthesis of CCMs is exemplified for path generation applications though the proposed method can be employed for any generic kinematic task.

Basic principles and aims of model order reduction in compliant mechanisms

Abstract. Model order reduction appears to be beneficial for the synthesis and simulation of compliant mechanisms due to computational costs. Model order reduction is an established method in many technical fields for the approximation of large-scale linear time-invariant dynamical systems described by ordinary differential equations. Based on system theory, underlying representations of the dynamical system are introduced from which the general reduced order model is derived by projection. During the last years, numerous new procedures were published and investigated appropriate to simulation, optimization and control. Singular value decomposition, condensation-based and Krylov subspace methods representing three order reduction methods are reviewed and their advantages and disadvantages are outlined in this paper. The convenience of applying model order reduction in compliant mechanisms is quoted. Moreover, the requested attributes for order reduction as a future research direction meeting the characteristics of compliant mechanisms are commented.

Synthesis of Compliant Multistable Mechanisms Through Use of a Single Bistable Mechanism

A compliant multistable mechanism is capable of steadily staying at multiple distinct positions without power input. Many applications including switches, valves, relays, positioners, and reconfigurable robots may benefit from multistability. In this paper, two new approaches for synthesizing compliant multistable mechanisms are proposed, which enable designers to achieve multistability through the use of a single bistable mechanism. The synthesis approaches are described and illustrated by several design examples. Compound use of both approaches is also discussed. The design potential of the synthesis approaches is demonstrated by the successful operation of several instantiations of designs that exhibit three, four, five, and nine stable equilibrium positions, respectively. The equations for determining the actuation force required to move a multistable mechanism are provided. The synthesis approaches enable us to design a compliant mechanism with a desired number of stable positions.