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Shorya Awtar - One of the best experts on this subject based on the ideXlab platform.

  • A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Strain Energy Formulation
    Journal of Mechanical Design, 2010
    Co-Authors: Shorya Awtar, Shiladitya Sen
    Abstract:

    The beam constraint model (BCM), presented previously, captures pertinent nonlinearities to predict the constraint characteristics of a generalized beam flexure in terms of its stiffness and error motions. In this paper, a nonlinear strain energy formulation for the beam flexure, consistent with the transverse-direction load-displacement and axial-direction geometric constraint relations in the BCM, is presented. An explicit strain energy expression, in terms of beam end displacements, that accommodates generalized loading conditions, boundary conditions, initial curvature, and beam shape, is derived. Using energy-based arguments, new insight into the BCM is elucidated by fundamental relations among its stiffness, constraint, and energy coefficients. The presence of axial load in the geometric constraint and strain energy expressions—a unique attribute of distributed compliance flexures that leads to the elastokinematic effect—is highlighted. Using the principle of virtual work, this strain energy expression for a generalized beam is employed in determining the load-displacement relations, and therefore constraint characteristics, of a flexure mechanism comprising multiple beams. The benefit of this approach is evident in its mathematical efficiency and succinctness, which is to be expected with the use of energy methods. All analytical results are validated to a high degree of accuracy via nonlinear finite element analysis.

  • a generalized constraint model for two dimensional beam flexures nonlinear load displacement formulation
    Journal of Mechanical Design, 2010
    Co-Authors: Shorya Awtar
    Abstract:

    To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form parametric load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates a wide range of loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified by nonlinear finite elements analysis.

  • constraint based design of parallel kinematic xy flexure mechanisms
    Journal of Mechanical Design, 2007
    Co-Authors: Shorya Awtar, Alexander H Slocum
    Abstract:

    This paper presents parallel kinematic XY flexure mechanism designs based on systematic constraint patterns that allow large ranges of motion without causing over-constraint or significant error motions. Key performance characteristics of XY mechanisms such as mobility, cross-axis coupling, parasitic errors, actuator isolation, drive stiffness, lost motion, and geometric sensitivity, are discussed. The standard double parallelogram flexure module is used as a constraint building-block and its nonlinear force-displacement characteristics are employed in analytically predicting the performance characteristics of two proposed XY flexure mechanism designs. Fundamental performance tradeoffs, including those resulting from the nonlinear load-stiffening and elastokinematic effects, in flexure mechanisms are highlighted. Comparisons between closed-form linear and nonlinear analyses are presented to emphasize the inadequacy of the former. It is shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in improved performance. The nonlinear analytical predictions are validated by means of computational finite element analysis and experimental measurements.

Radaelli G. - One of the best experts on this subject based on the ideXlab platform.

  • Synthesis of mechanisms with prescribed elastic load-displacement characteristics
    2017
    Co-Authors: Radaelli G.
    Abstract:

    In this dissertation a collection of concepts to synthesise nonlinear springs is presented. Such springs can be useful in various application domains where, e.g., multi-stability or static balancing is desired. These behaviors are often sought to alleviate the effort required for actuation. The explored concepts are presented by showing the design methods, numerical or analytical models, and assessing their viability with experimental evaluations.In part~I two concepts show how the linear moment characteristic of torsion bars can be reshaped into a nonlinear one. Torsion bars are often suitable energy storage elements because they can be conveniently integrated within the hinge of a mechanism. In both examples the synthesised nonlinear characteristic is determined such that it counteracts the moment of a turning pendulum. The way how the characteristic is reshaped is, however, very different. In the first concept multiple springs are employed, but activated or deactivated by mechanical stops in order to create a piecewise linear characteristic. In the second concept the characteristic is reshaped by a set of non-circular gears. These gears are arranged in a planetary way to obtain a compact transmission. In part~II the focus is on planar compliant mechanisms that by virtue of their optimized shape exhibit the desired behavior. A few examples demonstrate that, even with relatively simple topologies, complex characteristics can be synthesised accurately. For example, a single beam clamped at one end and pivoted at the other end, is able to match a sinusoidal moment characteristic for a half period. In a second example we were able to produce a constant force by a doubly clamped optimally shaped beam. The constant force of this minimalistic design can be applied to balance a weight over a range of motion approximately equal to the largest dimension of the design. In another example it is shown that an optimized beam shape can emulate the behavior of zero free-length springs. These springs have ideal properties but are in practice difficult to make. We also show that a meta-material constituted by a lattice of zero free-length springs, exhibits very peculiar properties as zero Poisson's ratio, isotropy, and constant Young's modulus, up to large strains. Obtaining the required spring bahaviour at such small scale would become possible by the use of optimally shaped beam springs. In the last example of part~II a design consisting of four symmetric beams that move over a straight line of continuous static equilibrium is shown. As an aid to the design process, a representation of the elastokinematic behavior is introduced, based on the potential energy field (PEF). The PEFs characterise the behavior of compliant systems not only instantaneously, but over an area of possible displacement locations of the endpoint of the system. Part~III of this dissertation is dedicated to compliant shell mechanisms. The design of compliant mechanisms as spatial, thin walled, and possibly double curved structures has some interesting and promising aspects. Because of their inherent nonlinear behavior, for example, they lend themselves good for synthesising the nonlinear equilibrium path. With compliant shell mechanisms it is also possible to conveniently create anisotropic stiffness, such that some motion directions are travelled much easier with respect to others. This type of effects can be tailored to create a desired kinematic function. In applications as wearable devices and interactive structures, compliant shell mechanisms can yield to slender, lightweight, aesthetically pleasing, and highly functional solutions. In this dissertation some progresses are made in this infant field of research. As a showcase, in the first chapter of this part, a self-balanced shell is designed. The optimized doubly curved shape of this shell is in continuous equilibrium with its own weight over a fairly large range of motion. In the subsequent two chapters, a tailored moment-angle characteristic is realized by optimizing the parameters of a basic origami mechanism. In the last chapter of this part a spiral spring with various cross-sections is analyzed to understand the anisotropic stiffness behaviors that can be achieved. In particular, the out-of-plane spatial behavior is studied. This is done by using the PEFs, for the first time in three dimensions. In part~IV two application examples are shown. First a shell mechanism, designed to provide a constant force, is applied to the tip of a heart ablation catheter. The constant force at the tip of the catheter helps maintaining contact with the heart wall while preventing dangerously high forces. The second example shows the concept of a large scale collapsible wall, consisting of a doubly curved shell that balances its own weight. Such wall, employed as e.g. a sound barrier, could be hidden flat when not in use, and be lifted upright when it is needed. The concepts presented in this dissertation are applied to selected examples. However, they can be applied to synthesise a broader scope of desired characteristics. Also, the ideas can be generalised by moving from springs to mechanisms, i.e. where input and output have distinct locations. A step even further is to apply distributed actuation, sensing, and control on the deforming bodies such to obtain real automata, where advantage is taken of the synthesised elastic behavior. It is also advisable to direct future research into the use of composites as spring material. It can be expected that their high strength, their tailorable anisotropy, and the possibility to deliberately introduce prestress will lead to springs with increased performance and improved control of the behavior. Future research should also be directed towards improving the available design aids, including PEFs, for compliant mechanism designers. Furthermore, it is expected that the developments of this dissertation can be beneficially applied in an increasing number of application areas

  • Synthesis of mechanisms with prescribed elastic load-displacement characteristics
    2017
    Co-Authors: Radaelli G.
    Abstract:

    In this dissertation a collection of concepts to synthesise nonlinear springs is presented. Such springs can be useful in various application domains where, e.g., multi-stability or static balancing is desired. These behaviors are often sought to alleviate the effort required for actuation. The explored concepts are presented by showing the design methods, numerical or analytical models, and assessing their viability with experimental evaluations.In part~I two concepts show how the linear moment characteristic of torsion bars can be reshaped into a nonlinear one. Torsion bars are often suitable energy storage elements because they can be conveniently integrated within the hinge of a mechanism. In both examples the synthesised nonlinear characteristic is determined such that it counteracts the moment of a turning pendulum. The way how the characteristic is reshaped is, however, very different. In the first concept multiple springs are employed, but activated or deactivated by mechanical stops in order to create a piecewise linear characteristic. In the second concept the characteristic is reshaped by a set of non-circular gears. These gears are arranged in a planetary way to obtain a compact transmission. In part~II the focus is on planar compliant mechanisms that by virtue of their optimized shape exhibit the desired behavior. A few examples demonstrate that, even with relatively simple topologies, complex characteristics can be synthesised accurately. For example, a single beam clamped at one end and pivoted at the other end, is able to match a sinusoidal moment characteristic for a half period. In a second example we were able to produce a constant force by a doubly clamped optimally shaped beam. The constant force of this minimalistic design can be applied to balance a weight over a range of motion approximately equal to the largest dimension of the design. In another example it is shown that an optimized beam shape can emulate the behavior of zero free-length springs. These springs have ideal properties but are in practice difficult to make. We also show that a meta-material constituted by a lattice of zero free-length springs, exhibits very peculiar properties as zero Poisson's ratio, isotropy, and constant Young's modulus, up to large strains. Obtaining the required spring bahaviour at such small scale would become possible by the use of optimally shaped beam springs. In the last example of part~II a design consisting of four symmetric beams that move over a straight line of continuous static equilibrium is shown. As an aid to the design process, a representation of the elastokinematic behavior is introduced, based on the potential energy field (PEF). The PEFs characterise the behavior of compliant systems not only instantaneously, but over an area of possible displacement locations of the endpoint of the system. Part~III of this dissertation is dedicated to compliant shell mechanisms. The design of compliant mechanisms as spatial, thin walled, and possibly double curved structures has some interesting and promising aspects. Because of their inherent nonlinear behavior, for example, they lend themselves good for synthesising the nonlinear equilibrium path. With compliant shell mechanisms it is also possible to conveniently create anisotropic stiffness, such that some motion directions are travelled much easier with respect to others. This type of effects can be tailored to create a desired kinematic function. In applications as wearable devices and interactive structures, compliant shell mechanisms can yield to slender, lightweight, aesthetically pleasing, and highly functional solutions. In this dissertation some progresses are made in this infant field of research. As a showcase, in the first chapter of this part, a self-balanced shell is designed. The optimized doubly curved shape of this shell is in continuous equilibrium with its own weight over a fairly large range of motion. In the subsequent two chapters, a tailored moment-angle characteristic is realized by optimizing the parameters of a basic origami mechanism. In the last chapter of this part a spiral spring with various cross-sections is analyzed to understand the anisotropic stiffness behaviors that can be achieved. In particular, the out-of-plane spatial behavior is studied. This is done by using the PEFs, for the first time in three dimensions. In part~IV two application examples are shown. First a shell mechanism, designed to provide a constant force, is applied to the tip of a heart ablation catheter. The constant force at the tip of the catheter helps maintaining contact with the heart wall while preventing dangerously high forces. The second example shows the concept of a large scale collapsible wall, consisting of a doubly curved shell that balances its own weight. Such wall, employed as e.g. a sound barrier, could be hidden flat when not in use, and be lifted upright when it is needed. The concepts presented in this dissertation are applied to selected examples. However, they can be applied to synthesise a broader scope of desired characteristics. Also, the ideas can be generalised by moving from springs to mechanisms, i.e. where input and output have distinct locations. A step even further is to apply distributed actuation, sensing, and control on the deforming bodies such to obtain real automata, where advantage is taken of the synthesised elastic behavior. It is also advisable to direct future research into the use of composites as spring material. It can be expected that their high strength, their tailorable anisotropy, and the possibility to deliberately introduce prestress will lead to springs with increased performance and improved control of the behavior. Future research should also be directed towards improving the available design aids, including PEFs, for compliant mechanism designers. Furthermore, it is expected that the developments of this dissertation can be beneficially applied in an increasing number of application areas.Mechatronic Systems Desig

Xiang Liu - One of the best experts on this subject based on the ideXlab platform.

  • Elastokinematics of a rectilinear rear independent suspension
    Proceedings of the Institution of Mechanical Engineers Part D: Journal of Automobile Engineering, 2016
    Co-Authors: Xiang Liu, Jing-shan Zhao, Jie Zhang, Wei Chen
    Abstract:

    The rectilinear rear independent suspension investigated in this paper benefits from its excellent kinematic characteristics. Because of the over-constraints of the rectilinear rear independent sus...

  • Elastokinematics and compliance of a rectilinear rear independent suspension
    Proceedings of the Institution of Mechanical Engineers Part D: Journal of Automobile Engineering, 2015
    Co-Authors: Xiang Liu, Jing-shan Zhao, Jie Zhang, Zhijing Feng
    Abstract:

    A rectilinear rear independent suspension has a distinct difference from the traditional ones in that its wheel alignment parameters remain invariable in theoretical kinematics. However, they change within a narrow interval during jounce and rebound when the elasticity of parts, especially the rubber bushings, is taken into account. With the aim of investigating the compliance of the rectilinear rear independent suspension, an elastokinematic model is established in accordance with static equilibrium equations and compatibility conditions. The elastokinematic model has 28 unknowns corresponding to the 5 static equilibrium equations and 23 compatibility equations. Different configurations of rubber bushing and the sensitivity of the suspension stiffness to that of the rubber bushing are analysed. The analytical results indicate that the rubber bushings are best mounted close to the knuckle, and the suspension stiffness is sensitive to the compressive stiffness and the torsional stiffness about the z-axis of the rubber bushing. In addition, the results from kinematic and compliance tests not only verified the elastokinematic model but also revealed the excellent wheel alignment capacity of the rectilinear rear independent suspension compared with that of the MacPherson suspension. This work provided the foundations for the engineering design of a rectilinear rear independent suspension.

Wei Chen - One of the best experts on this subject based on the ideXlab platform.

Vrána Tomáš - One of the best experts on this subject based on the ideXlab platform.

  • ELASTOKINEMATIC COMPUTATIONAL MODEL OF SUSPENSION WITH FLEXIBLE SUPPORTING ELEMENTS
    'Czech Technical University in Prague - Central Library', 2017
    Co-Authors: Vrána Tomáš, Bradáč Josef, Kovanda Jan
    Abstract:

    This paper analyzes the impact of flexibility of individual supporting elements of independent suspension on its elasto-kinematic characteristics. The toe and camber angle are the geometric parameters of the suspension, which waveforms and their changes under the action of vertical, longitudinal and transverse forces affect the stability of the vehicle. To study these dependencies, the computational multibody system (MBS) model of axle suspension in the system HyperWorks is created. There are implemented Finite-Element-Method (FEM) models reflecting the flexibility of the main supporting elements. These are subframe, the longitudinal arms, transverse arms and knuckle. Flexible models are developed using Component Mode Synthesis (CMS) by Craig-Bampton. The model further comprises force elements, such as helical springs, shock absorbers with a stop of the wheel and the anti-roll bar. Rubber-metal bushings are modeled flexibly, using nonlinear deformation characteristics. Simulation results are validated by experimental measurements of geometric parameters of real suspension

  • Kinematics and Elastokinematics of independent multi-link suspension of axle using flexible supporting elements
    Česká zemědělská univerzita v Praze, 2016
    Co-Authors: Vrána Tomáš
    Abstract:

    This thesis deals with elasto-kinematic properties of multi-link rear suspension system, based on simulations. The creation of computational model and simulation of Elastokinematics are based on specialized modules of the HyperWorks software. The thesis idea is to create new models and improve their properties. The chapter introduction presents and discusses the current knowledge state in the issue of elasto-kinematic characteristics of the vehicle suspension. Previously published works are presented in this section. The following section defines basic terms, features and design elements concerning the topic vehicle suspension and vehicle axle, which can help readers to orientate in this field. The first part of the thesis is focused on the collection of high-quality input data to create the MBS computational model based on the real suspension components. The determination of kinematic suspension points, experimental measurements of inertia moments of supporting elements of the suspension and measurements of deformation characteristics of rubber-metal bushings are presented in the thesis. There are also measuring characteristics of force elements such as springs or shock absorbers. Then the proposed method of measuring elasto-kinematic characteristics of the suspension using testing machine for model validation is also introduced. The second and main part is devoted to creating a new MBS simulation models of multi-link rear suspension using HyperWorks system. The suspension model is improved by successive steps, from kinematic model, through model with flexibility of the bushings, to the complex model in which the flexible properties of all supporting elements are reflected. The properties of the used models are described together with arising calculation problems. The results discuss the impact of elements flexibility and individual structural alternatives on elasto-kinematic characteristics of the suspension system