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Showing papers on "Direct stiffness method published in 2011"


Journal ArticleDOI
01 Apr 2011
TL;DR: The stiffness controller is introduced, based on an accurate approximation of a continuum robot's coupled kinematic and static force model, that achieves the desired stiffness in steady state, provides good dynamic performance, and exhibits stability during contact transitions.
Abstract: This paper introduces the first stiffness controller for continuum robots. The control law is based on an accurate approximation of a continuum robot's coupled kinematic and static force model. To implement a desired tip stiffness, the controller drives the actuators to positions corresponding to a deflected robot configuration that produces the required tip force for the measured tip position. This approach provides several important advantages. First, it enables the use of robot deflection sensing as a means to both sense and control tip forces. Second, it enables stiffness control to be implemented by modification of existing continuum robot position controllers. The proposed controller is demonstrated experimentally in the context of a concentric tube robot. Results show that the stiffness controller achieves the desired stiffness in steady state, provides good dynamic performance, and exhibits stability during contact transitions.

227 citations


Journal ArticleDOI
TL;DR: In this paper, a computational strategy is proposed for robust structural topology optimization in the presence of uncertainties with known second order statistics, which combines deterministic top-ology optimization techniques with a perturbation method for the quantification of uncertainties associated with structural stiffness, such as uncertain material properties and/or structure geometry.

172 citations


Journal ArticleDOI
TL;DR: A generic, port-based model for variable stiffness actuators is presented, with which a wide variety of designs can be modeled and analyzed, and kinematics should be such that the apparent output stiffness can be varied without changing the potential energy that is stored in the internal elastic elements.
Abstract: Variable stiffness actuators are a particular class of actuators that is characterized by the property that the apparent output stiffness can be changed independent of the output position. To achieve this, variable stiffness actuators consist of a number of elastic elements and a number of actuated degrees of freedom, which determine how the elastic elements are perceived at the actuator output. Changing the apparent output stiffness is useful for a broad range of applications, which explains the increasing research interest in this class of actuators. In this paper, a generic, port-based model for variable stiffness actuators is presented, with which a wide variety of designs can be modeled and analyzed. From the analysis of the model, it is possible to derive kinematic properties that variable stiffness actuator designs should satisfy in order to be energy efficient. More specifically, the kinematics should be such that the apparent output stiffness can be varied without changing the potential energy that is stored in the internal elastic elements. A concept design of an energy-efficient variable stiffness actuator is presented and implemented. Simulations of the model and experiments on the realized prototype validate the design principle.

160 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed detailed two-and three-dimensional finite element models which can be used to calculate the torsional mesh stiffness of sparsified spur gears.
Abstract: The torsional mesh stiffness is one of the most important characteristics of spur gears. This paper presents the development of detailed two- and three-dimensional finite element models which can be used to calculate the torsional mesh stiffness. Using the parametrical design language of the FE software ANSYS the models offer the possibility to generate various different pairs of spur gears and include an adaptive meshing algorithm for the contact zones. Due to the short computation times the 2D model is well suited to simulate a variety of different gear pairs in a short time period. The more complex 3D model features more options in terms of investigating tooth face modifications for further studies. The resulting values of the torsional stiffness can be used – for example – in multi body simulations of gearboxes. The results from the 2D FEA are used to derive a simple formula for the combined torsional stiffness of spur gears in mesh. The results presented are based on the individual stiffness of the three main components – body, teeth and contact. Hence, the introduced formula uses these three parts to determine the overall stiffness for a wide range of gears and gear ratio combinations. Finally, the results from both the two- and three-dimensional finite element model and the derived formula are compared and the results from the 3D model are checked against results obtained by analytical equations.

91 citations


Journal ArticleDOI
TL;DR: In this article, the full closed-form solution of the governing equations describing the behavior of a shear-deformable two-layer beam with partial interaction is presented. But the effect of possible transversal separation of the two members has been neglected.

72 citations


Journal ArticleDOI
TL;DR: In this article, a braced frame analogy and its periodical unit cell are used as the basis for deriving transverse shear stiffness relationships using the modified stiffness matrix approach.

55 citations


Journal ArticleDOI
TL;DR: In this paper, a Laplace-Hankel transform is applied to the governing equations of Biot's consolidation by using the eigenvalue approach, and the analytical layer-element of a single soil layer can be obtained in the transformed domain by synthesizing the generalized displacements and stresses, which are both expressed by six arbitrary constants.

53 citations


Journal ArticleDOI
TL;DR: In this article, the inplane free vibration behavior of plates is investigated using the dynamic stiffness method and some distinctive modes which went unnoticed in earlier investigations using the Dynamic Stiffness method have been addressed by revisiting the problem and focusing on the special set of missing solutions.

51 citations


Journal ArticleDOI
TL;DR: In this article, the results of experimental tests conducted with the aim of establishing geometrical parameters for a semi-rigid joint that may be used in single-layer structures are presented.

50 citations


Journal ArticleDOI
QW Yang1
TL;DR: In this paper, a new method for structural damage identification based on flexibility disassembly is presented, which decomposes a structural flexibility matrix into a matrix representation of the connectivity between degrees-of-freedom and a diagonal matrix containing the magnitude information.
Abstract: This paper presented a new method for structural damage identification based on flexibility disassembly. The basic idea of the developed theory is to decompose a structural flexibility matrix into a matrix representation of the connectivity between degrees-of-freedom and a diagonal matrix containing the magnitude information. Using the flexibility disassembly, a new damage detection scheme is presented to approach the damage identification problem in three steps. The scheme has a unique advantage that it can accurately compute the stiffness perturbation parameter without any higher-order sensitivity analysis or iteration. The efficiency of the proposed method is demonstrated by five numerical examples.

48 citations


Journal ArticleDOI
TL;DR: Fast algorithms for applying finite element mass and stiffness operators to the B-form of polynomials over d-dimensional simplices are derived by factoring stiffness matrices into products of sparse derivative matrices with mass matrices.
Abstract: Fast algorithms for applying finite element mass and stiffness operators to the B-form of polynomials over d-dimensional simplices are derived. These rely on special properties of the Bernstein basis and lead to stiffness matrix algorithms with the same asymptotic complexity as tensor-product techniques in rectangular domains. First, special structure leading to fast application of mass matrices is developed. Then, by factoring stiffness matrices into products of sparse derivative matrices with mass matrices, fast algorithms are also obtained for stiffness matrices.

Journal ArticleDOI
TL;DR: In this article, a train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities.
Abstract: Dynamic responses of track structure and wave propagation in nearby ground vibration become significant when train operates on high speeds. A train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities. The one-quarter car model is used to represent the train as lumped masses connected by springs. The embankment and the underlying ground are modeled by the 2.5D finite element approach to improve the computation efficiency. The Fourier transform is applied in the direction of train’s movement to express the wave motion with a wave-number. The one-quarter car model is coupled into the global stiffness matrix describing the track-ground dynamic system with the displacement compatibility condition at the wheel-rail interface, including the irregularities on the track surface. Dynamic responses of the track and ground due to train’s moving loads are obtained in the wave-number domain by solving the governing equation, using a conventional finite element procedure. The amplitude and wavelength are identified as two major parameters describing track irregularities. The irregularity amplitude has a direct impact on the vertical response for low-speed trains, both for short wavelength and long wavelength irregularities. Track irregularity with shorter wavelength can generate stronger track vibration both for low-speed and high-speed cases. For low-speed case, vibrations induced by track irregularities dominate far field responses. For high-speed case, the wavelength of track irregularities has very little effect on ground vibration at distances far from track center, and train’s wheel axle weights becomes dominant.

Proceedings ArticleDOI
09 May 2011
TL;DR: A novel approach for estimating the nonlinear stiffness of robot joints with flexible transmissions based on the definition of dynamic residual signals that uses only position and velocity measurements on the motor side and needs only the knowledge of the dynamic parameters of the motors.
Abstract: We propose a novel approach for estimating the nonlinear stiffness of robot joints with flexible transmissions. Based on the definition of dynamic residual signals, we derive stiffness estimation methods that use only position and velocity measurements on the motor side and needs only the knowledge of the dynamic parameters of the motors. In particular, no extra force/torque sensing is needed. Two different strategies are considered, a model-based stiffness estimator and a black-box stiffness estimator. Both strategies consist of two stages. The first stage of the model-based estimator generates a residual signal that is a first-order filtered version of the flexibility torque of the transmission, while in the second stage a least squares fitting method is used to estimate the model parameters of the stiffness. The black-box estimator uses in the first stage a second-order residual that is directly a filtered version of the stiffness multiplied by the deformation rate of the transmission. In the second stage, a simple regressor provides the transmission stiffness in a singularity-robust way. Numerical results reported for the cases of constant, nonlinear, or variable stiffness transmissions demonstrate the effectiveness of the approach and the relative merits of the two estimation strategies.

Proceedings ArticleDOI
09 May 2011
TL;DR: This paper provides a parametric identification method that can provide, after a sufficiently long learning period, a complete model of the nonlinear stiffness, which can be applied henceforth even in the absence of excitation.
Abstract: We consider the problem of estimating non-linear time-varying stiffness of a mechanical system based only on force and position measurements. A recent work presented a non-parametric stiffness observer, which converges to within an Uniformly Ultimately Bounded neighborhood of the real stiffness value. The method provides excellent results for applications where the system is persistently excited. In this paper, we provide a parametric identification method that complements the previous solution in that it can provide, after a sufficiently long learning period, a complete model of the nonlinear stiffness, which can be applied henceforth even in the absence of excitation. Convergence conditions for the proposed method are discussed. Simulation and experimental results are provided, illustrating the performance of the proposed algorithm.

Journal ArticleDOI
TL;DR: In this article, the authors propose a strategy to control the variable stiffness actuator optimally, with respect to a cost criterion, to a desired periodic motion of the output, i.e., the actuator is controlled such that its passive behavior is as close as possible to the desired behavior and thus that the control effort is minimized.

Journal ArticleDOI
TL;DR: In this article, a modified finite strip method embracing the harmonic coupled Fourier series treatment is described, where all harmonics are coupled, and the stiffness matrix order and bandwidth are proportional to the number of harmonics used.
Abstract: The paper describes a modified finite strip method embracing the harmonic coupled Fourier series treatment. The well known uncoupled formulation, first developed in the context of thin plate bending analysis, represents a semi-analytical finite element process. As far as linear analysis is concerned, it takes advantage of the orthogonality properties of harmonic functions in the stiffness matrix formulation. However in the case of the geometric stiffness matrix calculation, the integral expressions contain the products of trigonometric functions with higher-order exponents, and here the orthogonality characteristics are no longer valid. All harmonics are coupled, and the stiffness matrix order and bandwidth are proportional to the number of harmonics used.

Proceedings ArticleDOI
09 May 2011
TL;DR: This paper proposes a (model-based) unified control methodology that is able to exploit the benefits of variable stiffness independent of the specifics of the mechanical design.
Abstract: Considerable research effort has gone into the design of variable passive stiffness actuators (VSAs). A number of different mechanical designs have been proposed, aimed at either a biomorphic (i.e., antagonistic) design, compactness, or simplified modelling and control. In this paper, we propose a (model-based) unified control methodology that is able to exploit the benefits of variable stiffness independent of the specifics of the mechanical design. Our approach is based on forming constraints on commands sent to the VSA to ensure that the equilibrium position and stiffness of the VSA are tracked to the desired values. We outline how our approach can be used for tracking stiffness and equilibrium position both in joint and task space, and how it may be used in the context of constrained local optimal control. In our experiments we illustrate the utility of our approach in the context of online teleoperation, to transfer compliant human behaviour to a variable stiffness device.

Journal ArticleDOI
TL;DR: The proposed approach presents an effective design tool for evaluation and limitation of stiffness of machines and robots.
Abstract: New stiffness performance indices using the collinear stiffness value (CSV) associated with a given configuration of the machine are proposed. The minimal CSV (MinCSV) is applied to stiffness evaluation for all types of configurations. Similar to the determinant, the MinCSV equals zero in singular configurations. In regular configurations, the MinCSV is applied to evaluation of local stiffness for a given configuration and global stiffness in the workspace, wherein stiffness limitations are satisfied. A screw stiffness value, i.e., the CSV during a screw displacement, presents the general case of the CSV. There are two important special cases: rotational and translational stiffness values. Procedures for evaluation of the MinCSV are developed in natural and dimensionless forms. The CSV of the hexapod are simulated and compared with those of serial-type mechanisms. The proposed approach presents an effective design tool for evaluation and limitation of stiffness of machines and robots.

Journal ArticleDOI
TL;DR: In this paper, the authors describe a procedure for taking into account distributed loads in the dynamic stiffness matrix formulation, also known as the continuous element method, where concentrated or linearly distributed loads are taken into account by considering the necessary number of elements in such a way that these loads are applied on element boundaries.

Journal ArticleDOI
TL;DR: The obtained stiffness model of the hybrid robot is analytical and the deformation results of the robot workspace under certain external load are presented.

Proceedings ArticleDOI
13 Apr 2011
TL;DR: In this article, a variable mechanical stiffness control based on human stiffness estimation is proposed for controlling wire rope tension and interaction force of a human-robot interaction system, where the advantage points of high mechanical bandwidth and low stiffness transmission are combined together.
Abstract: Control of the human-robot interaction system presents many challenges, which include the consideration in terms of the properties of human operators, sensor device, and linkage mechanisms of the robot. This paper presents the application of a variable mechanical stiffness control based on a human stiffness estimation. In the controller design, dual disturbance observers with respect to two operation modes, namely the common mode and the differential mode, are designed and applied for controlling wire rope tension and interaction force of human. The human stiffness estimation plays a dominant role in achieving this intelligent behavior, and smooth interaction force, by allowing a robot system to adapt the mechanical stiffness of the twin direct-drive motor system. The advantage points of the high mechanical bandwidth and low stiffness transmission are combined together. The experiment results from two separate experiments show that the above strategy was able to regulate the mechanical stiffness of the robot and provide a smooth interaction force.

Journal ArticleDOI
TL;DR: In this paper, a Lagrangian formulation for the total dynamic stiffness and damping matrices of a rigid rotor carrying noncentral rigid disk and supported on angular contact ball bearings (ACBBs) is presented.
Abstract: A lagrangian formulation is presented for the total dynamic stiffness and damping matrices of a rigid rotor carrying noncentral rigid disk and supported on angular contact ball bearings (ACBBs). The bearing dynamic stiffness/damping marix is derived in terms of the bearing motions (displacements/rotations) and then the principal of virtual work is used to transfer it from the bearing location to the rotor mass center to obtain the total dynamic stiffness/damping matrix. The bearing analyses take into account the bearing nonlinearities, cage rotation and bearing axial preload. The coefficients of these time-dependent matrices are presented analytically. The equations of motion of a rigid rotor-ACBBs assembly are derived using Lagrange's equation. The proposed analyses on deriving the bearing stiffness matrix are verified against existing bearing analyses of SKF researchers that, in turn, were verified using both SKF softwares/experiments and we obtained typical agreements. The presented total stiffness matrix is applied to a typical grinding machine spindle studied experimentally by other researchers and excellent agreements are obtained between our analytical eigenvalues and the experimental ones. The effect of using the total full stiffness matrix versus using the total diagonal stiffness matrix on the natural frequencies and dynamic response of the rigid rotor-bearings system is studied. It is found that using the diagonal matrix affects natural frequencies values (except the axial frequency) and response amplitudes and pattern and causes important vibration tones to be missig from the response spectrum. Therefore it is recommended to use the full total stiffness matrix and not the diagonal matrix in the design/vibration analysis of these rotating machines. For a machine spindle-ACBBs assembly under mass unbalnce and a horizontal force at the spindle cutting nose when the bearing time-varying stiffness matrix (bearing cage rotation is considered) is used, the peak-to-valley variation in time domain of the stiffness matrix elements becomes significant compared to its counterpart when the bearing standard stiffness matrix (bearing cage rotation is neglected) is used. The vibration spectrum of the time-varying matrix case is marked by tones at bearing outer ring ball passing frequency, rotating unbalnce frequency and combination compared to spectrum of the standard stiffness matrix case which is marked by only the rotating unbalnce frequency. Therfore, it is highly recomended to model bearing stiffness matrix to be a time-dependent.

Journal ArticleDOI
TL;DR: In this paper, the stiffness of flexible transmissions in robots with variable stiffness actuation in agonistic-antagonistic configuration is estimated using a dynamic residual that provides a filtered version of the unmeasured flexibility torques, combining it with a recursive least squares algorithm that fits a polynomial model to the data, and proceeding then by analytical derivation.

Journal Article
TL;DR: The hereby paper briefly presents the two methods emphasizing the penalty based ones, known as the penalty function method and the Lagrange multipliers method, and underscores the influence of input parameters for the case of the two method on the results when using the software ANSYS 12.
Abstract: The finite element method is a numerical method that can be successfully used to generate solutions for problems belonging to a vast array of engineering fields: stationary, transitory, linear or nonlinear problems. For the linear case, computing the solution to the given problem is a straightforward process, the displacements are obtained in a single step and all the other quantities are evaluated afterwards. When faced with a nonlinear problems, in this case with a contact nonlinearity, one needs to account for the fact that the stiffness matrix of the systems varies with the loading, the force vs. stiffness relation being unknown prior to the beginning of the analysis. Modern software using the finite element method to solve contact problems usually approaches such problems via two basic theories that, although different in their approaches, lead to the desired solutions. One of the theories is known as the penalty function method, and the other as the Lagrange multipliers method. The hereby paper briefly presents the two methods emphasizing the penalty based ones. The paper also underscores the influence of input parameters for the case of the two methods on the results when using the software ANSYS 12.

Proceedings ArticleDOI
05 Dec 2011
TL;DR: This work improves the previous general approach, combining a residual-based flexibility torque estimator that uses also a kinematic Kalman filter to handle discretization and quantization errors with an enhanced recursive least squares algorithm that does not suffer from lack of persistent excitation.
Abstract: We consider the problem of estimating on line the nonlinear stiffness of flexible transmissions in robot joints, with special reference to actuation devices with adjustable stiffness in serial configuration. These joints are characterized by a principal motor for controlling the link motion and secondary motor for adjusting the stiffness. In this actuation configuration, the flexible transmission undergoes relatively small deformations and the stiffness estimation problem is more challenging due to poor excitation conditions. We improve our previous general approach, combining a residual-based flexibility torque estimator that uses also a kinematic Kalman filter to handle discretization and quantization errors with an enhanced recursive least squares algorithm that does not suffer from lack of persistent excitation. As a result, stiffness is estimated in a more robust way using only position measurements on the motor sides and motor dynamic parameters. The performance of the proposed estimation method is illustrated through simulations and experiments on the AwAS joint developed at IIT.

Journal ArticleDOI
TL;DR: In this article, the structural topology optimization of the bed of a large machine tool was studied based on the results of the finite element analysis, with the optimization target is minimum volume of the rib plate and the bed constraint conditions are stiffness and natural frequency.
Abstract: Taking the bed of a large machine tool as an example, static stiffness and modal analysis were studied by the software HyperWorks Based on the results of the finite element analysis the structural topology optimization of the bed was compiled, with the optimization target is minimum volume of the rib plate and the bed constraint conditions are stiffness and natural frequency The lightest topology shape of the bed was obtained in the premise of its stiffness and strength which can provide the guidance for the next precise design of the structure The results showed that the mass of the bed was reduced by 858% while the stiffness improved 741%

Book ChapterDOI
06 Dec 2011
TL;DR: The overall stiffness properties and the different stiffness contributors are presented for an exemplary structure of the spatial 3-DOF DELTA robot.
Abstract: This work deals with the structural stiffness properties of the spatial 3-DOF DELTA robot. Firstly, the kinematic model is presented. Based on the kinematic model a static model is derived. The static model is able to map all relevant constraint forces of the parallel structure. Based on this relationship the stiffness matrix of the DELTA robot can be deduced. As a result, the overall stiffness properties and the different stiffness contributors are presented for an exemplary structure.

Journal ArticleDOI
TL;DR: In this article, the relationship between material characteristics and temperature was introduced into the fundamental equations of thermoelasticity and using mathematic methods of Laplace and Hankel integral transformation, the stiffness matrix for a layer was derived firstly.
Abstract: The asphalt pavement is regarded as a multilayered elastic half space axisymmetrical body. By introducing the relationship between material characteristics and temperature into the fundamental equations of thermoelasticity and using mathematic methods of Laplace and Hankel integral transformation, the stiffness matrix for a layer is derived firstly. Then the global stiffness matrix is established for multilayered elastic half space using the finite element concepts in which layers are completely contacted. Therefore, explicit solution for thermal stresses of the asphalt pavement is obtained from the solution of the algebra equation formed by global stiffness matrix and the inverse Hankel and Laplace integral transformation. Because the elements of matrix do not include positive exponential function, the calculation is not overflowed and the shortages of transfer matrix method are overcome. This approach serves as a better model for real pavement structure as it takes into account the relationships between the material characteristics and temperature in the pavement system.

Book ChapterDOI
06 Dec 2011
TL;DR: An uncertain approach to identify the stiffness of a welding manipulator KUKA-KR16 is proposed and the distribution of the joint stiffness is obtained, based on which the compensation results are proved to be effective in Cartesian space.
Abstract: Stiffness of the robot manipulator plays a crucial role in improving welding accuracy. Due to the relatively low stiffness, the robot can hardly achieve the specified accuracy under the loading condition. Hence, identifying the joint stiffness and compensating the displacement in Cartesian space is an intuitive work to do in welding industry. Although substantial works had been done on stiffness modeling and identification, the uncertainties existed in transmission and manufacturing were neglected which may affect the manipulator's stiffness and accuracy to a certain extent, in practice. In this paper, we propose an uncertain approach to identify the stiffness of a welding manipulator KUKA-KR16. Firstly, the uncertainties of the D-H parameters are considered and simulated by Monte-Carlo method. Then, the Cartesian stiffness is identified through an experiment which is composed of API laser tracker and a cable pulley system with deadweights. Finally, combining the previous enhanced stiffness model, we obtain the distribution of the joint stiffness, based on which the compensation results are proved to be effective in Cartesian space.

Moe Key1
01 Jan 2011
TL;DR: In this article, a train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities.
Abstract: Dynamic responses of track structure and wave propagation in nearby ground vibration become significant when train operates on high speeds.A train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities.The one-quarter car model is used to represent the train as lumped masses connected by springs.The embankment and the underlying ground are modeled by the 2.5D finite element approach to improve the computation efficiency.The Fourier transform is applied in the direction of train's movement to express the wave motion with a wave-number.The one-quarter car model is coupled into the global stiffness matrix describing the track-ground dynamic system with the displacement compatibility condition at the wheel-rail interface,including the irregularities on the track surface.Dynamic responses of the track and ground due to train's moving loads are obtained in the wave-number domain by solving the governing equation,using a conventional finite element procedure.The amplitude and wavelength are identified as two major parameters describing track irregularities.The irregularity amplitude has a direct impact on the vertical response for low-speed trains,both for short wavelength and long wavelength irregularities.Track irregularity with shorter wavelength can generate stronger track vibration both for low-speed and high-speed cases.For low-speed case,vibrations induced by track irregularities dominate far field responses.For high-speed case,the wavelength of track irregularities has very little effect on ground vibration at distances far from track center,and train's wheel axle weights becomes dominant.