On large displacement-small strain analysis of structures with rotational degrees of freedom

The matrix displacement analysis of geometrically nonlinear structures becomes an intricate task as soon as finite elements in space with rotational degrees of freedom are considered. The fundamental reason for these difficulties lies in the non-commutativity of successive finite rotations about fixed axes with different directions. In order to circumvent this difficulty, a new definition of rotations — the so-called semitangential rotations — is introduced in this paper. Our new definition leads to a reformulation of the theory of [1,2]which in itself is clearly consistent and correct.In contrast to rotations about fixed axes these semitangential rotations which correspond to the semitangential torques of Ziegler [3]possess the most important property of being commutative. In this manner, all complexities involved in the standard definition of rotations are avoided ab initio.A specific aspect of this paper is a careful exposition of semitangential torques and rotations, as well as the consequences of the semitangential definitions for the geometrical stiffness of finite elements. In fact, these new definitions permit a very simple and consistent derivation of the geometrical stiffness matrices. Moreover, the semitangential definition automatically leads to a symmetric geometrical stiffness which clearly expresses that the nonlinear strain-displacement relations must satisfy the condition of conservativity of the structure itself — independently of any loading.The general theory of geometrical stiffness matrices as evolved in this paper is applied to beams in space. The consistency of the theory is demonstrated by a large number of numerical examples not only of straight beams but also of the lateral and torsional buckling and post-buckling behaviour of stiff-joined frames. Most of the former developments appear to be inadequate.     

On degrees of freedom of the cellular network

In this paper, we consider the capacity limits of the cellular network by modeling it as consisting of two mutually interfering multiple access channels with multiple antennas at each receiver (e.g., base station). By developing a tight outerbound as well as an achievable scheme which exploits the idea of interference alignment, we are able to exactly characterize the sum degrees of freedom (DoF) of the network when the channel coefficients are timeor frequency-varying, which equals KM K+min(M,K) (where M a...     

Optimal design of a parallel mechanism with three rotational degrees of freedom

This paper presents the concept design of a pose-adjustment system applied in the large fuselage or wing assembly of aircraft manufacturing which including a 3-degree-of-freedom rotational parallel mechanism (3-DoFs RPM), pogo columns and three tracks. The optimal design of the 3-DoFs RPM with its topology a 3-PUS&S mechanism is detailed, which is designed as a rigid yet compact module that can act as a pose-adjustment mechanism moving along three long tracks for large aircraft structural component assembly, a middle fuselage for example. Inverse kinematics of the 3-DoFs RPM with the exponential product method is achieved to lay the foundation for its kinematic synthesis. Next, with the commercial mathematical software, one can get the reachable workspace and define the prescribed workspace, respectively. Then, dimensional synthesis of the 3-DoFs RPM is executed to achieve a relatively good kinematic performance within its workspace. With the commercial CAE software, stiffness analysis is carried out for performance evaluation of the 3-DoFs RPM virtual prototype.     

A finite volume method for solid mechanics incorporating rotational degrees of freedom

A novel finite volume (FV) based discretization method for determining displacement, strain and stress distributions in loaded two dimensional structures with complex geometries is presented. The method incorporates rotation variables in addition to the displacement degrees of freedom employed in earlier FV based structural analysis procedures and conventional displacement based finite element (FE) formulations. The method is used to predict the displacement fields in a number of test cases for which solutions are already available. The effect of mesh refinement upon the accuracy of the solutions predicted by the method is assessed. The results of this assessment indicate that the new method is more accurate than previous FV procedures incorporating displacement variables only, particularly in cases where bending is the predominant mode of deformation, and therefore the new method represents a significant advance in the development of this type of discretization procedure. Interestingly, the results of the accuracy assessment exercise also indicate that the new FV procedure is also more accurate than the equivalent FE formulation incorporating displacement and rotational degrees of freedom.     

Independent degrees of freedom of dynamical systems

Numerical evidence is presented demonstrating the possibility of obtaining reduced equations of motion for dynamical systems in terms of a small number of variables. Some implications of these results are discussed.     

A generalized geometrically nonlinear formulation with large rotations for finite elements with rotational degrees of freedoms

A generalized geometrically nonlinear formulation using total Lagrangian approach is presented for the finite elements with translational as well as rotational degrees of freedoms. An important aspect of the formulation presented here is that the restriction on the magnitude of the nodal rotations is eliminated by retaining true nonlinear nodal rotation terms in the definition of the element displacement field and the consistent derivation of the element properties based on this displacement field. The general derivation and the formulation steps are applicable to any element with translational and rotational nodal degrees of freedoms. The specific forms of the formulation for axisymmetric shells, two-dimensional isoparametric beams, curved shells, two-dimensional transition elements and solid-shell transition elements can be easily derived by considering the explicit forms of the nonlinear nodal rotations for the element at hand. The specific forms of this formulation have already been well tested and applied to various two- and three-dimensional elements, the results for some of which are presented here. Currently it is being applied to the three-dimensional isoparametric beam elements.     

Robotic welding system with parallel degrees of freedom

This paper considers some problems concerning robotic welding of large structures. If spot welding is applied, then the task consists of fast motions between welding points, and at each point the end effector stops and maintains position for a short time. Similar examples can be found in arc welding applications. Since large structures and, accordingly, large robots are considered, a significant problem appears when extremely nonuniform motion is required. One way to solve this problem is to introduce parallel degrees of freedom. Two methods for this distribution of motion to parallel degrees of freedom are discussed. The theory resulted in the design of a large portal robot with high dynamic capabilities.     

Control performance with three translational degrees of freedom

For multiple degree-of-freedom (DOF) systems, it is important to determine how accurately operators can control each DOF and what influence perceptual, information processing, and psychomotor components have on performance. Sixteen right-handed male students participated in 2 experiments: 1 involving positioning and 1 involving tracking with 3 translational DOFs. To separate perceptual and psychomotor effects, we used 2 control-display mappings that differed in the coupling of vertical and depth dimensions to the up-down and fore-aft control axes. We observed information processing effects in the positioning task: Initial error correction on the vertical dimension lagged in time behind the horizontal dimension. The depth dimension error correction lagged behind both, which was ascribed to the poorer perceptual information. We observed this perceptual effect also in the tracking experiment: Tracking error along the depth dimension was 3.8 times larger than along the other dimensions. Motor effects were also present, with tracking errors along the up-down axis of the hand controller being 1.1 times larger than along the fore-aft axis. These results indicate that all 3 components contribute to control performance. Actual applications of this research include interface design for remote control and virtual reality.     

On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources

This study considers the dynamic response of electrostatic actuators with multiple degrees of freedom that are driven by multiple voltage sources. The critical values of the applied voltages beyond which the dynamic response becomes unstable are investigated. A methodology for extracting a lower bound for this dynamic pull-in voltage is proposed. This lower bound is based on the stable and unstable static response of the system, and can be rapidly extracted because it does not require time integration of momentum equations. As example problems, the dynamic pull-in of two prevalent electrostatic actuators is analyzed.     

On the hybrid-mixed formulation of C0 curved beam elements

Two C⁰ curved beam elements based on the hybrid-mixed formulation are studied in the form of membrane-shear locking, mesh convergence, and stress predictions. At the element level, both the displacement and stress fields are approximated separately. The stress parameters are then eliminated from the stationary condition of the Hellinger-Reissner variational principle so that the standard stiffness equations are obtained. The stress functions are chosen from two important considerations: (i) kinematic deformation modes must be avoided, and (ii) the constraint index counting of the element, when applied to limiting cases, must be equal to or greater than one. Based on these considerations, two curved beam elements are derived by including the effect of shear deformation and with linear and quadratic displacement fields. The elements are found to be lock-free for thin-walled beams. Several numerical examples are given to demonstrate the performance of the two curved elements.     

Stability of sitting postures: the influence of degrees of freedom

Observational studies of sitting have shown that, during spontaneous sitting, people adopt a variety of postures. Various researchers have formulated theories to explain why people adopt their sitting postures. Branton (1969) hypothesized that there is continual need for postural stability while sitting. Dempster (1955) stated that additional stability could be obtained through temporarily closing chains of body segments, or, in other words, through decreasing the number of degrees of freedom of the body. The present study elaborates on Dempster's theory. The aim of this study was to determine the influence of the degrees of freedom of the body on postural stability in sitting postures. For 21 different sitting postures, the total number of degrees of freedom was determined. Postural sway, a measure for postural stability, was determined using a 3D motion and position measurement system with ten healthy subjects. This study shows that the mean path length at the level of the second thoracic vertebra (PL0.05), a measure derived from postural sway, increases significantly (p < 0.0001) with an increase of the number of degrees of freedom of the body (DoFB). Closer examination of the data showed that a model taking into account only the degrees of freedom of the lumbar and thoracic spine and pelvis seems to be a better predictor of postural sway than the total number of degrees of freedom of the body.     

Basic considerations of the degrees of freedom of multi-legged locomotion machines

All multi-legged locomotion machines that do not need any dynamic balance control can be classified functionally into several levels. We define the minimum walking functions of multilegged locomotion machines as follows: (i) two-dimensional walking; (ii) keeping the body horizontal on irregular terrains; (iii) keeping the absolute height of main body constant. Our main interest is in how many active degrees of freedom are necessary and sufficient to realize the above functions. Although consideration of the degrees of freedom seems to be fundamental in developing multi-legged locomotion machines, this problem has not yet been studied. The active degrees of freedom are examined in this paper using a four-legged machine which offers the minimum number of legs necessary to maintain static stability. It is shown that six active degrees of freedom are necessary and sufficient to realize the above functions.     

Three-dimensional elasto-static analysis of 100 million degrees of freedom

GeoFEM, a parallel finite element analysis system, is application software that is being developed for conducting simulations of solid earth. This system is currently run on a massively parallel computer and can perform linear elastic analysis of a simple shape involving up to 100,000,000 degrees of freedom. In the present study, the memory capacity required and elapsed time were estimated for large-scale structural analyses, and the efficiencies were examined to investigate the parallel performance. This paper shows the possibility of performing super large-scale analyses with GeoFEM and a parallel computer.     

Self-calibration of wireless cameras with restricted degrees of freedom

This paper presents an approach for the automatic calibration of low-cost cameras which are assumed to be restricted in their freedom of movement to either pan or tilt movements. Camera parameters, including focal length, principal point, lens distortion parameter and the angle and axis of rotation, can be recovered from a minimum set of two images of the camera, provided that the axis of rotation between the two images goes through the camera’s optical center and is parallel to either the vertical (panning) or horizontal (tilting) axis of the image. Previous methods for auto-calibration of cameras based on pure rotations fail to work in these two degenerate cases. In addition, our approach includes a modified RANdom SAmple Consensus (RANSAC) algorithm, as well as improved integration of the radial distortion coefficient in the computation of inter-image homographies. We show that these modifications are able to increase the overall efficiency, reliability and accuracy of the homography computation and calibration procedure using both synthetic and real image sequences.     

六自由度电动平台控制系统设计研究

采用多轴运动控制器MAC作为控制主体,基于"工控机+运动控制卡"的模式,构建了一个开放式的六自由度电动平台控制系统。实现了六自由度电动平台的基本控制功能。建立了六自由度电动平台的故障保护系统及故障监控系统,并详细介绍了系统组成部分及实现过程。     

Method of calculating the collision integral and solution of the Boltzmann kinetic equation for simple gases,gas mixtures and gases with rotational degrees of freedom

The conservative method of calculating the Boltzmann collision integral for simple gases, gas mixtures and gases with rotational degrees of freedom of molecules is presented. In all cases the common approach based on the projection technique of summing up the contributions in the collision integral is used. The method is applied for solving the Boltzmann kinetic equation for two fundamental rarefied gas flow problems: the heat transfer problem and the problem of shock wave structure. A comparison with experimental and numerical data of other authors is reported. It is shown that the considered numerical method allows one to solve the Boltzmann equation for real gases with high accuracy.