An incremental finite element analysis of mechanisms and robots

In this paper, we present an incremental finite element method of analysis of mechanisms/robots. Our method is based on the idea to decompose any large displacement of a mechanism or robot arm in a series of successive small displacements, so small that the linear finite element method can be applied in their analysis between two successive positions. Evidently, at the end of any small displacement, the position of a deformed member of the mechanism gives us the initial conditions for the following small displacement. After presentation of all the theoretical background of the method, we illustrate it by application to the crank-slider mechanism and to the four-bar-linkage mechanism.     

Cutting path generation of the Stewart-Platform-Based Milling Machine using an end-mill

This paper investigates an algorithm for generating the cutting path of a Stewart-Platform-Based Milling Machine (SPBMM) using an end-mill. While using the iso-scallop method in the process of generating the cutting path, we use the Genetic Algorithm (GA) to find the configurations of the tool without a singular position. After choosing the objective function, using GA to find the optimum value is an extremely effective method for both quickly converging to a reasonable value and avoiding a futile blind search. In our results, when the curvature of the workpiece is equal to the curvature of the cutter at the contact point, one equation in terms of curvature and two degrees of freedom of the end-mill are formed. Keeping the six axial forces of the SPBMM as small as possible is our objective function. We can find an optimal set of solutions in this equation at every contact point. Finally, we find a planned cutting path without a singular position.     

4WID-4WIS智能车阿克曼转向轨迹规划及位置估算

针对四轮独立驱动与四轮独立转向(four-wheel independent drive and four-wheel independent steering,4WID-4WIS)智能车的转向行驶工况,基于阿克曼转向原理,提出一种利用三阶贝塞尔曲线进行轨迹规划的新方法.首先,采用最优函数获取一条满足智能车初始状态约束...     

三向类网架结构弯曲和振动分析的分解刚度法

把三向类网架结构简化为夹层板,采用考虑剪切变形的具有三个广义位移的平板弯曲理论进行分析。基于分解刚度思想提出了三向类网架(三角锥网架、三向网架)静力分析和固有振动分析的方法,给出了简便实用的计算公式。通过有限元法的验证,表明了分解刚度法作为一种简化的计算方法,其精度是比较高的,绝大多数的误差都小于5%。可以应用于工程结构设计,便于快速得出网架结构挠度和内力的计算结果及分布规律。此外,与其它的计算方法相比其计算公式大大简化了。     

Experimental determination of the energy of a gas vortex motion during autooscillations in a free convective flow

Free convective gas flow in a “singing” flame and in a Rijke tube was studied in the case of small Reynolds numbers (Re < 1000). A method for determining the dissipated gas flow energy is proposed, which is based on the measurement of displacements of a resonator tube from the position of mechanical equilibrium upon a change from stationary to autooscillatory flow regime, which is accompanied by the spontaneous formation of vortex structures. It is shown that the vortex motion in the gas leads to a decrease in thermal flux in the tube cross section. The energy of rotational motion as a function of the heat-source power exhibits a hysteresis behavior.     

生成正多边形和圆的新算法

针对正多边形各顶点坐标的计算,构造了新的递推公式并加以证明。以新公式为基础给出了正多边形和圆生成算法,并对算法误差进行了分析。计算正多边形每个顶点需要两次乘法和两次加法,优于目前＂多边形逼近法＂所采用的顶点计算方法。算法具有构造简单、执行速度较快和精度高的特点。理论分析和上机验证算法可行,完全可以满足常规的应用。     

Focal plane position detection with a diffractive optic for shack-hartmann wave-front sensor fabrication

During construction of a Shack-Hartmann wave-front sensor it is critical that the spacing between the lens array and the detector array be equal to the lens array focal length to obtain accurate and precise measurements of a wave front. This separation is often difficult to determine with large f/# lenses, because their focal spot diameter does not change substantially for small displacements on either side of the focal plane. We describe a method with an array of off-axis lens segments for determining the location of the focal plane. Because the lenses are off axis, changes in the distance from the optic to the detector array result in transverse focal spot position variations as a function of their separation from the lenses. By analyzing the focal spot pattern on a CCD, we achieved 12-mum rms error in the axial position measurement while moving a 4-mm-focal-length optic over 1 mm.     

Structural damage evaluation of industrial masonry chimneys

This document presents a systematic analysis of the damage causes of industrial masonry chimneys, i.e. cracking patterns, materials’ degradation and structural displacements. The methodology includes an adequate geometric evaluation with identification of each observed lesion, their situation and their environmental conditions. The industrial process temperatures have been documented, hence maximum temperatures and gradients during chimney’s service life were evaluated, and any possible crack pattern because thermal loads was analyzed. In addition, chemical composition (SEM, EDS and DRX) and mechanical properties (compressive and bending strengths) were assessed. Microstructural analyses were useful to detect certain elements and compounds related to corrosion or degradation processes of mortar and steel. Analytical and FE models were made to evaluate the influence of each possible damage source, i.e. temperature gradients, corrosion and chemical reactions producing expansion in the mortar. The effect of internal pressures (because corroded steel) were successfully modelled as spring elements in vertical and horizontal cracks, which matched experimental data obtained in real structures. These results have demonstrated the relation between horizontal displacements of the crown and the position of the internal stairs (made in steel bars embedded in the masonry). Once cracked, either by corrosion or by temperature, the water entrance through the cracks produces chemical reactions with the combustion sulphurs, present in the mortar because of combustion gasses. These reactions generate an expansion inside the masonry located only in one façade. Hence, differential displacements generate the curvature and the consequent drift.     

Efficiency gained with the use of scanning in precision photoelectric systems for measurement of displacement

Questions related to efforts aimed at decreasing the position error of the moving parts of measuring transducers when measuring displacements are considered. It is remarked that scanning by the indicator element of the measurement coupling is most effective in photoelectric transducers, since it makes it possible to optimize the measuring circuit of the system and mode of operation of the system’s transducers. __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 13–14, March, 2008.     

Speckle tracking methods for ultrasonic elasticity imaging using short-time correlation

In ultrasound elasticity imaging, strain decorrelation is a major source of error in displacements estimated using correlation techniques. This error can be significantly decreased by reducing the correlation kernel. Additional gains in signal-to-noise ratio (SNR) are possible by filtering the correlation functions prior to displacement estimation. Tradeoffs between spatial resolution and estimate variance are discussed, and estimation in elasticity imaging is compared to traditional time-delay estimation. Simulations and experiments on gel-based phantoms are presented. The results demonstrate that high resolution, high SNR strain estimates can be computed using small correlation kernels (on the order of the autocorrelation width of the ultrasound signal) and correlation filtering.     

Detecting and locating burrs of industrial parts

Burrs (excess material) are usually squeezed out around the periphery of the mould, and are irregular and vary considerably between parts. This paper aims at the development of a machine vision system for automatic detection of burrs and peripheral defects of casting parts. This non-contact detection result can be applied to automatic deburring systems and used for automatic inspection of peripheral breakdown.

This research concentrates on flat casting parts comprising piecewise smooth curves on the boundaries. The detection procedure is based on the fact that the irregular burrs show high curvature changes in a small segment of the boundary, whereas a smooth segment without burrs presents a succession of low curvature points. Given a casting part with burrs, we arbitrarily select a few boundary points from the smooth segments and connect these points to form a polygon. The matching process then finds a corresponding polygon from the model part. The transformation parameters of rotational angle and translation between the part in the image and the model part are evaluated from these two equivalent polygons. The proposed matching algorithm is computationally fast and the time complexity is bounded by O(m), where m is the number of points on the digital boundary of the model part.     

Analysis of 2D flexible mechanisms using linear finite elements and incremental techniques

In this paper, a fully linear method for the kinetoelastodynamic analysis of mechanisms of engineering praxis, characterized by large displacements and rotations (rigid body motion) but small elastic displacements and strains, based on the standard Euler–Bernoulli finite elements is proposed and investigated. The method is a co-rotational approach and relies on the principle to decompose the motion of a mechanism in a series of successive time steps, so small that the linear finite element method can be applied within each step, adding a correction procedure in order to compensate errors resulting from not incorporating the exact (non-linear) beam theory. After presentation of the method, we apply it to test cases well known in the literature and discuss its characteristics.     

Three‐dimensional Displacement and Shape Measurement with a Diffraction‐assisted Grid Method

The grid method is a full‐field optical technique for computing surface displacements and strains of a material by analyzing the phase of grid lines patterned on the specimen. To date, most experiments using the grid method have measured only two‐dimensional in‐plane deformations. Here, the grid method is extended to three dimensions by using a crossed grid pattern and a diffraction grating which enables acquiring images from multiple viewing angles on a single camera. In‐plane displacements and strains are computed using the conventional grid method, and the corresponding three‐dimensional (3D) displacements—including out‐of‐plane displacements or shapes—are computed by analyzing the images collected at different viewing angles. The technique is demonstrated by measuring 3D rigid body motion, the 3D displacements of a membrane in a pressure‐bulge experiment, and the out‐of‐plane curvature of a cylindrical specimen.     

基于曲率自适应的航空零件法矢量测量研究

现有的法矢量测量技术无法满足测量准确度和实时性的双重要求,法矢量计算方法不能适用于不同曲率的曲面。利用双目立体视觉,本文提出了一种基于曲率自适应的法矢量测量方法。首先,在双目立体视觉的基础上,基于变曲率曲面特征建立制孔区域曲面模型,提出投影点的布局方法;然后,基于三维重建的投影点数据,提出了基于曲面曲率自适应识别的法矢量计算方法;最后,针对小曲率曲面样件的测量结果,与三坐标测量仪测得的法矢量进行对比,用以验证本双目视觉测量方法的精度。实验结果表明:该方法测量法矢量误差为1.6°。该方法可有效提高法矢量测量的准确度,满足大型航空零件现场测量的工程要求。     

New algorithm to minimise kinematic tool path errors around 5-axis machining singular points

The singular points of a given 5-axis CNC machine could be found in the domain of the joint variables of the machine. In the neighbourhood of a singular point, even for a small change of the tooltip position, an enormous change of axis displacements of the machine is often required. This causes a large deviation between the real cutting path and the desired tool path, and the machining surface could be destroyed. This paper provides with an analytical scheme for identifying singular configuration of 5-axis CNC machines. In particular, an efficient and robust algorithm is proposed to compute the cutter path across the neighbourhood of the singular points identified such that the computed cutter path tracks the desired tool path within a controllable error. Numerical examples and real cutting parts are carried out and discussed to show the effectiveness and the efficiency of the presented method.     

Influence of boundary curvature on tangential stresses for the displacement discontinuity method

It is known that in the displacement discontinuity modeling, tangential stresses evaluate incorrectly near curved boundaries when flat elements are used. This paper shows that this error is intrinsic to the use of flat elements and hence cannot be corrected by element refinement. It derives a correction factor that is a function of boundary curvature and local applied stress, and shows how this factor can be used to correct the results of the traditional displacement discontinuity method. The possible generalization of the curvature effect to higher-order geometric domains is also discussed.     

Non‐linear spatial Timoshenko beam element with curvature interpolation

The paper presents a spatial Timoshenko beam element with a total Lagrangian formulation. The element is based on curvature interpolation that is independent of the rigid‐body motion of the beam element and simplifies the formulation. The section response is derived from plane section kinematics. A two‐node beam element with constant curvature is relatively simple to formulate and exhibits excellent numerical convergence. The formulation is extended to N‐node elements with polynomial curvature interpolation. Models with moderate discretization yield results of sufficient accuracy with a small number of iterations at each load step. Generalized second‐order stress resultants are identified and the section response takes into account non‐linear material behaviour. Green–Lagrange strains are expressed in terms of section curvature and shear distortion, whose first and second variations are functions of node displacements and rotations. A symmetric tangent stiffness matrix is derived by consistent linearization and an iterative acceleration method is used to improve numerical convergence for hyperelastic materials. The comparison of analytical results with numerical simulations in the literature demonstrates the consistency, accuracy and superior numerical performance of the proposed element. Copyright © 2001 John Wiley & Sons, Ltd.     

A control algorithm for improving the accuracy of five-axis machine tools

An algorithm for reducing the influence of geometrical, thermal, kinematic and stiffness errors in five-axis machine tool components on the desired tool position and orientation is given. This new algorithm is based on the calculation of the cutting tool error matrix for orthogonal machine tools. In the new model of this matrix, all angular errors of the machine links are considered as infinitesimal rotations. The error matrix is a function of the commanded machine component positions and the errors in these positions. To correct errors in the three translational and two angular tool positions, a matrix of commanded tool position and orientation is multiplied by the inverse error matrix in every period of the tool trajectory interpolation. This corrected matrix of the tool position and orientation provides the inverse kinematics used for calculation of the successive links positions required for achieving the given tool trajectory. The control algorithm for five-axis machine tools with the error compensation is implemented both in the CNC system and in the postprocessor. The proposed algorithm is applied on a vertical five-axis turning centre with two translational and three rotational axes. Twenty-four errors that could cause inaccurate machining are recognised on this machine. The machine links and their coordinate frames are denoted using the Denavit–Hartenberg parameters.     

Exact Solutions and Mode Transition for Out-of-Plane Vibrations of Nonuniform Beams with Variable Curvature

The two coupled governing differential equations for the out-of-plane vibrations of non-uniform beams with variable curvature are derived via the Hamilton's principle. These equations are expressed in terms of flexural and torsional displacements simultaneously. In this study, the analytical method is proposed. Firstly, two physical parameters are introduced to simplify the analysis. One derives the explicit relations between the flexural and the torsional displacements which can also be used to reduce the difficulty in experimental measurements. Based on the relation, the two governing characteristic differential equations with variable coefficients can be uncoupled into a sixth-order ordinary differential equation in terms of the flexural displacement only. When the material and geometric properties of the beam are in arbitrary polynomial forms, the exact solutions with regard to the outof- plane vibrations of non-uniform beams with variable curvature can be obtained by the recurrence formula. In addition, the mode transition mechanism is revealed and the influence of several parameters on the vibration of the non-uniform beam with variable curvature is explored.     

铝型材构件多点变曲率拉弯制件回弹研究

目的 研究不同预拉伸量和补拉伸量对矩形变曲率构件回弹的影响,以提高柔性三维拉弯成形精度。方法 用有限元模拟了矩形变曲率铝型材三维拉弯成形过程,并用试验验证了有限元模拟的精度,设计了5组不同的预拉伸量参数和补拉伸量进行三维拉弯成形有限元模拟。结果 大曲率和小曲率段试验和有限元模拟的回弹误差小于2 mm,表明有限元模拟分析可以很好地对矩形变曲率构件进行模拟。得出的数据表明预拉伸量对于小曲率弧段回弹的影响比对大曲率弧段的影响更大,当预拉伸量增长到1.0%以后,回弹的下降幅度不再明显;随着补拉伸量的增大,变曲率拉弯制件两段的回弹均得到较好的抑制,当补拉伸量为1.4%时,制件靠近夹钳端出现了缩颈缺陷,产生了较大的质量缺陷。结论 研究证明适量增加预拉量和补拉量能有效减小柔性三维拉弯成形回弹。