Application of symbolic manipulation to inverse dynamics and kinematics of elastic robots

An inverse dynamics and kinematics of a flexible manipulator is derived in symbolic form based on the recursive Lagrangian assumed mode method. A PC-based program has implemented the algorithm to automatically generate the inverse dynamics and kinematics for an elastic robot in a symbolic form. A case study is given to illustrate how to use this program for inverse dynamic and kinematic generation. Simulation results for a case study by considering different mode shape are compared with the rigid case.Nomenclature A _i joint transformation relates systemi to systemi-1 - E _i link transformation relates the deflection of systemi to systemi - F _i joint torque acting on jointi - g gravity vector expressed at the base coordinates - J inertia = - K kinetic energy of the system - l _i length of linki - M _i a mass concentrated at the joint i - m _i number of modes used to describe the deflection of link i - n number of links - q _h joint variable of thehth joint - q _hk time-varying amplitude of mode k of link h - R vector of remaining dynamics and external forcing terms = - r _i vector locating the centre of mass of linki - R _j dynamics from the joint equation j, excluding second derivatives of the generalized coordinates - R _if dynamics from the deflection equation jf, excluding second derivatives of the generalized coordinates - V potential energy - W _i transformation from the base to theith link - transformation from the base to the systemî - z the vector of generalised coordinates = - link density     

Improving the Accuracy in Determining the Insulator Capacitance in Metal–Insulator–Semiconductor Structures

The results of the voltage–capacitance spectroscopy of interface states in metal–insulator–semiconductor (MIS) structures are critical functions of the accuracy in determining the insulator capacitance C _i, which is typically no higher than a few fractions of a percent. This substantially limits the energy range of the observed spectrum of the interface states (E 0.5 eV for Si-based MIS structures) and the sensitivity to the density of the interface states at the spectrum edges (N _ss 1 × 10¹⁰ cm^–2 eV^–1). We propose a method for minimizing these errors that is based on a sequential variation of the initial estimate C _i C _{i 0} C _ij, j = 0, 1, 2, ... and the identification of singular points in the dependences and on C _ij, where are the mean arithmetic values of the voltage difference between the experimental and ideal voltage–capacitance characteristic and are the rms deviations of the voltage values taken in the high-accumulation (ac) and inversion (in) regions from values. The highest (10^–4%) accuracy in determining C _i is achieved in the regions of the equidistant experimental and ideal voltage–capacitance characteristic. This method, combined with the technique of _s / _s diagrams, ensures an extension of E to 0.9 eV at N _ss 1 × 10¹⁰ cm^–2 eV^–1 and the possibility of determining the sign and density of the fixed charge in the gate insulator.     

Relation between the Residual Magnetization and Change in Magnetization on Steel and Alloy Return Curves

The relation between the residual magnetization M _r and change in magnetization on the return curves as a function of the coercive force is studied experimentally for heat-treated steels of different chemical compositions and a number of polycrystalline iron–nickel–cobalt alloys. It is shown that in the quenched condition the ratios M _s /M _r and M _r / are almost constant and close to 2 and 4, respectively, for all investigated steels regardless of their chemical composition. For highly tempered steels and annealed alloys these ratios represent structurally sensitive quantities depending on the critical fields in the material and characterize the relation between reversible and irreversible remagnetization processes. A model interpretation of the results obtained is given.     

Atmospheric effects of friction,friction noise and wear with silicon and diamond. Part III. SEM tribometry of polycrystalline diamond in vacuum and hydrogen

In this part III of a multi-part paper series, the results of additional SEM tribometric experiments are described, performed with polished, mostly C(100)-oriented polycrystalline CVD diamond film [PCD_C(100) vs. PCD_C(100)] counterfaces sliding in Torr and in 0.1–0.3 Torr partial pressures of pure hydrogen gas. These tests were completed under a 28 g (0.27 N) normal load, under standard and slow thermal ramping conditions at temperatures ranging from room temperature to 1000^°C. The friction data were examined per the computer logging and analysis techniques described in part I. The treatment of the data is similar to that of Si in part II: the maximum and the average coefficients of friction (MAX.COF and COF) and their ratios (the friction noise FN) are employed to measure possible lubricative interaction of the diamond surfaces with rarefied hydrogen. The results indicate that excited species of molecular hydrogen enter into tribothermally catalyzed reactions not only with Si but with PCD_C(100) surfaces as well. Similar to the behavior of Si, the most beneficial friction-reducing regime occurs in a temperature range just before the thermal desorption of adsorbates. The general magnitudes of MAX.COF, COF and the FN are significantly lower than those of the Si crystallinities, in both vacuum and . The wear rate of the PCD_C(100) film characteristic of the standard thermal ramping test procedure performed mostly in is around , in good agreement with the wear rate previously measured in vacuum for unpolished, fine-cauliflowered diamond films. The data indicate that smooth polycrystalline diamond is a significantly better bearing material for miniaturized moving mechanical assembly applications than Si. This revised version was published online in July 2006 with corrections to the Cover Date.     

Diagnostics of Multilayered Composite Structures with the Help of a Fiber-Optic System for Strain Measurements

The paper considers a built-in fiber-optic array system for technical diagnostic of composite structures measuring local strains in hazardous cross sections of these structures. The effect of repeated microscopic bends of optical fibers on the transmitted flux in structures strained by a tensile force of up to 1 kN over a temperature range of 20 to 100°C has been investigated. The increase in the tensile stress in components of a composite structure leads to a growth in the optical losses of up to 20–23% of the initial optical flux. The loss function (F) is linear in the region of mechanical forces of up to 1 kN and temperatures up to 40°C. An explanation has been suggested for the nonlinearity of (F) at temperatures above 40°C. The conclusion is that the developed system enables one to estimate the strength of multilayered composite structures and detect their prefracture states using singular points on opto-mechanical characteristics of optical fibers.     

Developing Algorithms for Estimating Strength on the Base of Imitating Structural Model of Acoustic Emission. II. Effect of Structural Inhomogeneity of a Material

The first part was dedicated to the theoretical basis for estimating strength characteristics of materials developed from the ideas that had been put forth in the earlier publications [1–5]. A formalized technique based on the earlier studies [2, 3] was also discussed. Its main assumption was that the material was homogeneous, and it enabled one to process real experimental data on a computer. This paper is devoted to the effect of structural inhomogeneities of materials, which is identified with a large spread of the parameter . This factor must be taken into account in a number of cases when the assumption that a tested body is structurally homogeneous does not apply.     

Atmospheric effects of friction,friction noise and wear with silicon and diamond. Part II. SEM tribometry of silicon in vacuum and hydrogen

Scanning electron microscope (SEM) tribometric data on polycrystalline silicon (poly-Si) vs. poly-Si, Si(100) vs. Si(100) and Si(111) vs. Si(111) interfaces, obtained in Torr and in 0.2 Torr partial pressure of hydrogen gas ( ) from room temperature to 850^°C, were performed under standard and much slower thermal ramping rates. The friction data were analyzed per the methodology described in part I of this paper series. The results indicate a highly beneficial friction- and wear-reducing regime within a relatively narrow thermal region. This desirable region coincides with some chemisorption of excited species of molecular hydrogen just before the mass thermal desorption of surface hydrides. These data represent the tribochemical equivalent of a method routinely used in electronics, whereby deep electron traps (dangling Si bonds) are passivated by baking in molecular hydrogen. The also exerts a moderating influence on the size of the friction noise at all test temperatures. However, the general level of friction beyond the beneficial thermal region is high. In parallel, the general wear rate of Si representative of the entire range of standard thermal ramping in both atmospheric environments is in the extremely high 10^-12m³/(N m) range. Operating strictly in the beneficial, low-friction thermal regime resulted in a several orders-of-magnitude reduction in the wear rate over those measured under standard thermal ramping conditions. Although the results confirm previous findings that Si is not a good material of construction for miniaturized moving mechanical assemblies (e.g., microbearings and gears), there seems to be some limited possibility of gas-phase lubrication of Si micromechanisms with rarefied hydrogen at surface temperatures between 100 and 300^°C. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Contribution of a Soft Thin (Metallic) Film to a Friction Pair in the Running-In Process

Analytical and experimental studies have been conducted on silver-film-covered and uncoated metallic surfaces to investigate the role of the soft, thin, metallic film in the running-in process. The experimental results have shown that a low coefficient of friction of about 0.22 and especially low wear can be obtained at the inception of sliding when there is a thin film. The analysis has shown that for the coated case the improvements can be obtained owing to the increase of the true area of contact and thus the reduction of contact pressures. In the presence of such a thin film, it has been pointed out that the friction force arises due to shear of the film and substrate instead of solely shearing of the film. Based on the experimental and analytical results, a new physical model for the film-covered case was proposed where a plastic deformation for the thin film was assumed. To account for the role of the film in preventing the substrate/pairing materials from wear, the effect of the coefficients of friction on the maximum shear stresses and maximum tensile stresses in the subsurface was calculated in light of the von Mises yield criterion .     

Cyclic Scheduling of Operations for a Part Type in an FMS Handled by a Single Robot: A Parametric Critical-Path Approach

We consider two problems of periodic scheduling of parts in a robotic production system functioning under a given repetitive robot's route. The objective is to determine the starting times and durations of processing operations so as to minimize the cycle length. We reduce the problems to finding parametric critical paths in networks with varying arc lengths. In contrast to previously known methods, which solve these cyclic scheduling problems in cubic time, the parametric network approach solves the problems in time, m being the problem size.     

Accuracy and strength of a joint loaded by suddenly applied torque

The influence of the required quality (fit and degree of accuracy) of prismatic joints to achieve guaranteed clearance was a speciality of experienced designers. The problem becomes quite complicated owing to stresses arising in the joint elements during torque transmission under dynamic loading.In this paper a widely used prismatic joint with a hexagonal cross-section is considered. A dynamic loading, generated by a spring mechanism is applied. D'Alambert's principle was employed in solving the kinesthetic problem.The paper presents equations for the dynamic coefficient, the angle of clearance, _i and the maximum tangential stress. It is pointed out that torque-loaded elements cannot be produced from rolled stock, obtained from drawings.The presented graphs permit selection of the steel grade in accordance with the fit and the degree of accuracy of the joint and with the permissible torsional stress.The proposed procedures may be used for computer-aided design of torque-transmitting prismatic splines, key joints and torsion mechanisms.Nomenclature d ₁ diameter of hole (see Fig. 1) - d _max D _n + es maximum limit of shaft size - d _min D _n + is minimum limit of shaft size - D _max D _n + ES maximum limit of hole size - D _min D _n + EI minimum limit of hole size - D _n nominal size of the hole and of shaft - ES, es upper deviation of hole and shaft - EI, ei lower deviation of hole and shaft - F area of hexagon - G modulus of transverse elasticity - (see Fig. 1) - I _p polar moment of intertia - polar moment of inertia of hexagon - polar moment of inertia of circle - K dynamic coefficient - l length of shaft - m number of polygon sides - M _d torque under dynamic loading - M _s torque under static loading - S _i clearance - S _max = ES-ei maximum clearance of joint - S _min = EI-es minimum clearance of joint - T tolerance - W section modulus of torsion - W _c circle section modulus of torsion - W _h hexagon section modulus of torsion - (see Fig. 1) - maximum tangential stress under dynamic loading - maximum tangential stress under static loading - _d twist angle under dynamic loading - _i angular displacement - _s twist angle under static loading     

Modelling of Tool Wear Based on Component Forces

Polynomial and exponential wear models of the joint effect of different combinations of component forces or ratios were fitted to determine the wear model that would give the best approximation of actual tool wear rates. Statistical analysis revealed the combination of force ratios: F ₁=F _f/F _t, F ₂=F _r/F _t and F ₄ = to have the highest statistical significance with tool wear rate based on F _cal and r ² statistics for both polynomial and exponential models, with the latter giving the best approximation of the actual tool wear rates. A wear map was established using the exponential wear model of the force ratios for the machining of a nimonic C-263 nickel-base alloy with PVD TiN/TiCN/TiN-coated carbide insert grade.     

Magnetic-Powder Inspection of the Crystallographic Texture of Electrical Steel

A theoretical model of the formation of rhombic (in the case of an edge texture) or square (on cubic texture) indicator patterns upon magnetization of single crystals of electrical steel orthogonally to the (110) and (100) planes is described. The model is based on a solution of Maxwell's equations for a magnetostatic problem, with magnetic permeability introduced as a tensor. Two field sources are considered as limiting cases: (a) loop, short coil; (b) semi-infinite magnet, long coil. Two cases of permanent magnet diameters are considered: thin, d = 4 mm; thick, d = 20 mm. Two cases of density of magnetic charges are considered: (a) = const; (b) = ₀/ .     

Effect of coating layer for spheres under Hertzian contact

A model is constructed to analyze the effects of layer hardness and thickness upon contact stresses for the coated elastic sphere under normal loading. It is assumed that the layer is perfectly bonded to the elastic substrate and the radius of contact is very small compared to the radius of indenter. By following a linear theory of elasticity, Fredholm integral equation is developed and it is solved numerically. The resulting contact stresses are calculated at the layer surface as well as the layer-substrate interface. Also, the second invariant of the deviatoric stress tensor, are calculated for various layer substrate combinations and for several layer thickness.     

The curved wall jet over a circular cylinder before the interaction of two opposing curved wall jets

A curved wall jet before the interaction of two identical curved wall jets over a circular cylinder was investigated experimentally. Using hot-wire anemometry, the mean velocity, Reynolds stresses, and high order moments of the fluctuating velocity were measured. The turbulent kinetic energy and shear stress budgets were evaluated using the measured data. The correlation coefficient, ${{\overline {uv} } \mathord{\left/ {\vphantom {{\overline {uv} } {u'v'}}} \right. \kern-0em} {u'v'}}$ , the normal stress ratio, ${{\overline {v^2 } } \mathord{\left/ {\vphantom {{\overline {v^2 } } {\overline {u^2 } }}} \right. \kern-0em} {\overline {u^2 } }}$ , and the principal direction of the Reynolds stress are presented. The effects of curvature and adverse pressure gradient on these diistributions are also discurssed. The turbulent kinetic energy and shear stress budgets in two regions before the interaction are analyzed in detail to illuminate the effect of the adverse pressure gradient on the turbulent transport.     

A note on productivity gains in flexible robotic cells

Flexible robotic cells combine the capabilities of robotic flow shops with those of flexible manufacturing systems. In an m-machine flexible cell, each part visits each machine in the same order. However, the m operations can be performed in any order, and each machine can be configured to perform any operation. We derive the maximum percentage increase in throughput that can be achieved by changing the assignment of operations to machines and then keeping that assignment constant throughout a lot's processing. We find that no increase can be gained in two-machine cells, and that the gain in three- and four-machine cells each is at most 14 %.     

Procedures for testing manufacturing precision Cpbased on (\bar{x},R) or (\bar{x},S) control chart samples

Process precision index C_p has been widely used in the manufacturing industry for measuring process potential and precision. Estimating and testing process precision based on one single sample have been investigated extensively. In this paper, we consider the problem of estimating and testing process precision based on multiple samples taken from ( ,R)or ( ,S)control chart. We first investigate the statistical properties of the natural estimator of C_p and implement the hypothesis testing procedure. We then develop efficient MAPLE programs to calculate the lower confidence bounds, critical values, and p-values based on m samples of size n. Based on the test, we develop a step-by-step procedure for practitioners to use in determining whether their manufacturing processes are capable of reproducing products satisfying the preset precision requirement.     

Studies of chipping mechanisms for dicing silicon wafers

The purpose of this study was to investigate the chipping modes produced in the die edges of dicing silicon wafer using the thin diamond blades. The effects of dicing directions and different wafer types on the chipping size were studied. Furthermore, scratching tests were also used to assist the analysis of studying chipping conditions of the silicon wafer. The experimental results showed that the trace behaviors produced by the diamond indenter in the scratching test of silicon wafer can be divided into the three stages: rubbing, plastic deformation, cracking. The plastic pile up and crack of the scratching traces on the wafer mainly propagate along the development of the easiest slip direction family <110>. The chipping modes produced in dicing silicon wafer can be broadly classified as four types: (1) 30° chipping; (2) 60° chipping; (3) 90° chipping; (4) irregular chipping, which causes these mechanisms of chipping modes due to the meeting between the radial cracks of 30°, 60°, and 90° along the easiest slip direction family <110> and the lateral cracks along the easiest cleavage plane family {111}. When using the thin diamond blade diced on the (111) silicon wafer along the $ {\left[ {\overline{1} 10} \right]} $ direction, the size of top chipping produced was smaller than that of along the $ {\left[ {11\overline{2} } \right]} $ direction. Besides, for the (100) plane of silicon wafer, the size and the distribution of the chipping modes produced along the $ {\left[ {\overline{1} 10} \right]} $ and $ {\left[ {\overline{1} \overline{1} 0} \right]} $ directions were similar.     

The effect of fluorination on the surface chemistry of alkyl ethers on Cu(111)

By using small fluorinated ethers as models for perfluoropolyalkylether (PFPAE) lubricants, we have been able to determine the effect of fluorination on the bonding of the alkyl ethers adsorbed on the Cu(111) surface. The desorption energies have been determined by using temperature programmed desorption (TPD). The model compounds studied were dioxolane , diethyl ether ((CH₃CH₂)₂O), dimethoxymethane ((CH₃O)₂CH₂), dimethyl ether ((CH₃)₂O) and their perfluorinated analogues. All of the molecules studied adsorb molecularly and reversibly on the Cu(111) surface exhibiting first-order desorption kinetics. Upon fluorination of the alkyl ethers, the adsorbate-metal bond was weakened by 14 to 8 kcal/mol. The intermolecular interaction parameters for the hydrogenated ethers indicated repulsive adsorbate-adsorbate interactions, while the fluorinated ethers have attractive adsorbate-adsorbate interactions.     

A near-wall reynolds stress model for backward-facing step flows

A near-wall Reynolds stress model has been used in numerical computations for two-dimensional, incompressible turbulent flows over backward-facing steps. Numerical results are compared with Direct Numerical Simulation data as well as experimental data for flow quantities such as the skin friction, wall pressure,U-velocity and the Reynolds stress. Budgets of the transport equations for theU-velocity, turbulence kinetic energy,k and the Reynolds shear stress,— are also calculated and compared with the Direct Numerical Simulation data. The comparison reveals that the near-wall Reynolds stress model predicts the reattachment length fairly accurately. The near-wall Reynolds stress model also predicts the development of the boundary layer downstream of the reattachment point correctly when the Reynolds number is low. However, the model generally predicts a weak separation bubble and a slowly developing boundary layer when the Reynolds number is high.