Synthesis of the forward kinematics problem algebraic modeling for the general parallel manipulator: displacement-based equations

This paper closes a triptic to address the issue of the forward kinematics problem (FKP) aimed at certified solving with an exact algebraic method. This solving method was described in the first article published in Advanced Robotics. The second one investigated the formulation specifically applied to the planar parallel manipulators. This third paper is the logical one in the footsteps of the formersones, since it continues the formulation analyses and brings them to the general spatial parallel manipulator. Hence, this paper focuses on the displacement-based equation systems. This paper is the first one to present a synthesis on forward kinematics modeling focusing on finding an optimal mathematical formulation based on the displacement-based equation systems. The majority of parallel manipulators in applications can be modeled by the 6-6 hexapod or so-called Gough platform which is constituted by a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two revolute or Cardan joints. Again, in order to implement algebraic methods, the parallel manipulator kinematics shall be formulated as polynomial equations systems where the equation number is at least equal to the unknown numbers. Six geometric formulations were derived. The selected algebraic proven method is implementing Gröbner bases from which it constructs an equivalent univariate polynomial system. The resolution of this last system exactly determines the real solutions which correspond to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. Several instantiations shall be computed in order to select the model which leads to the FKP resolution with the lowest response times and smaller file sizes. It was possible to reject three modelings leading to bad performances or resolution failure. It was possible to determine one formulation where the solving computations were definitely better than the others.     

Properties of reacto-thermitically sintered stainless steel

Abstract

Reacto-thermitic sintering (RTS) is a novel process capable of producing near net shape powder metallurgical stainless steel components with negligible interconnected porosity at sintering temperatures of 1150°C. It utilises chemical reactions between oxides present on the surface of conventional stainless steel powders and small quantities of reactive additives to produce a transient liquid phase. This liquid can be frozen during cooling to consolidate the component without slumping. Previous work by the authors has studied the fundamental mechanisms underpinning the evolution of this liquid phase and its subsequent behaviour in eliminating porosity. The present paper investigates the effect of varying the quantity of reactive additive on the dimensional stability, mechanical properties, and corrosion resistance of stainless steel specimens produced by RTS in the light of this work.     

Pack formation and long term oxidation kinetics of TiAl3 coating on γ-TiAl

Abstract

The aim of this study is to produce microcracking free TiAl₃ coatings on γ-TiAl alloy by the pack cementation process and to determine the long-term oxidation kinetics and thermal stability of the coating at high temperatures. It was shown that microcracking free coatings could be prepared in the AlCl₃ activated packs containing 4 wt-%Al as the depositing source. The conditions required for the formation of a microcracking free coating are discussed in relation to the pack chemistry at high temperatures. The TiAl₃ coatings formed were oxidised in air for more than 6200 h, during which weight gains were measured at regular intervals. The major oxide in the scale was Al₂O₃. It was observed that a TiAl₂ phase zone formed in the subsurface of the scale as a result of preferential oxidation of Al in the TiAl₃ coating. It was found that a linear relationship existed between the weight gain and logarithm of time of oxidation at 800°C: Δm _t = k _lln(αt+ 1). The thermal stability of the coating was assessed by measuring the growth kinetics of the TiAl₂ interlayer at the boundary between the TiAl₃ coating and substrate, which was determined to be d^1·4 = 0·1t (d and t in μm and h respectively) at 800°C using the experimental data measured over a diffusion annealing period of more than 6200 h.     

Influence of heat treatment processes on fatigue performance of particle reinforced aluminium alloys

Abstract

The fatigue performance of particle reinforced metal matrix composites improves as the matrix strength is increased. However, the heat treatment required for high matrix strength induces residual stresses into the material, which need to be balanced against potential distortion during machining of components. This paper reports results showing the fatigue behaviour of a 2124 aluminium alloy reinforced with 25 vol.-% of silicon carbide particles. The effect of quench medium on tensile and rotating bend fatigue strength is reported. Results are correlated with residual stress profiles measured in quenched plates of the material.     

Effect of interfacial shear strength on reliability of strength and fracture process of SiC–Al composite

Abstract

A unidirectional SiC fibre reinforced pure aluminium composite was fabricated by the hot press method. Tensile testing of the SiC–Al was carried out to determine composite and interfacial shear strengths. A Monte Carlo procedure based on the elastic–plastic finite element method, involving the interfacial layer around the fibres, was constructed to simulate the tensile testing and to calculate the strength and Weibull parameters for the SiC–Al composite. The effect of the interfacial shear strength on the composite strength and its reliability is discussed. The results show that the composite strength and the Weibull shape parameter increase with increasing interfacial shear strength. The contribution of the interfacial shear strength to the composite strength and reliability is efficient when the interfacial shear strength is lower than the matrix shear strength. It is concluded that both composite strength and reliability are closely related to the fibre fracture process.     

基于MODELS的工频弧光接地过电压的仿真

弧光接地过电压是中性点不接地系统中危害最大的过电压之一.目前,关于弧光接地过电压的研究大都采用系统仿真,基于工频熄弧理论,通过控制开关的闭合来模拟电弧的熄灭和重燃,观察弧光接地过电压情况.由于电弧的熄灭和重燃具有强烈的统计特性,电弧不一定是在工频过零时熄灭,也不一定是在电压达到最大值时重燃.因此,按一个工频周期来设定开关的开闭时间模拟弧光接地过电压时,模型不够准确.鉴于这种情况,在对弧光接地过电压产生机理深入研究的基础上,提出了一种新的开关控制方法,采用EMTP中的控制系统暂态分析TACS模块和MODELS模块对开关的控制部分进行处理.运用MODELS模块中特定的MODELS语言编写控制程序,输出一个信号作为TACS开关的输入控制信号,当满足给定电压和电流门槛值时,开关便会相应地闭合及断开.不必按一个工频周期来设定开关的开闭时间,提高了仿真模型的精确性.将其应用于10 kV中性点不接地系统及小电阻接地系统的弧光接地过电压的研究,取得了预期效果,具有很好的应用前景.     

Distribution Around the Oxide-Substrate Interface of Alloying Elements in Low-Carbon Steel

In order to study the physicochemical evolutionduring oxidation of Fe-C-X_i alloyssurfaces (X_i = Cu, Ni, Al, Si, S, withX_i% < 0.5 wt.%, C% < 0.1 wt.%), anoriginal analysis method has been used. After separating the oxide from the metalsubstrate, the first atomic layers of both innersurfaces have been observed by Auger ElectronSpectroscopy (AES). The depth profiles obtained, around0.4 m thick on both sides of the oxide-metal interface,have been compared for four steels of differentcomposition. Significant differences have been observedand described in this paper. A qualitativeinterpretation of diffusion processes has been proposed. Ametallographic study illustrates some physicalconsequences of alloying elements, especially on thescale thickness.     

Influence of clamping support distance on distortion of welded T joints

Abstract

A study is presented on the influence of the clamping support distance on welding distortion of 6 mm thick gas metal arc welded structural steel T joints. Experiments were performed for two clamping conditions and are compared to simulations based on a previously presented model. It was found that clamping closer to the weld seam reduces angular as well as bending distortion. In order to assess the accuracy of the results, sensitivity analyses were performed on the influence of predeformation and material parameters. It is shown that an initial predeformation has an influence on the final welding distortion. Additionally, it has been found that selection of material properties within the range of variations permitted by the material norms has a strong influence on the predicted distortion. Results were improved using material specific data rather than generic data for the relevant material class. Also the assumed phase volume change plays an important role.     

41—THE RETRACTION AND STRETCH OF WRAPPED ELASTOMERIC-FIBRE CORE YARNS

Equations are given that relate the structure of spirally wrapped elastomeric-fibre core yams to their stretch properties. The model employed improves upon previous ones by considering the effect of covering-yarn diameter. Graphs are given that facilitate the use of the theory for manufacturing purposes.

A comparison with available experimental data indicates an improved agreement between actual and predicted values of retraction in the most important case, where the input and output yarn lengths are measured. It is expected that the improved theory given here will show to much greater advantage with the present commercial fine-core wrapped structures.

In the special case where the wrapping or covering yarns have very low twist, the basic theory is inadequate. Modifications to account for compression of the cover yarn are accordingly included to enable an approximate relationship between yarn structure and stretch to be obtained in this case.     

Welding of Ti–6Al–4V and TiB2–Ni cermet using pulsed current heating

Abstract

Ti–6Al–4V alloy was joined with TiB₂–Ni cermet by using pulsed current heating and hot pressing. The properties were found to be better with the pulsed current process, because the current enhanced the growth of Ni–Ti phase at the junction between the two materials. Furthermore, the heat affected zone is localised in the pulsed current process relative to that in the hot pressed material.