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.     

Study of microstructural evolution of friction taper plug welded joints of C–Mn steels

Abstract

This paper describes the microstructural evolution of friction taper plug welded joints of C–Mn steels. Experimental and numerical analyses included calculations based on Calphad and continuous cooling transformation curves, and characterisation techniques. The studied friction taper plug welded joint contains three macroregions: plug material, thermomechanically affected zone (TMAZ) and base material. The thermomechanical conditions imposed in the studied friction taper plug welded joint precluded the formation of a heat affected zone. However, seven subregions were identified within the TMAZ region and details are discussed. The interface zone is found in the TMAZ region, where the most relevant phase transformations take place. It is suggested that the phase transformations in TMAZ region depend on local conditions, such as chemical composition, deformation rate, thermal history and the previous thermomechanical history of the parent materials.     

Characterisation of mechanical properties of electrochemically deposited thin silver layers

Abstract

In the present work, mechanical properties of electrochemically deposited thin silver layers with known thickness over brass substrates were investigated. For determination of mechanical properties of the layers, a method was used which is novel compared to those traditionally used in practice (in which, for example, a tensile test is carried out on a deposit after removal of the deposited layer from the substrate). The method developed and reported here is a combination of microindentation experimentation and numerical simulations and gives the opportunity to obtain mechanical properties of thin layers without their removal from the substrate. Vickers' microindentation experiment of the silver layer was realized and as a result, led to experimental a load–displacement curve. After that the process of microindentation was modelled numerically by means of finite element method. The numerically obtained load–displacement curve was compared with the experimental one and the result shows good correlation between numerical and experimental curves. For some kinds of layers, which are difficult or impossible to strip away from the substrate, this method reported in this paper is the only one feasible.     

Design and Modeling of a Snake Robot Based on Worm-Like Locomotion

In this paper we restrict our attention to worm-like, vertical traveling wave locomotion and present detailed kinematics and dynamics of a planar multi-link snake robot. Lagrange's method is used to obtain the robot dynamics. Webots software is used for simulation and to experimentally investigate the effects of link shape on motor torques. Using the dynamics model and Webots simulation, a nine-link snake robot is designed and constructed. Physical experiments are carried out to validate the mathematical model. Webots software is also used to perform simulation and further validate theoretical results. Finally, stability of the snake robot is experimentally investigated.     

Numerical modelling for rotational moulding with non-isothermal heating

Abstract

In the rotational moulding process, the internal air temperature has been widely recognised as a tool to predict an optimum cycle time. This paper presents a new numerical approach to predict the internal air temperature in a two-dimensional (2-D) static model without requiring the consideration of the tumbling motion of polymer powder. The initial non-isothermal heating of the static model is actually formed by two changeable plastic beds (stagnant and mixing beds), which represent the actual stagnant and mixing pools inside a rotating mould respectively. In the numerical approach, the lumped-parameter system and coincident node technique are proposed to incorporate with the Galerkin Finite Element Method in order to account for the complex thermal interaction of the internal air. It helps to overcome the difficulty of multidimensional static models in predicting an accurate internal air temperature during the heating stage of rotationally powdery plastic. Importantly, the predicted temperature profiles of the internal air, oven times for different part thicknesses and process conditions accord with the available experimental results.     

Error analysis of forward and reverse heat conduction and convection calculations considering uncertainties in welding

Abstract

Numerical models of fusion welding traditionally compute temperature field for a given set of welding conditions in a forward manner. The reliability of computed temperature profile depends on the accuracy of a number of model input parameters, values of which are uncertain in nature. Here, the authors show that a genetic algorithm (GA) assisted integrated numerical model, following either convection or conduction based calculations, can identify the suitable values of the uncertain model input parameters and in turn provide reliable computed results. Powered with GA, the integrated model is used further in a reverse manner to predict multiple sets of welding conditions for a target weld geometry. The convection based calculations have been able to provide more reliable multiple welding variables in reverse calculations.     

The Effect of Trace Elements on the Cooling Curves,Microstructure and Mechanical Properties of Eutectic Aluminium-Silicon Alloy

Abstract

The effect of trace elements, used for modification, on the cooling curves obtained during solidification, microstructure and mechanical properties of eutectic aluminium-silicon alloy was investigated. The results of this study indicate the following: 1 The addition of sodium or sodium plus strontium or antimony modifies the eutectic silicon while the addition of sulphur does not alter the microstructure.

2 Those elements which modify the eutectic-silicon, lower the eutectic solidification temperature, while those elements which do not bring about modification, do not alter the eutectic solidification temperature.

3 The addition of those elements which modify the eutectic aluminium-silicon alloy, viz., sodium or sodium plus strontium or antimony improves the UTS and percentage elongation. The addition of titanium to eutectic aluminium-silicon alloy containing these trace elements improves the UTS and percentage elongation to a further extent. Among the various trace elements added to eutectic aluminium-silicon alloy, the addition of sodium plus titanium improves the UTS and percentage elongation to the maximum extent.

     

Effects of particle size on deformation behaviour of metal matrix composites

Abstract

By incorporating the dislocation strengthening effect into the Mori–Tanaka method, a new hybrid approach is developed in the present paper for calculating the deformation response of SiCp/Al composites. The diameters of the particles are 1, 5, 20 and 56 μm. Both numerical and experimental results indicate a close relationship between the particle size and the deformation behaviour of the composites at a constant particle volume fraction. The yield strength and plastic work hardening rate of the composites increase with decreasing particle size. The predicted stress–strain behaviour of the composites is in qualitative agreement with the experimental results. By incorporating Weibull statistics for particle fracture, the results simulated are agreed well with the experimental results for particle size >5 μm.     

烟用香精中烟碱的气相色谱分析

以喹啉为内标,采用HP INNOWAX(30m×0 25mmi d ×0 25μmd f )色谱柱和NPD检测器建立了烟用香精中烟碱的气相色谱分析方法。线性范围为0 608～0 0135mg/mL,相关系数为0 99995;平均回收率为98 05%,RSD为1 79%。并用该法测定了8种烟用香精样品中的烟碱含量。