Advanced Materials Research Vols. 230-232

Abstract: The forward displacement analysis of parallel mechanism is attributed to find the solution of complex nonlinear equations which is a very difficult process. Take chaotic sequences as the initial value of Newton iterative method, we can find all the solutions of equations quickly. The paper investigated the initial point generated by hyper-chaotic circuit system and provided a new method and calculation step of finding the all real number solutions of nonlinear equations. Using quaternion, the mathematical model of forward displacement for the generalized 4SPS-2CCS Stewart parallel robot mechanism was established and an example was given. Compared to the topological continuations method the result shows the calculation is brief and general. It can be used in forward displacement of other parallel mechanism. The research builds the theory basis for dimensional design, trajectory planning and controlling of this type of manipulator.

Abstract: The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of Newton-downhill method, we can find all the solutions of equations quickly. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 4SPS-2CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic Newton-downhill method finding solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

Abstract: The forward displacement analysis of parallel mechanism is attributed to find the solution of complex nonlinear equations which is a very difficult process. Taking chaotic sequences as the initial values of the damp least square method, we can find all the solutions of equations quickly. The paper investigated the initial points generated by hyper-chaotic Hénon mapping and provided a new method and calculation step of finding the all real number solutions of nonlinear equations. Using quaternion, the mathematical model of forward displacement for the generalized 4SPS-2CCS Stewart parallel robot mechanism was established and an example was given. Example showed the calculation is brief and general. It can be used in forward displacement of other parallel mechanism. The research builds the theory basis for dimensional design, trajectory planning and controlling of this type of manipulator.

Abstract: The chaos improved Newton iterative method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 25^th nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining improved Newton iterative method with chaotic sequences, chaos improved Newton iterative method based on utilizing new type chaos system introduced by Chen to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Abstract: The anti-control of chaos Newton downhill method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 25th nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining Newton downhill method with chaotic sequences, anti-control of chaos Newton downhill method based on utilizing anti-control of chaos in body motion system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given.The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Abstract: The hyper-chaotic least square method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 31^th 2-coupled–degree nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining least square method with hyper-chaotic sequences, hyper-chaotic least square method based on utilizing parameter coupling hyper-chaotic discrete system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given. Comparison was also done with other finding solution method. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Abstract: The forward displacement analysis of parallel mechanism can be transformed into solving complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of damp least square method, all the solutions of equations can be found and the solving efficiency is related to modeling methods. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the chaos sequences-based damp least square method. Based on the connection topology of chaotic neural network composed of the four chaotic neurons, hyper-chaos exists in the chaotic neural network system. Combining hyper-chaos with damp least square method, a new method to find all solutions of nonlinear questions was proposed, in which initial points are generated by utilizing hyper-chaotic neural network. For the first time, based on quaternion, the model of the forward displacements of 6-SPS parallel mechanism is built up. The result is verified by a numerical example.

Abstract: Mechanism synthesis questions can be transformed into nonlinear equations to be found. Interval Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The characteristic of hyper-chaotic sequences produced by two dimensional hyper-chaotic discrete systems was analyzed. Making use of the advantage of giving rigorous bounds for the exact solution, for the first time, combining hyper-chaos sequences and interval Newton iteration with Krawczyk operator, a new method to find all solutions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

Abstract: The paper introduces computer vision into the detection of end points of flame burning during the process of refuse incineration and proposes a method to detect the end points of flame by image processing. Firstly, filter image and enhance the special quality of shade by total variation de-noising. Secondly, extract the main edge of the flame image by method based on binary morphology algorithm. Thirdly, detect and output the end points of flame by median method which has removed the spike of the image. The results show that the presented method is efficient and the system can meet the requirement of both detection accuracy and processing speed. Also it increases the safety of incineration equipment and saves plenty of labor force.

Abstract: Surface modifiers with different lipophilic chain lengths, such as, lauric acid diethanolamine, myristic acid diethanolamine, palmitic acid diethanolamine and stearic acid diethanolamine, were used to prepare four kinds of LaF₃ nanoparticles in the mixture solvent of water-ethanol. Morphology and surface modification of LaF₃ nanoparticles were investigated by TEM, FTIR and TG. Effect of length of surface modifier lipophilic chain on tribological properties of LaF₃ nanoparticles and their susceptibility to base oils were investigated by a four-ball machine. Results show that the tribological properties of LaF₃ nanoparticles in the base oil in build up as lipophilic chain length of surface modifiers increases; the longer the lipophilic chain is, the better the susceptibility of the nanoparticles to liquid paraffin wax is. This is mainly because that the lipophilic chain length influences the interface activity of the nanoparticles, moreover, for homologous organic acid soaps, the longer the lipophilic chain is, the better its friction reducing performance is; the properties of base oils also influence the interface activity of the nanoparticles.