You Xin Luo

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Newton-Downhill Method

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. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the Newton-downhill method based on Chaos sequences. 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 3SPS-3CCS 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.

Forward Displacement Analysis of the 4SPS-2CCS Generalized Stewart Parallel Robot Mechanism Based on Hyper-Chaotic Sequences

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.

Forward Displacement Analysis of the 6-SPS Stewart Mechanism Based on Quaternion and Hyper-Chaotic Damp Least Square Method

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.

Grey New Information GOM(1,1) Model and its Application Based on Opposite-Direction Accumulated Generating and Background Value Optimization

The accuracy of the traditional grey model is not high for the monotonic decreasing data. The paper uses the opposite-direction accumulated method and makes full use of new information combined with optimization of the background values. It induces the formula of the parameters in the model and establishes the grey new information GOM(1,1) model in which it is based on the opposite-direction accumulated operation and optimization of the background values. It is a new method of the grey model. The examples show it is with higher accuracy than that of non-new information model.

Grey New Information GOM(1,1) Model Based on Opposite-Direction Accumulated Generating and its Application

As the monotonic decreasing data the traditional grey model is characteristic with low accuracy, using the opposite-direction accumulated generating operation, making full use of the new information, the formula of the parameters was induced and the grey new information GOM(1,1) model was established based on opposite-direction accumulated generating operation. It provides a new way for the grey model. The examples show the model is practical and reliable.

Differential Evolution Algorithm with Hybrid Discrete Variables and its Application to Mechanical Optimization

The optimization design about hybrid discrete variables is very significant but also difficult in engineering, mathematics for programming and operational research. Aimed at shortages of existing optimum methods, in this paper, according to the search mechanism of differential evolution algorithm (DEA), a new differential evolution algorithm is proposed to complex optimization problem with hybrid discrete variables The dynamic penalty function was constructed. DEA algorithm program with hybrid discrete variables is developed. The computing examples of mechanical optimization design show that this algorithm has no special requirements on the characteristics of optimal designing problems, it has a fairly good universal adaptability and a reliable operation of program with a strong ability of overall convergence and high efficiency.

Grey New Information Unbiased GOM(1,1) Model Based on Opposite-Direction Accumulated Generating and its Application

Monotonically decreasing sequence data for the use of traditional modeling methods to establish the grey model accuracy is not high, grey GM (1,1) model, there is a deviation, the model does not meet the conditions for coordination, generated using the definition of reverse accumulation, full use of system information and unbiased grey GM (1,1) model parameters of the model derived formula, based on reverse incremental build new interest generated by an unbiased model grey GOM (1,1) model for the grey model provides a new method. Data processing examples show that the models practicality and reliability.

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Three-Step Iterative Method

The forward displacement analysis of parallel mechanism is transformed into find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of the three-step iterative method, we can find all the solutions of equations quickly. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the three-step iterative method based on Chaos sequences. 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 3SPS-3CCS 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 three-step iterative method to find 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.

Grey Unbiased GRM(1,1) Model Based on Accumulated Generating Operation in Reciprocal Number and its Application

The accuracy of the grey model is not high for the monotonic decreasing data and the error can not avoided. The model can not satisfy the compatibility conditions and then it is not accordant with the linear transformation. The paper adopts the equal interval unbiased model and takes one of the components in as the initial values. By this method it induces the parameters in the grey unbiased GRM(1,1) model and establishes the equal interval unbiased model based on the reciprocal AGO process. The model has high accuracy and has good value in the theory and practice. The examples show it is practical and reliable.

The Research of Composite Nonlinear Discrete Chaos Dynamical Systems to Mechanism Synthesis

Many questions in natural science and engineering are transformed into nonlinear equations to be found. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point.　A composite discrete chaos dynamical system was constructed by two special discrete chaos dynamical systems and initial points were produced by proposed chaos system. For the first time, a new method based on composite discrete chaos dynamical system to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.