| For half a century, parallel robot has been thoroughly studied and widely used. However, there are still some problems in their research fields, such as kinematics, dynamics, workspace, singularity, etc. Forward solution of stewart platform which is one of the 100 interdisciplinary sciences puzzles of the 21st century is being increasingly widespread concerned. The accurate, fast, stable kinematic position solution algorithm are needed, and optimized dynamics control strategies,more precise and detailed description of the workspace are needed too in practical applications, such as space exploration, ocean development, atomic energy applications, military, disaster relief, etc. it is very necessary either in theory or in practice to research in-depth on kinematics, dynamics and working space of parallel mechanism, especially the forward position solution about the parallel robot.The study of the forward kinematics numerical solution,dynamics and workspace of parallel robot issues:â‘ The method of forward kinematics solution lack simple, rapid and general numerical algorithm which ensure that iteration is convergent.â‘¡There is less research on the relationship between the parallel mechanisms composed of different limb.â‘¢There is a lack of general algorithm of the positive solutions ,inverse solution and cross solution; lack of the study of equivalent substitution to input conditions of the forward solutions; also lack of the research on multiple parallel mechanism with relationship in parallelâ‘£The research on workspace is not comprehensive and systematic enough, and the study about efficiency of space utilization is poor.The main contents of this dissertation include:â‘ reviewed current situation of the numerical algorithm, the forward kinematics solution of the parallel mechanism;â‘¡presented a forward kinematics numerical solution which is applicable for all kinds of parallel mechanisms;â‘¢presented a indirect method suitable for parallel mechanisms dynamics;â‘£Establish a simple ontology about workspace of the parallel mechanism .The novelties of the dissertation include:(1) Put forward and defined the concept of ideal parallel mechanism, put forward arthropodization method of the non-ideal parallel mechanism .Ideal parallel mechanism is a parallel mechanism whose branch is a straight line limb .Arthropodization method includes two aspects: analysis and synthesis, and decomposed the complex parallel mechanism into a number of arthropods which are connected in series, including the main arthropod, transmission arthropod, drive arthropods. Then connect the plurality of arthropod in series to form a whole .Each arthropod is a simple parallel mechanism. According to the known conditions, analyses various arthropods, and the links them. Finally gets a comprehensive solution of non-ideal parallel mechanism.Arthropodization method is a kind of new method to indirectly solve the problems such as kinematics, dynamics, workspace, singularity of the non-ideal parallel mechanism. Arthropod analysis method of non-ideal parallel mechanism could study the parallel mechanism from a new perspective and can share a lot of research results of the ideal parallel mechanism. The concept of ideal parallel mechanism can popular and apply the geometric iteration method to all of the parallel mechanism, and also can be used to study the kinematics, dynamics, workspace and singularity of the non ideal parallel mechanism.(2) Presented a new forward numerical algorithm method suitable for all parallel mechanism----geometric iteration method. The feasibility, stability and reliability of the geometric iteration method are confirmed using empirical and theoretical analysis method. Geometric iteration method is mainly composed of three parts: the pan similarity hypothesis, the mathematics model of the parallel mechanism and the iterative process.The similarity hypotheses of Geometric iteration method include three parts:â‘ Universal geometrical similarity hypothesis of the parallel mechanism: Hypothesize that the graph of parallel mechanism has universal geometric similarity hypothesis in the geometric iteration process;â‘¡Graph similarity hypothesis of the hinge pivot: Hypothesize that the graphics formed by actual hinged fulcrums of the moving platform (flat or three-dimensional graphics, referred to as the true hinge pivot graphics) is similar to the graphics formed by the hinged fulcrum in the iterative process (referred to as iterative hinged fulcrum graphic) structural similarity;â‘¢Graph similarity hypothesis of the reference point : Hypothesize that the iteration variable (reference point) is similar to the relative position of each iteration hinge pivot and the real reference point is similar to the relative position of the true hinge pivot. Every step of the iterative process follows the similarity hypothesis.The establishment of mathematical model is to transform a given parallel mechanism into an ideal parallel mechanism, then calculate the number of the DOF and analysis the combination of the DOF; Establish a formula of the geometry inverse solution based on the basic coordinate system; Finally determine the iterative initial value and new structure parameters of the ideal parallel mechanism.The iterative calculation process begin from iterative initial value (home position parameters), then find out the platform hinge pivot position by geometrical inverse solution formula; Use basic input (e.g., known limb's length ) to amend relevant hinge pivot position; Use the modified hinged fulcrum coordinate to comprehensive determine a new platform on a plane according to thepan-similarity hypothesis; Use the new platform plane to get a new set of position data, to replace the original iterative initial value; Judge if the iteration meets accuracy requirements, determine continuing the iteration or ending the program.Of novel algorithm, the physical model is clarity, the programming is simple, the workload of programming is small, the iterative convergence speed is high. It can achieve arbitrary precision and the precision is controllable, stable and reliable.An universal Initial value which is a Parameter in home position assures the reliability of algorithm operation.The novel algorithm completely avoids nonlinear equations, and does not need the derivative operation and the Jacobi matrix inverse operation. Generally speaking, geometric iteration method is better than the Newton-Raphson method or as well as the Newton-Raphson method.Geometric iteration method can be applied to all of the parallel mechanism. And can complete the task of positive solution, inverse solution and cross solution. Geometric iteration method is suitable for the solution of multiple parallel mechanism and parallel system, it is also used to calculate the complex polyhedron and variable geometry parallel mechanism.(3) Establish a simple ontology about workspace of the parallel mechanism. Analyse the robot workspace from the perspective of ontology. Extend the connotation and extension of the concept of the workspace.This paper has the effects and significance as follows:â‘ The arthropodization analysis methods set up a bridge between the ideal and non ideal parallel mechanism, and provided a new train of thought for the analysis of kinematics, dynamics, workspace and singularity characteristics of the non ideal parallel mechanism.â‘¡Geometric iteration method witch completely avoided the nonlinear equations provided a new choice for all forward solutions of the parallel mechanism. The novel algorithm has been successfully applied to a variety of different types of parallel mechanism, and provided a new way to solve nonlinear equations with the numerical methods, and provided a new method to solve the intersection solution, and equivalent input solutions. It reduced overall difficulty of the forward solution and lay a foundation for the popularization and application of the parallel mechanism.â‘¢Established a ontology about workspace of robot. Not only widened the research field of the robot working space, but also offered the theoretical foundation for optimization design. For example, various disturbance space of the mechanism, space utilization rate of the mechanism, spatial regularity and other new contents, which can be used and need further study.
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