Research On Some Fundamental Problems Of Parallel Mechanism

With the development of science and technology, parallel mechanisms have been paid more and moreattention, and the application of parallel mechanisms is more and more extensively. Different from theserial mechanism, it is only a few decades that the parallel mechanisms have been developed. Somefundamental problems of the parallel mechanisms have not been fully solved so far, which hinders thedevelopment and application of parallel mechanisms.6-SPS parallel mechanism is a typical parallelmechanism. The forward kinematics analysis and the singularity analysis of the6-SPS parallelmechanism, the cable-driven parallel mechanism have been deeply researched and discussed in thisthesis.The forward kinematics analysis is one of the fundamental problems of parallel mechanisms, andwhat's more, it is the basis of researching some other problems of parallel mechanisms. The forwardkinematic equations are highly coupled nonlinear equations about the position and orientationvarables, and it is difficult to be solved analytically. Through analyzing the coupling relationshipsamong the position and orientation variables of the moving platform, appliying the Gr bner basisalgorithm,15four order compatible algebraic equations, which containing three orientation variables,are obtained. Based on the15compatible equations, using the orthogonal complement method andeliminating the higher terms step by step, the problem of the forward kinematics analysis of the6-SPSparallel mechanisms can be expressed as higher order algebraic equations in the end. The results showthat, the forward kinematics analysis of the general6-SPS parallel mechanisms can be expressed as a20order algebraic equation. Although it is still20order equation, it is more quickly and practicable.The forward kinematics analysis of the symmetrical6-SPS parallel mechanisms has beeen studied byseveral methods, and each of them can express this problem as a14order algebraic equation. Theforward kinematics analysis of both3/6-SPS and3/3-SPS parallel mechanisms can be expressed as a8order algebraic equation. This thesis presents a kind of Elliptical6-SPS parallel mechanisms, ofwhich the forward kinematics analysis can also be expesed as a14order algebraic equation.Singularity analysis is one of the fundamental problems of parallel mechanisms too. Thisproblem can not been avoided in the research on workspace, motion planning and the design ofcontrolling system. How to express the singularity locus in an analytical form is the research emphasisfor many researchers for a long time. This thesis presents a new method for the singularity analysis ofthe6-SPS parallel mechanisms. The rotation matrix is been described by quaternion, and both the rotation matrix and the coordinates vectors have been expanded to four dimensional forms. Throughanalyzing the coupling relationship between the position variables and the orientation variables,utilizing properties of the quaternion, eight equivalent equations are obtained. A new kind of Jacobianmatrix is derived from those equations, and the analytical expression of the singularity locus isobtained by calculating the determinant of the new Jacobian matrix. The singularity analysis of allkinds of6-SPS parallel mechanisms can be solved by this analytical method.In this thesis, the relationship of forward kinematics and singularity has been studiedpreliminarily. The research shows that, the forward kinematics would have multiple roots if theparallel mechanisms are placed on singular configurations. It means that tha state of mtion will bechanged. And it forms a basis for deeply study in the future.The cable-driven parallel mechanism is a new type of parallel mechanism which has beendeveloping in recent years. Workspace, stiffness and other issues have been studied in the thesis. Atheoretical analysis platform has been constructed. Since a cable can only sustains pull rather thanpressure, the principle of keeping the tension positive should be satisfied while analyzing theworkspace of the cable-driven parallel mechanisms. The workspace of the cable-driven parallelmechanisms has been analyzed by the orthogonal complement method. Use the research methods ofindustrial robots for reference, the stiffness of cable-driven parallel mechanism has been studied inthis thesis.