Research On Identification Model And Method For Design Defects Of Mechanisms Based On Conformal Geometric Algebra

Design defect identification is a key technology in verifiable design system ofmechanical product. Traditional mechanical fault diagnosis is implemented by mappingfrom fault symptoms space to failure space, design defect identification is implementedby mapping from design model and parameter space to design defects space. Based onConformal Geometric Algebra (CGA), taking design defects identification as main clue,dead center point, singularity and function of rod rotation for parallel mechanism arestudied deeply and systemly in this thesis.Instantaneous static location point of mechanism appeared at the limiting positionare called the dead-center point. The continuous moving function of mechanism isseriously affected by the presence of the dead-center point. Based on CGA, closed-loopconstraint equations of Stephenson-III linkage mechanisms are established, by usingEuler formula, the closed-loop equations are expressed as compound exponential form.Mutual relationships between various parameters in the formula and vectors inconformal space are described. Depended on given input, input-output equations arederived to solve the position of the link mechanism. The value of Jacobian matrixdeterminant equals to0, so that the discriminative formulas of the dead-center positionsare derived and the dead-center position solutions are gained. Finally, the effectivenessand accuracy of this method are verified by contrasting with traditional numericalmethods.Singular position of parallel mechanism is the collection of uncontrolled pointduring the motion of mechanism. In this thesis, the kinematics of3-RPS parallelmechanism is modeled based on CGA. Movement of joint point is obtained byoperation of inner product and outer product between basic geometries. Depended ongiven input of the length of rod, input-output equations are established through thedistance of the joint points. The value of the matrix A equals to0, so that the singularequations with reference to three independent parameters are derived and the singularitysurface distribution is calculated. Calculation results indicate that modeling anddeveloping process of CGA do not involve coordinate selection, have advantage of strong geometric visibility. Singularity posture can be obtained by CGA quickly andefficiently.The process of motion for the spatial imperfect-DOF parallel mechanisms areseriously affected by the existence of the degree of freedom coupling, thus an instantmotion rather than a continuous motion can be achieved at the instantaneous moment.In this thesis, condition of instantaneous rotation and continuous rotation for linkages isanalyzed based on geometric algebra and screw theory. Value of virtual work andchanging rate of virtual work equaling to0simultaneously is the condition ofcontinuous rotation. Depended on this condition, kinetic characteristic of each rod isobtained, and rotating functions of the3TPS+1TP and2RPS+2TPS parallel mechanismare identified. Finally, singular posture of the2RPS+2TPS parallel mechanism isobtained, it occurs when the upper platform parallels the lower platform. This methodprovides basis for motion control and trajectory planning of parallel mechanism.Identification models and methodology for dead-center point, singular position androd rotation function based on CGA will provide some effective theories, methodologiesand techniques support for identification of mechanisms design defects.