Performance Analysis And Dimension Optimization Of 2-DOF Parallel Manipulators

Parallel manipulator has many advantages that serial manipulator does not possess,so they can compensate for each other in the practical application. 2-DOF parallelmanipulator plays a very important role in the family of parallel manipulators. It will bedeveloped and used in many fields in the near future due to its low manufacturing cost,ease in control and simplicity in structure. Focusing on 2-DOF parallel manipulators, thisthesis presents an extensive study of the kinematics of plane 2-DOF 5R parallelmanipulator, plane 2-DOF parallel manipulator with redundant actuation, spherical2-DOF 5R parallel manipulator and spherical 2-DOF parallel manipulator with redundantactuation. Based on results obtained from the study, the kinematical optimum design isalso carried out.The constraint equations of four kinds of parallel manipulators are first presented,respectively, according to the geometrical constraint of mechanism and by using victoralgebra and spherical analytic geometry. The position solution to the mechanism isstudied. The Jacobian matrix of the 2-DOF parallel manipulator used in kinematics isderived by means of derivation of constraint equations. Jacobian matrix is the basis andthe premise of analyzing performance indices of mechanism.On the basis of the geometrical constraint condition and the assembling requirement,design dimension and space needed of four kinds of 2-DOF parallel manipulator arederived. With the aid of geometry and spherical analytic geometry, the theoreticaloperating space configuration of the manipulator is analyzed. As to the sphericalmechanism, the theoretical operating space configuration is transformed to planarrepresentation by virtue of conformal mapping. Based on the mathematic description ofthe variation of mechanism's theoretical operating space configuration, design space isdivided into several sub-zones and mechanism character of manipulator in each sub-zoneis figured out. In addition, the relationship between theoretical operating spaceconfiguration, area and lever dimension is studied and the distributing regulation inmechanism design space is discussed.According to the geometrical characters and physical definition of singularconfiguration, the mechanism singular configuration is classified. By means of victoralgebra, mathematic conditions and geometrical characters of three kinds of singularconfigurations of 2-DOF parallel manipulator with no redundancy are analyzed. Inaddition, the geometrical characters of corresponding mechanism having singularconfiguration is studied. The singular configuration distributing regulation of bothmanipulator operation space and its design space is in depth analyzed. Based on theanalysis of singular configuration 2-DOF parallel manipulator with no redundancy, thesolution to the geometrical characters and singularity path of 2-DOF parallel manipulatorwith redundant actuation is presented.According to the definition of the full performance indices, the dexterity, output rate ,load capacity and stiffness are calculated. The theory of design space are adopted to studythe relationship between the full performances and the lever sizes of manipulator and todraw the performances diagram.Finally, based on the analyses of these performance indices, the design principles aregeneralized which should be observed in the design of 2-DOF parallel manipulator usingperformance diagram. Sample design is given as illustration. Meanwhile, onemanipulator with redundancy, and the other manipulator with no redundancy, both ofthem have the same lever sizes, are compared in performance indices, and the charactersof manipulator with redundant actuation are further studied...