| Spherical2-DOF parallel manipulator has two degrees of freedom moving alongspherical surface, which can be applied to the locating equipment of point on thespherical surface, and it has an important application prospect. Spherical5R parallelmanipulator possesses the simplest structure, but researches show that there are lots ofsingular curve in its workspace, and its bearing capacity and stiffness are also limited. Soour thesis group proposes spherical2-DOF parallel manipulator with redundant actuationwhich is obtained by increasing an identical kinematic chain on the basis of spherical5Rparallel manipulator to overcome the above problems. This paper studies the statics, staticstiffness, trajectory planning, error, calibration, prototype manufacture, development ofcontrol system and experimental researches of non-redundant and redundant spherical2-DOF parallel manipulator in depth, and the main work is as follows:Constraint equations including all structural parameters of spherical2-DOF parallelmanipulators are established on the basis of D-H parameter of the manipulators, theactual position solution of the manipulators are obtained, and the kinematics models ofthe manipulators are also established.The static equilibrium equations of spherical2-DOF parallel manipulators areestablished via the traditional dismantle-bar method, the deformation equations ofcompatibility are established by utilizing the micro-deformation and superpositionprinciple, the static full-solutions of spherical2-DOF parallel manipulators are obtainedby adding input torque optimization equation to redundant actuation manipulators. Basedon the result of static analysis, the relationship between the outer loads and the angulardisplacement of output axis and linear displacement of spherical center point isestablished, that is to say, the static stiffness matrices of spherical2-DOF parallelmanipulators are obtained. Through numerical example, the comparative analysis ofstatic stiffness of non-redundant and redundant parallel manipulator is carried on.Kinematics track of spherical2-DOF parallel manipulators is planned by two kindsof trajectory planning methods that acceleration are continuous segmental function and combined sine function in Cartesian space. With the help of Lagrange inverse dynamicsmodel, the joint torque model of redundant actuation manipulator is established throughforce optimization method.The position and posture error models of spherical2–DOF parallel manipulators areestablished based on the loop increment method, the relationships between the positionand posture error and each original error sources are analyzed, and the sensitivity is alsoanalyzed. At the same time, the conditions that the manipulator can move smoothly arestudied, the processing and assembly process design method of restraining pose error isproposed, which lay the foundation for processing and calibration of the prototype. Onthe basis of error analysis, the simplified model of position and posture kinematicscalibration is established, which simplifies the calculation of parameter identification anderror compensation; and the end-effectors’ actual position of the manipulator is measuredby using three coordinate measuring machine and3d drawing software; at last thevalidity of the method of calibration is verified through the calibration experiment.The prototype of spherical2-DOF parallel manipulators are designed and processed,and its control system adopting master-slave distributed structure system based on “PC+PMAC motion control card” is developed. For spherical2-DOF parallel manipulator withredundant actuation, the hybrid control of force/position that redundant chain usingtorque control in combination with position judgment and kinetic differential predictivecontrol and other chains using position control is proposed, and the coordinated motionof prototype is realized. Finally, the trajectory tracking experiments of non-redundant andredundant spherical parallel manipulators are carried on. |
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