| Driven by the important requirements for independent innovation of parallel/hybrid mechanism equipments in advanced equipment manufacturing industry,this thesis takes a 3 degree-of-freedom(DoF)parallel mechanism as an example to systematically investigate the type synthesis,integrated modeling of topology and performance and performance matching optimization by using Finite and Instantaneous Screw(FIS).The following contributions have been made.(1)Type synthesis of 3 DoF parallel mechanisms.The algebraic analytical characterization of the parallel mechanism and its motion pair and open limb finite motions are described based on the finite screw theory,and the process of type synthesis for the 2R1 T parallel robots is proposed.The standard type of the finite screw for the3,4 and 5 DoF limbs is obtained by the the desired motion,and derivative limbs are obtained by transforming the type and position of the motion pair in the limb.The assembly conditions of the 2R1 T parallel mechanisms are defined by using intersection operation of finite screw.A 2R1 T parallel mechanism(TriX parallel mechanism)is selected for performance modeling and optimization design according to the application requirements.(2)Integrated modeling and analysis of topology and performance.Based on the FIS theory,the TriX parallel mechanism is taken as an example to carry out the integrated modeling of topology and performance.The topological model is established by using finite screw,and the inverse kinematics and workspace analysis of the TriX parallel mechanism are completed.With the stepwise differential mapping law of finite screw and instantaneous screw,the first-order differential of TriX parallel mechanism topology model is used to obtain the velocity model and Jacobian matrix,and the stiffness modeling and analysis are carried out.The acceleration model and the Hessian matrix are established by the second-order differential of the topological model,and the rigid body dynamics modeling and analysis are completed.(3)Performance matching optimization.Based on the topology and performance integration model of TriX parallel mechanism,the virtual power transmissibility kinematics evaluation index,the instantaneous deformation energy stiffness evaluation index and the inertia matrix condition number rigid body dynamics performance evaluation index of the TriX parallel mechanism are respectively defined.The dimensional parameters and sectional parameters of Trix parallel mechanism are defined as design variables,and the analytical models between performance evaluation,constraints and design variables are established through the response surface method.The random perturbation model of the design variables is established.The mean and variance of the performance evaluation index are defined as the optimization objectives,and the probability distribution is defined as the optimization constraint.Performance matching optimization resorting to Pareto-based approach is implemented,and cooperative equilibrium selection is employed to search for the optimal parameters.Based on FIS theory,the type synthesis,integrated modeling of topology and performance and optimization of parallel mechanism are investigated under the unified mathematical framework in this thesis.The problem of algebraic analytical characterization for type synthesis is solved,and the intrinsic association between the topology model and performance model is revealed.In addition,the multi-objective performance matching optimization is completed.The work is of great significance for breaking through the basic theory of parallel mechanism synthesis,analysis and design,and provides an important reference for the development of other types of parallel/hybrid robot equipment. |
