Research On Topological Characteristics,kinematics And Stiffness Of Reconfigurable Parallel Mechanisms With Low Coupling Degree

With the rapid development of science and technology and the requirements of multi-function and adaptability of the mechanism in manufacturing,reconfigurable parallel mechanisms have become one of the new research hotspot in the field of mechanism and robotics.In this dissertation,the research on the structure design,kinematics analysis and stiffness performance of the reconfigurable parallel mechanisms is carried out.Three representative reconfigurable parallel mechanisms with low coupling degree are proposed,namely 3-RPR planar reconfigurable parallel mechanism,9-3 and 12-6 spatial reconfigurable parallel mechanisms,aiming to explore and verify the calculation methods and improvement methods of the performance of reconfigurable parallel mechanisms.The specific research contents are as follows:(1)Aiming at the problems of heavy workload and repetitive operations in the process of topological characteristic calculation,three commonly used topological indexes are defined in modularization.A kind of metamorphic kinematic joint which can convert the prismatic joint and the rotation joint is designed,and the switching between 3-RPR and 3-RRR parallel mechanisms is realized.In order to reduce the coupling degree of the mechanism,a kind of double and triple compound spherical joints in which several rotation axes always intersect at one point are designed respectively.A kind of metamorphic prismatic joint which can convert actuated,passive and locked working modes is designed,so as to realize the topological reconfiguration of 9-3 and12-6 parallel mechanisms.Based on the topological design theory of the parallel mechanism and three topological index modules,the main topological characteristics of the three mechanisms are analyzed respectively,including POC set,degree of freedom and coupling degree.(2)Aiming at the current situation that the forward position solutions of most 6-DOF Stewart-type parallel mechanisms can not be described with full analytical form,or it is difficult to deduce the full analytical solutions,a semi-numerical semi-analytical algorithm with high accuracy and stability is proposed.First,structure coupling-reducing of parallel mechanisms is realized by reconfiguration based on the two union operation theorems.Then,according to the geometric relation between feature points of the moving platform,the compatibility equations of reconfigured parallel mechanisms are analytically derived and numerically solved.Combined with the virtual limb lengths,the symbolic forward solutions of two auxiliary parallel mechanisms are derived.Furthermore,numerical behaviors of the proposed algorithm and traditional numerical algorithm are compared and analyzed.The results show that the computational accuracy and stability of the former are substantially better than those of the latter,thereby demonstrating the effectiveness of the proposed algorithm.Finally,the coordinated relation of displacement input of the prismatic joints is explored.(3)Aiming at the problems of low calculation accuracy and unreliable prediction when calculating the workspaces of parallel mechanisms by traditional point discretization method,an interval discretization method with high accuracy and reliable prediction is proposed based on the interval mathematics theory.Firstly,the analytical forward and inverse kinematics of the mechanisms are derived and extended into interval-valued form.Then,the position and orientation workspaces are predicted and corrected in sequence.Furthermore,numerical behaviors of the proposed and traditional methods are compared.The results show that the computational efficiency,computational accuracy,and error sensitivity of the former are improved by 5.34,45.50,and 1.01 times respectively.The proposed method can realize the prediction of position and orientation workspaces,thereby demonstrating the effectiveness of the proposed method.(4)Aiming at the problem that there are various expression forms of Jacobian matrix in existing literatures,which is not conducive to the unified evaluation and comparison of index values,the basic reasons of the above phenomenon are found by analyzing the Jacobian matrix mechanism of parallel mechanisms:(i)the rotational velocities are expressed in different ways;(ii)different base points are selected for translational velocities;and(iii)the dimensions are not uniform.From the above three perspectives,four types of Jacobian matrices are derived respectively.The mapping relationships between different Jacobian matrices are deduced by using the angular velocity addition formula and the linear velocity base point method,and the correctness of mapping matrices is verified by a numerical example.A new approach is put forward to eliminate the singularity of parallel mechanisms by topological reconfiguration,and the feasibility of the proposed method is verified by numerical examples.(5)Aiming at the shortcomings of the existing stiffness enhancement methods,a new approach is put forward to enhance the stiffness of parallel mechanisms by topological reconfiguration.First,an overall rotational stiffness matrix is analytically deduced by relating the external loads exerted on the end-effector to the magnitude of the induced micro-angular displacements.Then,it is proved that the minimum eigenvalue of this matrix can serve as a stiffness index of the parallel mechanism.Subsequently,an optimization objective function is developed for stiffness enhancement through topological reconfiguration,and a singularity-free path planning model for full mobility motion control is formulated.Finally,numerical simulations are provided to compare the stiffness index values of pre-reconfiguration and post-reconfiguration mechanisms.The results show that the stiffness of the latter is substantially larger than that of the former,thereby demonstrating the effectiveness of the proposed approach.This work provides a new development of theoretical basis for the evaluation and improvement of the performance of reconfigurable parallel mechanisms,and has important scientific significance and application value for enriching configurations of reconfigurable parallel mechanisms and expanding their application fields.Meanwhile,it can also provide theoretical guidances for the design and analysis of other reconfigurable parallel mechanisms.