Theoretical Analysis And Experimental Study Of A Large Attitude Flexible Parallel Mechanism

Traditional rigid parallel mechanisms have large stiffness and high control accuracy,but their attitude workspace is limited and the range of stiffness is small,which limit their performance under conditions where large attitude and interactions with humans are required.In this paper,a large-attitude flexible parallel mechanism is proposed,which can avoid singularity and expand the attitude wrokspace by the fact that great curvature and large torsion bending deformation will appear in flexural legs under forces.The virtual Jacobian matrix concept is derived to obtain the mathematical model of the stiffness matrix of the flexible parallel mechanism.The principle of the motion redundancy variable stiffness through twisting the flexible legs is used to change the structural stiffness,and then the overall stiffness of the parallel mechanism can be adjusted.Firstly,the large deformation flexible actuation of flexible parallel mechanism with large attitude is analyzed.Based on this blank and challenging design difficulty,a pseudo-rigid structure design method for flexible parallel mechanism is proposed,which uses line decoupling theory and condition number index to optimize and determine structural parameters.Then,the constitutive equation and boundary conditions of flexible leg under different articulation forms are analyzed.Aiming at the difficulty of solving the ordinary differential constitutive equation of flexible leg,the numerical solution is obtained by shooting method,and the influence of the parameters in shooting method on the accuracy and efficiency of the algorithm is analyzed in detail,which lays a foundation for subsequent kinematics modeling.On the basis of mastering the constitutive equation of a single flexible leg,the kinematics of the large-attitude flexible parallel mechanisms is carried out.Because of the nonlinearity of the constitutive equations of the flexible legs,the force equations and articulation equations are also required besides the same closed-loop equations as those of the rigid parallel mechanisms in order to solve those ordinary differential equations.Based on the kinematics the workspace of the flexural parallel mechanisms are obtained by using the dichotomy traversal method.When static problems of flexible parallel mechanisms are analysed,the concept of virtual Jacobian matrix is presented by decomposing each flexural leg into a set of three orthogonal springs along the global coordinate system so as to obtain the statics model mathematically of the flexural parallel mechanism.On the basis of statics model,the stiffness matrix of a single flexible leg is derived.Then the stiffness matrix of a single flexible leg is mapped to the global stiffness matrix of the flexible parallel mechanism by virtual work method.The spatial distribution of the stiffness of the flexible parallel mechanism is evaluated by the index of homogeneous stiffness conditions and the index of homogeneous average stiffness.Then the variable stiffness mechanism of the flexible parallel mechanism is studied.Finally,the prototype and measuring devices of large-attitude flexible parallel mechanism are built according to configuration parameters,and the kinematics performance and stiffness theory are comprehensively verified by experiments.