Synthesis Of Actuation Spaces And Input Optimization For Lower-mobility Parallel Mechanism

The problem of input selection and input optimization are basic and important issues in the research of parallel mechanism.The traditional way to solve the input selection and optimization problems are to use the complete Jacobian matrix to judge the rationality of the input selection and use the condition number of the Jacobian matrix as an evaluation index to achieve optimization.However,the physical meaning of the Jacobian matrix is not clear,and the mapping relationship between the joint space of the mechanism and the operating space cannot be clearly characterized on kinematic performance by the Jacobian matrix.The motion/force transmission not only have a clear physical meaning,but also have a representative feature that distinguishes between the series mechanism and the parallel mechanism,and can reflect the transmission characteristics of motion/force in the joint space and the operation space.Therefore,it is necessary to use the motion/force transmission as a performance to evaluate the advantages and disadvantages of the input selection of the parallel mechanism.The purpose of this paper is to find a new method to solve the problem of input selection of lower-mobility parallel mechanism,that is,to obtain all reasonable input combinations through the synthesis of the actuation spaces,and lay a foundation for input optimization.At the same time,the motion/force transmission is used as an evaluation index to achieve input optimization.Firstly,based on the screw theory,the concept of actuation space in flexible mechanism is introduced into the research of lower-mobility rigid parallel mechanism,and the linear independence of the actuation space and the constrained space is proved under the condition of non-redundant drive and mechanism with certain movement.Based on this,a general expression of a reasonably actuation screw and a method for synthesizing actuation space of the lower-mobility parallel mechanism are obtained.Secondly,based on the existing motion/force transmission indexes,a new index reflecting the volatility of the motion/force transmission and an input optimization method based on the motion/force transmission index are proposed.Finally,the actuation spaces analysis of the parallel mechanisms such as 3-UPU with 2R1 T DOFs,3-PPU with 2TIR DOFs,3-RPRR with 3T DOFs and 2-RPS/2-UPS with 2T2 R DOFs are performed,and all reasonable actuation spaces and input combinations are obtained.Taking the 3-UPU and 3-PPU parallel mechanism as the research object,and based on the screw theory,the motion/force transmission performance of the mechanism in the whole workspace is analyzed,and the optimal input combination is obtained.