Research On Motion Precision Assurance Strategy Of Parallel Mechanism Based On Equivalent Stiffness

Compared with the serial mechanism, parallel mechanism has the advantages of high stiffness to weight ratio, high bearing capacity, good dynamic response and high precision. In terms of manufacturing equipment, intelligent structure, industrial robots and entertainment facilities, it can be widely used. Parallel mechanism motion planning is mostly based on inverse kinematics model solution, that don’t considerate the deformation of the mechanism under the external force. Meanwhile, it is difficult to directly measure the position of the parallel mechanism. Because of the semi-closed loop control, the parallel mechanism can’t eliminate the influence of deformation on the precision by control model. By analyzing the actual-time stiffness, it is important to consider the motion planning of the parallel mechanism with the deformation of the terminal to ensure the accuracy of the motion. This paper is mainly carried out from two aspects: it is important to optimize the structure parameters to improve the stiffness performance in parallel mechanism design stage, that the accuracy of the mechanism could be guaranteed; after the parallel mechanism is assembled, though considering terminal error introduced by component deformation, that strategy research is conducted to ensure the accuracy of the motion. Contents of this paper are as follows:(1) In view of the stiffness analysis of parallel mechanism, the principal diagonal element of the matrix is treated as the direction of the corresponding degree of freedom, whose expression is not accurate. So this paper presents the equivalent stiffness and equivalent force, which consider the coupling relation of each degree of freedom. Meanwhile, This takes into account the impact of all the elements of the matrix on the same degrees of freedom, treated as evaluation index of stiffness of each degree of freedom. Through the matrix element analysis and genetic algorithm analysis, the correctness is proved by the example, which lays the foundation for the following research.(2) Through the analysis of the stiffness matrix under the Hinge coordinate system and the Descartes coordinate system, the conversion relation is obtained. Based on the conservation of the stiffness matrix of the Descartes coordinate system, the equivalent stiffness for each degree of freedom is presented, which is considered both real-time and coupling and conducted to analysis the freedom of movement in the direction of deformation, aimed to ensure the accuracy of the movement to lay the foundation for strategic research.(3) In view of the structure parameter optimization method for parallel mechanism, its optimization function is only through stiffness matrix condition number or the main diagonal sum, that has some shortcomings such as incorrect of stiffness express, uneven distribution of stiffness and so on. Based on the study of the equivalent stiffness of parallel mechanism, a new optimization function is put forward. The results show that the stiffness value of each degree of freedom is improved in the whole or in part.(4) Based on the equivalent stiffness of the conservative coordinate transformation, a kinematic solution model considering the stiffness of the parallel mechanism is proposed. Meanwhile, an efficient kinematic analysis algorithm is presented. Proved by examples, the new input parameters can ensure the accuracy of the motion of the mechanism, which is beneficial to the popularization and application of the parallel mechanism.