基于有限和瞬时旋量理论的Exechon并联机器人运动学分析

运动学分析是并联机构性能分析、建模和优化设计的基础。传统的运动学分析方法中并联机构的拓扑模型与速度模型只能单独构建，无法揭示其内在联系，导致运动学模型的构建不够全面和准确；另外，以现有运动学性能指标作为运动学优化目标时，存在平转耦合机构运动学评价指标的物理意义不明确等问题。为此，以一平动两转动(1T2R)的Exechon并联机器人为研究对象，利用有限和瞬时旋量(finite and instantaneous screw, FIS)理论对其拓扑、运动学建模进行研究。根据FIS理论中的微分映射关系，在统一的数学框架下建立Exechon并联机器人的拓扑模型和速度模型，得到其速度和力雅克比矩阵。在此基础上，以可解析分析机构运动奇异性的虚功率传递率作为运动学性能指标，来有效评价Exechon并联机器人的运动/力传递性能。给定一组Exechon并联机器人模型的尺寸参数，借助MATLAB分析该机器人的局部虚功率传递率分布情况。研究结果为并联机构的性能分析与建模提供了参考，为Exechon并联机器人的优化设计奠定了理论基础。

Kinematic analysis of Exechon parallel robot based on finite and instantaneous screw theory

The kinematic analysis is the basis of performance analysis, modeling and optimization design of parallel mechanism. In the traditional methods, the topology model and velocity model of parallel mechanism are independently modeled, and the inherent relationship cannot be revealed, which results in incomplete and inaccurate kinematic modeling. In addition, when the existing kinematic performance indexes are used as the kinematic optimization objective, the physical significances of the kinematic evaluation indexes of horizontal rotation coupling mechanism are not clear. Therefore, the topology and kinematic modeling of the Exechon parallel robot with one translation and two rotations (1T2R) was studied by using the finite and instantaneous screw (FIS) method. Based on differential mappings of FIS method, the topology model and velocity model of the Exechon parallel robot were established in a unified mathematical framework, and the Jacobian matrices of velocity and force were obtained. On this basis, the virtual power transmissibility was proposed as kinematic performance index, which could analytically analyze the singularity of mechanism motion and effectively evaluate the motion / force transfer performance of Exechon parallel robot. Given a set of dimensional parameters for the Exechon parallel robot model, the local virtual power transmissibility distribution of the robot was analyzed by MATLAB. The research results provide reference for performance analysis and modeling of parallel robot, and lay a theoretical foundation for optimization design of Exechon parallel robot.