基于FIS理论的Myard环形组网机构运动学分析

为揭示折展机构连续与瞬时运动的本质与代数关联，将有限瞬时旋量理论（FIS理论）应用于一类过约束折展机构的分析中，提出包括折展单元及其组网机构的运动学分析方法。首先介绍了FIS理论的基本原理、Myard机构和Myard环形组网机构的组成原理。其次对于Myard机构，通过选定合适的初始位形，以构建有限旋量闭环方程的方式解决了折展单元的关节运动参数映射，基于旋量三角积与螺旋运动的定义提出了基于有限旋量的轨迹求解方法，随后由有限与瞬时旋量的微分映射关系得到Myard机构的速度模型。在此基础上，结合参数化的等效广义副将3-Myard环形组网机构简化为单闭环机构，以求解机构的参数映射关系，随后借助与Myard机构相同的分析流程便得到组网机构的位移与速度模型。提出折展单元及其环形组网机构的关节参数映射、运动轨迹和速度模型的分析方法，丰富了折展机构的运动学分析理论，为解决折展单元及其组网机构的运动学分析问题提供了新选择。

Kinematic Analysis of Myard Circular Network Based on FIS Theory

In order to reveal the nature and algebraic relation of finite and instantaneous motion of deployable mechanism, the finite and instantaneous screw theory is applied to the analysis of a class of over-constrained deployable mechanism, and a kinematic analysis method including the basic mechanism and the netted mechanism is proposed. Firstly, the basic principle of FIS theory, the composition of Myard mechanism and 3-Myard netted mechanism are briefly introduced. Secondly, initial configuration selection, finite screw based closed-loop equation formulation are combined to build the mapping the joint variables. Then, a finite screw based trajectory calculation is presented with the aid of screw triangle product and the definition of finite motion. According to the differential mapping between finite and instantaneous screws, the velocity model of Myard mechanism is obtained by the differentiation of displacement model. For the 3-Myard netted mechanism, it is simplified into a single closed-loop mechanism by defining a generalized joint, on which basis, the mapping of joint variables are built. The displacement and velocity models of the 3-Myard netted mechanism is finally obtained by using the same analytical process as the Myard mechanism. In the whole, the joint variable mapping, trajectory calculation and velocity modeling of the basic deployable mechanism and the netted mechanism are proposed based on FIS theory. It enriches the deployable mechanism theory and provides new way to the kinematic analysis.