平面弹性欠驱动并联机构刚度特性分析

根据多维运动模拟的需求,提出一种包含螺旋圆弹簧(圆柱形螺旋弹簧)的欠驱动运动模拟台。利用螺旋圆弹簧的轴向和横向刚度约束运动模拟台的工作空间,通过两个驱动分支和动力耦合实现其3个自由度的运动。将螺旋圆弹簧等效为RePeRe弹性运动支链,进而将并联运动模拟台等效为2RPR/2RePeRe弹性欠驱动机构,并利用Grassmann线几何分析该机构的输入选取原则。基于旋量及其迁移公式,建立等效机构的运动学模型。借助于影响系数和虚功原理,对该弹性欠驱动机构进行静力学分析,得到其静力学约束方程。最后,建立了该机构的连续非线性柔度模型,并以此为基础得到其方向刚度模型。

Stiffness Characteristics of Planar Elastic Underactuated Parallel Mechanism

According to the demand of multi-dimensional motion simulation, a class of planar underactuated simulator with cylindrical helical springs was put forward. The workspace of the proposed simulator was restricted by the axial and lateral stiffness of cylindrical helical spring, and 3-DOF of the proposed simulator was driven by only two drive limbs and dynamic coupling effects. The cylindrical helical springs could be seen as an elastic limb Re/Pe/Re, so the simulator can be transformed to an elastic underactuated mechanism, 2RPR/2Re/Pe/Re. The input selection of equivalent mechanism was analyzed by using Grassmann geometry. Based on screws, the kinematics of equivalent mechanism was given. The kinematics can be represented to any frame easily by using the shifting property of the screws. Referring to the influence coefficient and virtual work principles, the statics analysis was performed, and the statics constraint equation was gotten. Finally, the continuous nonlinear compliance model of the mechanism was established, and based on this, the direction stiffness was given.