球面三自由度并联机构瞬时运动分析  

Instantaneous motion analysis of a spherical 3-DOF parallel mechanism

作　　者：史革盟 SHI Ge-meng(College of Mechanical Engineering,Baoji University of Arts and Sciences,Baoji 721013,China)

机构地区：[1]宝鸡文理学院机械工程学院,陕西宝鸡721013

出　　处：《机电工程》2019年第1期7-12,共6页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学基金资助项目(11302003);陕西省教育厅资助项目(14JK1043);宝鸡市科学研究计划项目(14GYGG-3);宝鸡文理学院科研计划项目(ZK16042;YK2018014)

摘　　要：为解决球面三自由度并联机构末端构件上角锥的瞬时定位问题,结合该机构仅具有3个转动自由度的结构特点,采用四元数代数表示构件的有限转动,将机构运动分析转化为求解瞬时转动四元数算子。开展了该机构上角锥相对参考坐标系的微分转动分析,建立了描述上角锥瞬时转动四元数算子的运动微分方程和瞬时转动轴连续轨迹曲面的矢量方程,导出了机构运动微分方程的基础解系,提出了以瞬轴面导线的曲率和挠率量化机构在某一时刻微分运动的特征;在Matlab软件中通过数值积分和数值微分两种方法,求得了四元数算子瞬时转动轴线的变化轨迹和等效转角的变化曲线;瞬轴面导线变化平稳,预示了机构在所给的运动学参数下具有良好的运动学品质,得到了两种数值方法截断误差的预估值和所能达到的精度等级。仿真结果表明:数值积分方法精度略高。Aiming at solving the instantaneous location problem of the angle cone on the end member of the spherical 3-DOF parallel mechanism with only 3 rotational freedoms,the component finite rotation was expressed by the quaternion algebra,and the mechanisms kinematic analysis was transformed into solving quaternion operator with instantaneous rotation. By analyzing the differential rotation of the angle cone relative to the reference coordinate system on a spherical 3-DOF parallel mechanism,a quaternion operator of the motion differential equation describing the instantaneous rotation of the angle cone and the vector equation of the continuous curved surface of the instantaneous rotating axis was established,and the basic solution system of the mechanism motion differential equations was derived. The characteristics of differential motion of a mechanism at a certain moment were quantified by the axode curvature and torsion. With Matlab software,two methods of numerical integration and numerical differentiation were used to obtain the change trajectory of the quaternion operator instantaneous rotation axis and the change curve of the equivalent rotation angle,the change of the axode axis was stable,which indicated that the mechanism had good kinematics character under the kinematic parameters. The prediction value of the truncation error and the accuracy grades of the two numerical methods were given. The simulation results indicate that the accuracy of the numerical integration method is slightly higher.

关 键 词：球面并联机构 四元数代数 运动微分方程 数值积分 

分 类 号：TH112[机械工程—机械设计及理论]