3-RRR球面并联机器人正向运动学分析  

Positive Kinematics Analysis of 3-RRR Spherical Parallel Robot

作　　者：张林 郭旭侠 史革盟 贾兰生 王丽[2] Zhang lin;Guo Xuxia;Shi Gemeng;Jia Lansheng;Wang li(Mechanical Engineering Institute,Baoji University of Arts and Sciences,Baoji 721013,China;Mechanical Engineering Institute,Shanxi Polytechnic Institute,Xianyang 712000,China)

机构地区：[1]宝鸡文理学院机械工程学院,陕西宝鸡721013 [2]陕西工业职业技术学院机械工程学院,陕西咸阳712000

出　　处：《机械传动》2019年第7期27-34,共8页Journal of Mechanical Transmission

基　　金：国家自然科学基金(11302003);陕西工业职业技术学院院级科研项目(ZK16-02);宝鸡市科技计划项目(2018JH-28);宝鸡文理学院项目(ZK16042、YK2018014)

摘　　要：针对球面3自由度并联机器人所有关节均为转动关节且关节轴线汇交于一点的结构特点,借助球面上大圆弧与四元数代数的对应关系,将构件的位置用四元数表示。采用四元数的乘积描述关节转动引起的构件位置的变化,通过球面上大圆弧几何加法与四元数乘法之间的对应关系,得到关节轴线的方向余弦,建立了机器人约束方程。对约束方程进行巧妙的变量替换,减少了MATLAB符号运算中的数据,解决了运算中数据超出计算机内存而无法得到有效结果的问题,得到机器人正解封闭方程。利用影响系数法,建立机器人主动构件到末端构件上角锥的角速度和角加速度的传递关系。实例表明,对于给定的主动件的某些位置,上角锥最多有8组运动学解;以机器人主动构件连续运动仿真了上角锥位置、角速度和角加速度变化历程。In view of the structural characteristics of spherical 3-DOF parallel mechanism,which all the joints are rotating joints and the joint axes intersect at one point,the position of the component is expressed by quaternion by means of the corresponding relationship between the long arc on the sphere surface and quaterni on algebra.The product of quaternions is used to describe the component position change caused by joint rota tion,and the direction cosine of the joint axis is obtained through the corresponding relationship between the geometric addition of the long arc on the sphere surface and the multiplication of quaternions,thus the constraint equation of the robot is established.The constraint equation is proceed subtly by a clever variable,which re duced the data in the symbolic operation of MATLAB,solved the problem that the effective results could not be obtained when the operation exceeded the computer memory,and the positive closed equation of the robot is es tablished.By using the influence coefficient method,the transfer relation between the angular velocity and angu lar acceleration of the robot active component and the corner cone on the end component is established.The ex amples show that,there are 8 kinematics solutions for the given position of the active component in the top pyra mid group.And according to the example of the continuous motion of the active robot component,the changing course of angular velocity and angular acceleration in the position of the top pyramid is simulated.

关 键 词：球面并联机器人 四元数代数 正解封闭方程 影响系数 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]