球面手腕康复机构逆运动学解新方法及应用  

New method and application of inverse kinematic solution for spherical wrist rehabilitation mechanism

作　　者：焦文杰 姬帅旭 郝惠敏 黄家海 李利娜 李诗雨 JIAO Wen-jie;JI Shuai-xu;HAO Hui-min;HUANG Jia-hai;LI Li-na;LI Shi-yu(School of Mechanical and Transportation Engineering,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学机械与运载工程学院,山西太原030024

出　　处：《浙江大学学报（工学版）》2023年第7期1365-1373,共9页Journal of Zhejiang University：Engineering Science

基　　金：2020年山西省关键核心技术和共性技术研发攻关专项项目(2020XXX009);山西省应用基础研究计划青年科技研究基金资助项目(202103021223090)。

摘　　要：针对球面手腕康复机器人的末端执行机构——共轴3RRR球面并联机构(CSPM)存在逆运动学解不完整性或无解析解的问题,提出基于欧拉角的逆运动学分步求解方法.根据共轴球面并联机构的特性,可以将CSPM姿态欧拉角分解为绕Z轴和绕X、Y轴旋转的2个子姿态,求解绕X、Y轴旋转子姿态逆运动学解的集合.选取每个关节逆运动学解集合中的较小值,与绕Z轴旋转的角度相加作为CSPM逆运动学解,利用CSPM正运动学验证了所提方法的正确性.在真实手腕运动范围的基础上,以无连杆碰撞点和无奇异位形为约束条件,使用所提方法求解手腕康复装置的实际姿态空间.在实际的姿态空间内,将提出的逆运动学求解方法与单位四元数相互转换,将单位四元数插补应用于CSPM运动规划中,理论计算结果与试验结果均为光滑的轨迹曲线,两者误差的最大值不超过2.5°.The inverse kinematic step-by-step solution method based on Euler's angle was proposed to address the problem of incomplete or no analytical solution for the coaxial 3RRR spherical parallel mechanism(CSPM),which was the end-effector of the spherical wrist rehabilitation robot.The CSPM posture Euler angle can be decomposed into two sub-postures rotating around Z-axis and X,Y-axis based on the characteristics of the co-axial spherical parallel mechanism.The set of inverse kinematic solutions for the sub-postures rotating around X-axis and Y-axis was solved.The smaller value in the set of inverse kinematics solutions for each joint was selected and added to the angle of rotation around the Z-axis as the CSPM inverse kinematics solution.The correctness of the proposed method was verified by using CSPM forward kinematics.The actual attitude space of the wrist rehabilitation device was solved by using the proposed method with the constraints of no linkage collision point and no singularity configuration based on the real wrist motion range.The proposed inverse kinematics solution method was interconverted with unit quaternion in the actual posture space,and unit quaternion interpolation was applied to CSPM motion planning.The theoretical calculation results and experimental results were smooth trajectory curves,and the maximum value of both errors didn't exceed 2.5°.

关 键 词：手腕康复机构 球面并联机构 逆运动学 单位四元数插补 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]