3-RRR平面并联机器人的边界奇异位形个数研究  

Research on the Boundary Singularity of 3-RRR Planar Parallel Robots

作　　者：刘佳伟 尤晶晶[1] 王澍声 黄宁宁 LIU Jiawei;YOU Jingjing;WANG Shusheng;HUANG Ningning(College of Mechanical and Electronic Engineering,Nanjing Forestry University,Nanjing 210037,China)

机构地区：[1]南京林业大学机械电子工程学院,南京210037

出　　处：《机械设计与研究》2023年第6期57-62,67,共7页Machine Design And Research

基　　金：国家自然科学基金资助项目(51405237);江苏省高等学校大学生创新创业训练计划资助项目(202310298142H)。

摘　　要：在并联机器人的各种奇异位形中,边界奇异是最容易产生的,且该位形下机器人的运动学和力学传递性能极差。以3-RRR平面并联机器人为研究对象,从位置反解的角度,对边界奇异位形的个数进行了研究。首先,运用图解法,确定了并联机器人的位置反解退化为唯一解时的位形条件。其次,基于该条件,构造并代数求解了8个位形方程。研究发现,该机器人最多只可能存在28个完全边界奇异位形。接着,引入“尺度数轴”概念并结合尺度判别式,分析了姿态角失根和重根的情况,进而提出了一种计算实际完全边界奇异位形个数的新方法。最后,通过样机实验,验证了新方法的正确性。本研究为无奇异工作空间计算和路径规划奠定了理论基础。Among all kinds of singular configurations of parallel robots,boundary singularity is most likely to occur,and the kinematics and mechanical transmission performance of the robot in this configuration is extremely poor.Taking the 3-RRR planar parallel robot as the research object,the number of boundary singular configurations is studied from the perspective of inverse position solution.Firstly,the configuration condition when the inverse kinematics solution of the 3-RRR planar parallel robot degenerates into a unique solution is derived by graphic method.Then,based on this condition,8 configuration equations are constructed and solved.The results show that the 3-RRR planar parallel robot has 28 complete boundary singular configurations at most.Then,by introducing the concept of"scale axis"and combining with the scale discriminant,the situation of attitude angle losing root and multiple roots is analyzed,and then a new method for calculating the number of singular configurations of the actual complete boundary is proposed.Finally,the correctness of the new method is verified by the prototype experiment.The research contents lay a theoretical foundation for the calculation of nonsingular workspace and path planning.

关 键 词：并联机器人 运动学 边界奇异 判别式 工作空间 

分 类 号：TH112[机械工程—机械设计及理论]