2-SPR/RUPR并联机构的逆运动学与可达工作空间分析
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摘要
目的提出一种2-SPR/RUPR并联机构,用于在任意曲面上的雕刻与喷绘。方法基于螺旋理论建立2-SPR/RUPR并联机构的螺旋矩阵,使用修正的G-K公式计算出机构的自由度。采用几何法和D-H法求解并联机构的位置逆解。通过三维动态法进行机构工作空间的搜索,再将数据点导入Matlab中进行工作空间的绘制。结果求解得到2-SPR/RUPR并联机构的逆解,且工作空间呈实心蘑菇云状,给出了在曲面上雕刻和喷绘图案的实例。结论该机构可以应用于曲面雕刻和喷绘,使得刀具与曲面相垂直进而提升了雕刻与喷绘的效果,可以实现任意曲面上的雕刻和喷绘。
The work aims to propose a 2-SPR/RUPR parallel mechanism for engraving and painting on arbitrary surfaces. The screw matrix of 2-SPR/RUPR parallel mechanism was established based on screw theory. The degree of freedom of the mechanism was calculated by modified G-K formula. The position inverse of the parallel mechanism was solved by geometrical method and D-H method. The 3D dynamic method was used to search the workspace of the mechanism and then the data points were imported into MATLAB for drawing the workspace. The inverse solution of the2-SPR/RUPR parallel mechanism was obtained, and the working space was a solid mushroom cloud. An example of engraving and inkjet printing pattern on a surface was given. The mechanism can be applied for engraving and painting on curved surface, so that the cutter is perpendicular to the curved surface, thereby improving the effect of engraving and painting, and can realize engraving and painting on any curved surface.
The work aims to propose a 2-SPR/RUPR parallel mechanism for engraving and painting on arbitrary surfaces. The screw matrix of 2-SPR/RUPR parallel mechanism was established based on screw theory. The degree of freedom of the mechanism was calculated by modified G-K formula. The position inverse of the parallel mechanism was solved by geometrical method and D-H method. The 3D dynamic method was used to search the workspace of the mechanism and then the data points were imported into MATLAB for drawing the workspace. The inverse solution of the2-SPR/RUPR parallel mechanism was obtained, and the working space was a solid mushroom cloud. An example of engraving and inkjet printing pattern on a surface was given. The mechanism can be applied for engraving and painting on curved surface, so that the cutter is perpendicular to the curved surface, thereby improving the effect of engraving and painting, and can realize engraving and painting on any curved surface.
引文
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[12]梁世杰,李瑞琴,孟宏伟,等.RPR/RRPR球面并联机构的建模与工作空间分析[J].包装工程,2017,38(23):128-132.LIANG Shi-jie,LI Rui-qin,MENG Hong-wei,et al.Modeling and Workspace Analysis of RPR/RRPRSpherical Parallel Mechanism[J].Packaging Engineering,2017,38(23):128-132.
[13]叶勇.4SPS+SPR和2UPU+SPR并联机床法向加工3D自由曲面仿真[J].机械设计与研究,2015,31(2):16-19.YE Yong.Simulation of Three-dimensional Free-form Surface for Normal Machining by 4SPS+SPR and2UPU+SPR Parallel Machine Tools[J].Machine Design and Research,2015,31(2):16-19.
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[2]于靖军,刘辛军,丁希仑.机器人机构学的数学基础(第2版)[M].北京:机械工业出版,2016.YU Jing-jun,LIU Xin-jun,DING Xi-lun.Mathematic Foundation of Mechanisms and Robotics[M].Beijing:China Machine Press,2016.
[3]FAN Cai-xia,LIU Hong-zhou,ZHANG Yan-bin.Type Synthesis of 2T2R,1T2R and 2R Parallel Mechanisms[J].Mechanism and Machine Theory,2013,61:184-190.
[4]赵永生,郑魁敬,李秦川,等.5-UPS/PRPU 5自由度并联机床运动学分析[J].机械工程学报,2004,40(2):12-16.ZHAO Yong-sheng,ZHENG Kui-jing,LI Qin-chuan,et al.Kinematic Analysis of 5-DOF 5-UPS/PRPU Parallel Machine Tool[J].Journal of Mechanical Engineering2004,40(2):12-16.
[5]ZHAO Yan-zhi,LIANG Bo-wen.The Constant Balancing 6UPS/(3PRRR)+S Parallel Mechanism and its Balancing Performance Analysis[J].Mechanism and Machine Theory,2018,126:79-91.
[6]孟宏伟.基于非对称3-UPU并联机构的六足步行机器人的研究[D].太原:中北大学,2018.MENG Hong-wei.Research on Hexapod Walking Robot Based on Asymmetric 3-UPU Parallel Mechanism[D].Taiyuan:North University of China,2018.
[7]赵建文.可重构球面并联机构的构型设计与工作空间求解方法[D].太原:中北大学,2017.ZHAO Jian-wen.Configuration Design and Workspace Solving Method of Reconfigurable Spherical Parallel Mechanism[D].Taiyuan:North University of China2017.
[8]蒋俊香.6-PUS/UPS并联机器人结构设计及理论分析[D].秦皇岛:燕山大学,2010.JIANG Jun-xiang.Structural Design and Theoretical Analysis of a 6-PUS/UPS Parallel Manipulator[D]Qinhuangdao:Yanshan University,2010.
[9]WANG Li-ping,XU Hua-yang.A Novel 3-PUU Parallel Mechanism and its Kinematic Issues[J].Robotics and Computer-Integrated Manufacturing,2016,42:86-102.
[10]WANG Li-ping,XU Hua-yang.Optimal Design of a 3-PUU Parallel Mechanism with 2R1T DOFs[J].Mechanism and Machine Theory,2017,114:190-203.
[11]贺磊盈,涂叶凯,叶伟,等.一种可整周回转的新型3T1R并联机构运动学分析[J].机械工程学报,2018,54(11):151-160.HE Lei-ying,TU Ye-kai,YE Wei,et al.Kinematics Analysis of a Novel 3T1R Parallel Manipulator with Full Rotational Capability[J].Journal of Mechanical Engineering,2018,54(11):151-160.
[12]梁世杰,李瑞琴,孟宏伟,等.RPR/RRPR球面并联机构的建模与工作空间分析[J].包装工程,2017,38(23):128-132.LIANG Shi-jie,LI Rui-qin,MENG Hong-wei,et al.Modeling and Workspace Analysis of RPR/RRPRSpherical Parallel Mechanism[J].Packaging Engineering,2017,38(23):128-132.
[13]叶勇.4SPS+SPR和2UPU+SPR并联机床法向加工3D自由曲面仿真[J].机械设计与研究,2015,31(2):16-19.YE Yong.Simulation of Three-dimensional Free-form Surface for Normal Machining by 4SPS+SPR and2UPU+SPR Parallel Machine Tools[J].Machine Design and Research,2015,31(2):16-19.
[14]SCHREIBER L T,GOSSELIN C.Kinematically Redundant Planar Parallel Mechanisms:Kinematics,Workspace and Trajectory Planning[J].Mechanism and Machine Theory,2018,119:91-105.
[15]黄新帅.基于混联机构的船用螺旋桨加工装置及其控制算法研究[D].哈尔滨:哈尔滨工业大学,2014.HUANG Xin-shuai.Research of Hybrid Mechanism Machine and Control Algorithm for Marine Propeller Processing[D].Harbin:Harbin Institute of Technology,2014.