Abstract:Based on the 2-DOF (degree of freedom) spherical parallel Omni-Wrist V, a 3-DOF 2R1T (2 rotational and 1 translational) spheroid parallel mechanism is proposed by the configuration evolution method, and its kinematic analysis is systematically carried out. The DOF of the proposed mechanism is first analyzed with an atlas method based on constraint theory. An equivalent kinematic model is then established, the forward and inverse kinematic equations are derived in an analytical form, and its singularity is discussed. Finally, the workspace is generated by Monte Carlo method, and a 3D cutting method is proposed to analyze its characteristics. In the workspace analysis, the slice area and shape generated by level cutting are used to measure the rotational manipulability, and the radial displacement of sector piece generated by cutting slice with a fixed tilt angle is defined to evaluate the translational manipulability. The presented parallel mechanism can be used as a wrist at the end of Delta or SCARA (selective compliance assembly robot arm) robots, to form hybrid robots for electronic and light industries where large change of the object configuration (orientation and position) is to be performed.
[1] Merlet J P. Parallel robots[M]. Amsterdam, Netherlands:Springer, 2006.
[2] Hunt K H. Structural kinematics of in-parallel-actuated robot-arms[J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1983, 105(4):705-712.
[3] 汪满新,黄田.1T2R3自由度并联机构拓扑结构综合[J].机械工程学报,2015,51(17):1-7. Wang M X, Huang T. Type synthesis of 1T2R 3-DOF parallel mechanism[J]. Journal of Mechanical Engineering, 2015, 51(17):1-7.
[4] 杨启志,訾鹏飞,曹电锋,等.一种基于并联机构的2R-1T运动平台设计[J].机械设计与研究,2012,28(5):15-17,36. Yang Q Z, Zi P F, Cao D F, et al. Study on a 2R-1T moving platform based on parallel mechanism[J]. Machine Design and Research, 2012, 28(5):15-17,36.
[5] 王飞博,吴伟峰,陈祥,等.基于运动!/!力传递特性的1T2R并联机构构型优选[J].机械工程学报,2014,50(23):20-28. Wang F B, Wu W F, Chen X, et al. Optimal type selection of 1T2R parallel mechanisms based on motion/force transmissibility[J]. Journal of Mechanical Engineering, 2014, 50(23):20-28.
[6] 王程.三种2R1T三自由度并联机构静力分析研究[D].杭州:浙江理工大学,2015. Wang C. Static analysis of three 2R1T 3-DOF parallel mechanisms[D]. Hangzhou:Zhejiang University of Science and Technology, 2015.
[7] 付铁,韩信,朱涯涯,等.基于李群理论的2R1T并联机构构型综合[J].北京理工大学学报,2014,34(11):1106-1109,1119. Fu T, Han X, Zhu Y Y, et al. Type synthesis of 2R1T parallel mechanism based on Lie group theory[J]. Transactions of Beijing Institute of Technology, 2014, 34(11):1106-1109,1119.
[8] 齐明.一类2R1T三自由度并联机构的设计理论与方法研究[D].天津:天津大学,2007. Qi M. Research on design theory and methodology of a class of 2R1T 3-DoF parallel mechanisms[D]. Tianjin:Tianjin University, 2007.
[9] Li C, Wu Y Q, Wu J C, et al. Cartesian stiffness evaluation of a novel 2-DoF parallel wrist under redundant and antagonistic actuation[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2013:959-964.
[10] Fan C X, Liu H Z, Zhang Y B. Type synthesis of 2T2R, 1T2R and 2R parallel mechanisms[J]. Mechanism and Machine Theory, 2013, 61(1):184-190.
[11] 黄真,刘婧芳,李艳文.论机构自由度:寻找了150年的自由度通用公式[M].北京:科学出版社,2011:62-67. Huang Z, Liu J F, Li Y W. On the degree of freedom of mechanism:150-year unified mobility formula issue[M]. Beijing:Science Press, 2011:62-67.
[12] Blanding D L. Exact constraint:Machine design using kinematic principles[M]. New York, USA:ASME, 1999.
[13] 于靖军,裴旭,宗光华.机械装置的图谱化创新设计[M].北京:科学出版社,2014. Yu J J, Pei X, Zong G H. Graphical approach to creative design of mechanical devices[M]. Beijing:Science Press, 2014.
[14] 陈子明,张扬,黄坤,等.一种无伴随运动的对称两转一移并联机构[J].机械工程学报,2016,52(3):9-17. Chen Z M, Zhang Y, Huang K, et al. Symmetrical 2R1T parallel mechanism without parasitic motion[J]. Journal of Mechanical Engineering, 2016, 52(3):9-17.
[15] 魏敏和,韩先国,张军.3-UPS/S并联转台球铰链的优化研究[J].航天制造技术,2013,11(3):19-23,38. Wei M H, Han X G, Zhang J.\columnbreak Optimization research of spherical joints in 3-UPS/S parallel rotational table[J]. Aerospace Manufacturing Technology, 2013, 11(3):19-23,38.
[16] 李艳文.几类空间并联机器人的奇异研究[D].秦皇岛:燕山大学,2005. Li Y W. On singularity of several kinds of spacial parallel manipulators[D]. Qinhuangdao:Yanshan University, 2005.
[17] Rastegar J, Fardanesh B. Manipulator workspace analysis using the Monte Carlo method[J]. Mechanism and Machine Theory, 1990, 25(2):233-239.
[18] Yang G, Causon D M, Ingram D M. Calculation of compressible flows about complex moving geometries using a three-dimensional Cartesian cut cell method[J]. International Journal for Numerical Methods in Fluids, 2000, 33(8):1121-1151.
[19] 曹永刚,张玉茹,马运忠.6-RSS型并联机构的工作空间分析与参数优化[J].机械工程学报,2008,44(1):19-24. Cao Y G, Zhang Y R, Ma Y Z. Workspace analysis and parameter optimization of 6-RSS parallel mechanism[J]. Journal of Mechanical Engineering, 2008, 44(1):19-24.