Synthesis Method for Path Generation of a Planar Four-bar Mechanism Based on the Wavelet Feature Parameters

doi:10.3901/JME.2019.09.018

Abstract

Abstract: Wavelet function can extract the feature information of function curve in different scales. Based on the wavelet transform theory, a coupler curve generated by planar four-bar mechanism is decomposed to wavelet coefficients. A normalised process is proposed for extracting wavelet feature parameters. Then a description method for coupler curve of planar four-bar mechanism is established using wavelet feature parameters. The eleven dimensional open path synthesis problems are transformed to six basic dimensional types searching problems. A database is established, which contains 3 004 281 900 groups of dimensional types. The dimensional types are decomposed by using multidimensional search tree and an index keyword database is established. The leaf node which contains the desired mechanism can be obtained. A self-adaptive atlas database is established. Based on the design requirements, the desired mechanism can be obtained by comparing the similarity of wavelet feature parameters between the prescribed curve and the coupler curve in the self-adaptive atlas database. According to the internal relationship of wavelet coefficients, the actual sizes and installation positions of the desired linkage can be calculated. The arbitrary relative rotation interval open path synthesis is realized. Two examples are presented to demonstrate the effectiveness of the method proposed. Particularly, a roller feed mechanism for roller hemming is designed and manufactured to verify the validity and practicality of this method. The design results provide new ideas for the roller hemming.

Key words: multidimensional search tree, open path synthesis, planar four-bar mechanism, self-adaptive atlas database, wavelet feature parameters

CLC Number:

TH122

LIU Wenrui, SUN Jianwei, CHU Jinkui. Synthesis Method for Path Generation of a Planar Four-bar Mechanism Based on the Wavelet Feature Parameters[J]. Journal of Mechanical Engineering, 2019, 55(9): 18-28.

References

[1] 张均富,徐礼矩,王杰. 可调球面六杆机构轨迹综合[J]. 机械工程学报,2007,43(11):50-55. ZHANG Junfu,XU Liju,WANG Jie. Synthesis of adjustable spherical six-bar mechanisms for path generation[J]. Chinese Journal of Mechanical Engineering,2007,43(11):50-55.
[2] 张新歌. 基于神经网络的铰链四杆机构复演轨迹设计软件的开发[D]. 苏州:苏州大学,2008. ZHANG Xinge. Development of design software on generation of path curves with four-bar linkage mechanism based on neural networks[D]. Suzhou:Soochow University,2008.
[3] WU J,GE Q J,GAO F,et al. Fourier descriptors with different shape signatures:A comparative study for shape based retrieval of kinematic constraints[J]. Chinese Journal of Mechanical Engineering,2011,24(5):723-730.
[4] 孙晓斌,肖人彬,王雪. 基于曲线几何特征量化提取的轨迹机构检索生成方法[J]. 机械工程学报,2000,36(11):98-105. SUN Xiaobin,XIAO Renbin,WANG Xue. New approach to rapid searching path generating mechanisms[J]. Chinese Journal of Mechanical Engineering,2000,36(11):98-105.
[5] SUN J W,LIU W R,CHU J K. Dimensional synthesis of open path generator of four-bar mechanisms using the Haar wavelet[J]. Journal of Mechanical Design,2015,137(8):082303.
[6] 蓝兆辉,邹慧君. 基于轨迹局部特性的机构并行优化综合[J]. 机械工程学报,1999,35(5):16-19. LAN Zhaohui,ZOU Huijun. Concurrent optimum synthesis of path generating mechanisms based on the local characteristics[J]. Chinese Journal of Mechanical Engineering,1999,35(5):16-19.
[7] YU H Y,TANG D W,WANG Z X. Study on a new computer path synthesis method of a four-bar linkage[J]. Mechanism and Machine Theory,2007,42(4):383-392.
[8] UNRUH V,KRISHNASWAMI P. A Computer-aided design technique for semi-automated infinite point coupler curve synthesis of four-bar linkages[J]. ASME Journal of Mechanical Design,1995,117(1):143-149.
[9] 黄灿明,郭海鹏,陈永康,等. 基于B样条插值曲线的平面四杆机构轨迹复演优化设计[J]. 机械工程学报,1998,34(3):72-79. HUANG Canming,GUO Haipeng,CHEN Yongkang,et al. Optimization scheme for four-bar mechanism path synthesis based on B-spline[J]. Chinese Journal of Mechanical Engineering,1998,34(3):72-79.
[10] 于红英,赵彦微,许栋铭. 平面铰链四杆机构的轨迹综合方法[J]. 哈尔滨工业大学学报,2015,47(1):40-47. YU Hongying,ZHAO Yanwei,XU Dongming. A path synthesis method of planar hinge four-bar linkage[J]. Jouranl of Harbin Institute of Technology,2015,47(1):40-47.
[11] MCGARVA J R,MULLINEUX G. Harmonic representation of closed curves[J]. Applied Mathematical Modelling,1993,17(4):213-218.
[12] MCGARVA J R. Rapid search and selection of path generating linkages from a library[J]. Mechanism and Machine Theory,1994,29(2):223-235.
[13] 褚金奎,孙建伟. 基于傅里叶级数理论的连杆机构轨迹综合方法[J]. 机械工程学报,2010,46(13):31-41. CHU Jinkui,SUN Jianwei. Unified approach to synthesis of coupler curves of linkage by Fourier series[J]. Journal of Mechanical Engineering,2010,46(13):31-41.
[14] SUN J W,CHU J K. A unified model of harmonic characteristic parameter method for dimensional synthesis of linkage mechanism[J]. Applied Mathematical Modelling,2012,36(12):6001-6010.
[15] MULLINEUX G. Atlas of spherical four-bar mechanisms[J]. Mechanism and Machine Theory,2011,46(11):1811-1823.
[16] WU J,GE Q J,GAO F,et al. On the extension of a Fourier descriptor based method for planar four-bar linkage synthesis for generation of open and closed paths[J]. Journal of Mechanisms and Robotics,2011,3(3):031002.
[17] YUE C,SU H J,GE Q J. A hybrid computer-aided linkage design system for tracing open and closed planar curves[J]. Computer-Aided Design,2012,44(11):1141-1150.
[18] 吴鑫,褚金奎,曹惟庆. 平面四杆机构函数输出的小波变换分析[J]. 机械科学与技术,1998,17(2):180-182. WU Xin,CHU Jinkui,CAO Weiqing. Analysis of output function of 4-bar linkages using wavelet transform. Mechanical Science and Technology,1998,17(2):180-182.
[19] 王成志,纪跃波,孙道恒. 小波分析在平面四杆机构轨迹综合中的应用研究[J]. 机械工程学报,2004,40(8):34-39. WANG Chengzhi,JI Yuebo,SUN Daoheng. Research on applying wavelet analysis to path synthesis for coupler curves of planar four-bar linkages[J]. Chinese Journal of Mechanical Engineering,2004,40(8):34-39.
[20] GALÁN-MARÍN G,ALONSO F J,CASTILLO J M D. Shape optimization for path synthesis of crank-rocker mechanisms using a wavelet-based neural network[J]. Mechanism and Machine Theory,2009,44(6):1132-1143.
[21] SUN J W,LIU W R,CHU J K. Synthesis of spherical four-bar linkage for open path generation using wavelet feature parameters[J]. Mechanism and Machine Theory,2018,128:33-46.
[22] LIU W R,SUN J W,ZHANG B C,et al. Wavelet feature parameters representations of open planar curves[J]. Applied Mathematical Modelling,2018,57:614-624.
[23] LIU S Z,DAI J S,LI A M,et al. Analysis of frequency characteristics and sensitivity of compliant mechanisms[J]. Chinese Journal of Mechanical Engineering,2016,29(4):1-14.
[24] 陈放,李欣玲,佘霞,等. 平面轨迹机构时变可靠性分析的联合概率方法[J]. 机械工程学报,2017,53(15):119-124. CHEN Fang,LI Xinling,SHE Xia,et al. Joint probability method to time-dependent reliability for planar path mechanisms[J]. Journal of Mechanical Engineering,2017,53(15):119-124.
[25] 郑国峰,上官文斌,韩鹏飞,等. 基于小波变换的汽车零部件加速耐久性载荷谱编辑方法研究[J]. 机械工程学报,2017,53(8):124-131. ZHENG Guofeng,SHANGGUAN Wenbin,HAN Pengfei,et al. Study of load spectrum edition method based on the wavelet transform to the accelerated durability test of the vehicle component[J]. Journal of Mechanical Engineering,2017,53(8):124-131.
[26] 孙殿柱,郭洪帅,李延瑞,等. 基于局部泊松曲面重建的点云刚性配准方法[J]. 机械工程学报,2018,54(15):141-149. SUN Dianzhu,GUO Hongshuai,LI Yanrui,et al. Method of rigid registration based on Poisson reconstruction of local sample points[J]. Journal of Mechanical Engineering,2018,54(15):141-149.
[27] CHEN D K,DING J J,GAO M Z,et al. Form gene clustering method about pan-ethnic-group products based on emotional semantic[J]. Chinese Journal of Mechanical Engineering,2016,29(6):1134-1144.