基于小波特征参数的平面四杆机构轨迹综合方法
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摘要
小波分解可以在不同尺度下对函数曲线的特征进行提取,基于该理论,首先,对平面四杆机构连杆轨迹曲线进行小波分解,利用归一化处理方法提取轨迹曲线的小波特征参数,给出了平面四杆机构连杆轨迹曲线的小波特征参数近似描述方法。进而结合数值图谱法,将11维非整周期轨迹综合问题转换为6维机构尺寸型检索问题,同时建立包含3 004 281 900组平面四杆机构的机构尺寸型数据库。根据轨迹曲线小波特征参数的特点,利用多维搜索树,将各相对转动区间内的机构尺寸型进行分区,建立索引关键字数据库。从而通过比较给定轨迹曲线小波特征参数与索引关键字,查找并提取目标机构所在叶子结点中机构尺寸型的小波特征参数,建立自适应图谱库。在此基础上,根据给定设计要求的小波特征参数与自适应图谱库中的小波特征参数的相似程度,检索出满足设计要求的机构尺寸型。再根据理论公式计算目标机构的实际尺寸及安装位置,实现平面四杆机构非预定相对转动区间轨迹综合问题的求解。最后,利用小波特征参数法对滚压包边设备的滚轮进给机构进行设计,验证本方法实用性和有效性的同时,为传统滚压包边提供新的思路。
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.
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.
引文
[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.
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[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.
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[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,HANPengfei,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.
[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].ASMEJournal 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,HANPengfei,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.