Fourier Series Method for Motion Generation of RCCC Mechanism

Abstract

Abstract:

Based on the Fourier series theory, the geometrical model of the rigid body rotation angle of RCCC mechanism was established. Two numerical atlas databases which contained 91 125 groups of basic rotation angle dimensional types and 562 500 groups of basic dimensional types of RCCC mechanism were built up by harmonic analysis. Subsequently, the formulas which could compute the real size and installing dimensions of the RCCC mechanism were proposed. On the basis of the theoretical formulas and two numerical atlas databases, the problem of rigid body guided synthesis of RCCC was solved. Finally, an example was given to show the feasibility of this approach.

Key words: RCCC mechanism, motion generation, numerical atlas, characteristic parameter, harmonic analysis

摘要：

借助傅里叶级数理论建立了RCCC机构刚体转角输出的数学表达式。通过对刚体转角输出谐波成分的分析，建立了包含91 125组基本尺寸型的刚体转角输出特征参数和562 500组基本尺寸型的刚体位置输出特征参数数据库。推导了利用位置输出谐波参数计算RCCC机构实际安装尺寸和机构安装尺寸参数的理论公式。利用建立的两个特征参数数据库和理论公式实现了对RCCC机构刚体导引综合问题的求解。最后通过给出的算例证明了该方法的有效性。

关键词: RCCC机构, 运动综合, 数值图谱, 特征参数, 谐波分析

CLC Number:

HT122

孙建伟, 路贺, 褚金奎. 基于傅里叶级数的RCCC机构运动综合[J]. 中国机械工程, 2014, 25(21): 2841-2847.

References

[1]Bagci C.Geometric Methods for the Synthesis of Spherical Mechanisms for the Generation of Functions,Paths and Rigid-Body Positions Using Conformal Projections[J].Mechanism and Machine Theory，1984，19(1)：113-127.
[2]Russell K，Sodhi R S．Instant Screw Axis Point Synthesis of the RRSS Mechanism[J]．Mechanism and Machine Theory，2002，37(10)：1117-1126．
[3]Russell K，Sodhi R S．Kinematic Synthesis of Adjustable RRSS Mechanisms for Multi-phase Motion Generation[J]．Mechanism and Machine Theory，2001，36(8)：939-952．
[4]Russell K，Sodhi R S．Kinematic Synthesis of RRSS Mechanisms for Multi-phase Motion Generation with Tolerances[J]．Mechanism and Machine Theory，2002，37(3)：279-294．
[5]易伟，杨随先，徐礼钜．可调节型空间RSS′R机构刚体导引综合[J]．机械设计与研究，2005，21(6)：36-39．
Yi Wei，Yang Suixian，Xu Liju．Kinematic Synthesis of Adjustable RSS′R Mechanisms for Rigid-body Guidance[J]．Machine Design and Research，2005，21(6)：36-39．
[6]Lee W T，Russell K．On Two-phase Spherical Motion Generation[J]．Journal of the Chinese Society of Mechanical Engineers，2007，28(6)：617-622．
[7]Lee W T，Russell K，Shen Q，et al．On Adjustable Spherical Four-bar Motion Generation for Expanded Prescribed Positions[J]．Mechanism and Machine Theory，2009，44(1)：247-254．
[8]Wang Zhixing，Yu Hongying，Tang Dewei，et al．Study on Rigid-body Guidance Synthesis of Planar Linkage[J]．Mechanism and Machine Theory，2002，37(7)：673-684．
[9]褚金奎，曹惟庆．用快速傅里叶变换进行再现平面四杆机构连杆曲线的综合[J]．机械工程学报，1993，29(5)： 117-122．
Chu Jinkui，Cao Weiqing．Synthesis of Coupler Curves of Planar Four-bar Linkages through Fast Fourier Transform[J]．Chinese Journal of Mechanical Engineering，1993，29(5)：117-122．
[10]Mcgarva J R．Rapid Reseearch and Selection of Path Generating Mechanisms from a Library[J]．Mechanism and Machine Theory，1994，29(2)：223-235．
[11]吴鑫，褚金奎，曹惟庆．带有预定时标平面四杆刚体导引机构尺度综合的研究[J]．机械工程学报，1999，35(5)：106-110．
Wu Xin，Chu Jinkui，Cao Weiqing．Study on Dimension Synthesis of Planar Linkages for Rigid-body Guidance with Prescribed Timing[J]．Chinese Journal of Mechanical Engineering，1999，35(5)：106-110．
[12]褚金奎，孙建伟．RCCC机构轨迹综合的数值图谱法[J]．中国机械工程，2009，20(9)：1024-1028．
Chu Jinkui，Sun Jianwei．Research on RCCC Mechanism Path Generation by Using Numerical Atlas Method[J]．China Mechanical Engineering，2009，20(9)： 1024-1028．
[13]孙建伟，褚金奎，卫静．利用数值图谱法进行RCCC机构的函数综合[J]．中国机械工程，2008，19(6)：713-717．
Sun Jianwei，Chu Jinkui，Wei Jing．Research on RCCC Mechanism Path Generation by Using Numerical Atlas Method[J]．China Mechanical Engineering，2008，19(6)：713-717．

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