齿轮—五杆组合机构连杆曲线特性的研究
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摘要
齿轮—五杆机构由于比铰链四杆机构具有更多的参数，因而它能够实现比四杆机构更为丰富的轨迹，并且其轨迹曲线往往比较复杂而难以预测。由于齿轮—五杆机构中的参数比较多，故研究各参数对齿轮—五杆机构轨迹曲线的影响也变得困难一些。
本论文主要研究了齿轮—五杆机构中与机架相连的两连架杆的双曲柄的存在条件、齿轮—五杆机构的分类以及在每一分类中齿轮—五杆机构能够整周转动时其相位角和传动比的范围。然后，针对能够整周转动的齿轮—五杆机构，研究了其上的一点在齿轮机构的传动比、初始相位角、杆长以及两杆之间的夹角变化时的轨迹曲线以及速度和加速度曲线的情况。
首先根据N杆机构的理论，得到了五杆机构的分类以及五杆机构中两相邻杆的夹角为周转角时的充分必要条件以及五杆机构能够整周转动时的充分必要条件。然后详细的讨论了五杆机构在每一种分类情况下机构中存在双曲柄时机构的传动比及相位角的范围。根据该条件所得到的算法，以Windows为平台，以面向对象的Visual C++6.0为开发工具，开发了一套智能化的齿轮—五杆机构的轨迹生成软件系统，实现了机构参数的可视化输入、机构的轨迹曲线、速度和加速度曲线的动态生成，从而实现了齿轮—五杆机构轨迹曲线的动态模拟。
以该软件系统为平台，研究齿轮—五杆机构中的各参数对轨迹曲线的影响。由于齿轮—五杆机构轨迹图像的可控参数比较多，我们就详细的讨论了在只有一个参数改变时机构的轨迹图像变化情况，然后总结了齿轮—五杆机构在齿轮的传动比、初始相位角、杆长以及两杆之间的夹角变化时的轨迹曲线的变化规律。这对利用轨迹来设计齿轮—五杆机构中的各参数具有很重要的指导意义。
The geared five-bar linkage has more dimension parameters than four-bar linkage, so it can realize more versatile locus curves and its curves are complex and unpredictable. Then it's more difficult to research geared five-bar for it's more parameters.
The existence of a C-C (crank-crank) type of geared five-bar linkages linked with the ground link , the classification and the range of gear ratio and phase angle in the fully rotatability of geared five-bar linkages were mainly studied in this dissertation. Then the locus curves of one point in the geared five-bar were studied with the change of the gear ratio, the phase angle, the bar length and the angle between two bars.
The necessary and sufficient conditions for the input angle to be rotatable angle of N-bar linkages and the rotatability of five-bar are firstly proved according to the theory of N-bar linkages. Then we conclude the five-bar's classification and the gear ratio and phase angle in each classification to be full rotatability. According to the algorithm, with the tool of Visual C++6.0,1 developed a set of intelligent software to dynamically create geared five-bar's locus curves and velocity and acceleration curves, achieve the visualized input.
On the software platform we studied the effect of the five-bar's parameters on the locus curves. Because there are several parameters to control the locus curves, we particularly presented the locus curves in the case that only one parameter change while others remain. Finally, we concluded the law of geared five-bar's parameter to effect orbit curves. This is very helpful to design geared five-bar's parameters using locus curves.
本论文主要研究了齿轮—五杆机构中与机架相连的两连架杆的双曲柄的存在条件、齿轮—五杆机构的分类以及在每一分类中齿轮—五杆机构能够整周转动时其相位角和传动比的范围。然后，针对能够整周转动的齿轮—五杆机构，研究了其上的一点在齿轮机构的传动比、初始相位角、杆长以及两杆之间的夹角变化时的轨迹曲线以及速度和加速度曲线的情况。
首先根据N杆机构的理论，得到了五杆机构的分类以及五杆机构中两相邻杆的夹角为周转角时的充分必要条件以及五杆机构能够整周转动时的充分必要条件。然后详细的讨论了五杆机构在每一种分类情况下机构中存在双曲柄时机构的传动比及相位角的范围。根据该条件所得到的算法，以Windows为平台，以面向对象的Visual C++6.0为开发工具，开发了一套智能化的齿轮—五杆机构的轨迹生成软件系统，实现了机构参数的可视化输入、机构的轨迹曲线、速度和加速度曲线的动态生成，从而实现了齿轮—五杆机构轨迹曲线的动态模拟。
以该软件系统为平台，研究齿轮—五杆机构中的各参数对轨迹曲线的影响。由于齿轮—五杆机构轨迹图像的可控参数比较多，我们就详细的讨论了在只有一个参数改变时机构的轨迹图像变化情况，然后总结了齿轮—五杆机构在齿轮的传动比、初始相位角、杆长以及两杆之间的夹角变化时的轨迹曲线的变化规律。这对利用轨迹来设计齿轮—五杆机构中的各参数具有很重要的指导意义。
The geared five-bar linkage has more dimension parameters than four-bar linkage, so it can realize more versatile locus curves and its curves are complex and unpredictable. Then it's more difficult to research geared five-bar for it's more parameters.
The existence of a C-C (crank-crank) type of geared five-bar linkages linked with the ground link , the classification and the range of gear ratio and phase angle in the fully rotatability of geared five-bar linkages were mainly studied in this dissertation. Then the locus curves of one point in the geared five-bar were studied with the change of the gear ratio, the phase angle, the bar length and the angle between two bars.
The necessary and sufficient conditions for the input angle to be rotatable angle of N-bar linkages and the rotatability of five-bar are firstly proved according to the theory of N-bar linkages. Then we conclude the five-bar's classification and the gear ratio and phase angle in each classification to be full rotatability. According to the algorithm, with the tool of Visual C++6.0,1 developed a set of intelligent software to dynamically create geared five-bar's locus curves and velocity and acceleration curves, achieve the visualized input.
On the software platform we studied the effect of the five-bar's parameters on the locus curves. Because there are several parameters to control the locus curves, we particularly presented the locus curves in the case that only one parameter change while others remain. Finally, we concluded the law of geared five-bar's parameter to effect orbit curves. This is very helpful to design geared five-bar's parameters using locus curves.
引文
[1] 吕庸厚，组合机构设计，上海科学技术出版社1996．12
[2] 葛文杰，陈作模 齿轮—五杆机构的轨迹特性研究，西北工业大学学报，1997，11
[3] 吕传毅，曹维庆齿轮连杆机构研究进展，中国机械工程，1996，5
[4] 曹维庆，褚金奎，严天宏，吕传毅齿轮连杆机构结构分析的研究，西安理工大学学报，Vol．14 No．3，1998
[5] 褚金奎、严天宏、曹维庆齿轮连杆机构的通用运动分析算法及程序设计，西安理工大学学报，Vol．3，1999
[6] 吕传毅，曹维庆齿轮连杆机构运动分析广义型转化法的基本理论。机械科学与技术，1995(6)：13～18
[7] 吕传毅，曹维庆齿轮连杆机构运动分析广义型转化法的实现。机械科学与技术，1996(1)：75～80
[8] 李团结、曹惟庆、褚金奎，齿轮—五杆机构轨迹综合的连续法 西安理工大学学报Vol．15 No14 1999
[9] 褚金奎、郭晓宁，连杆机构的装配构形于机构拓扑结构的关系研究—平面连杆机构装配构形分析 机械科学与技术Vol．20，No．2 2001．3
[10] 田汉民、张策、张新华，二自由度平面五杆机构的双曲柄存在条件 机械设计 2001．3
[11] 褚金奎 五杆双输入机构的输出特性图谱及输出特性分析 机械科学与技术 1995．
[12] 胡继强 实现近似平行直线轨迹差动推送的齿轮—五杆机构包装工程Vol．18 No．(2．3)1997
[13] 孔向东、董平、杨基厚，平面四杆曲柄摇杆机构连杆曲线形状分部规律的研究机械科学与技术1994．2
[14] 张旭滨、刘葆旗，类四杆五杆机构连杆曲线的变化规律 机械设计1997．7
[15] 洪笃利，常用齿轮连杆机构的分组运动分析—常用齿轮连杆机构的分组方法。第七届机构学术讨论会论文集，秦皇岛，1990
[16] Ananthasuresh G K .Kinematic Symhesis and Analysis of the Rack and Pinion Multi—Purpose Mechanism .Trans. of the ASME, 1992,114:428～432
[17] Dan Gibson. Kinematic Design and Analysis of the Rack—and—Gear
Mechanism for Function Generation. M.M.T,1984,19(3):369～375
[18] Duschl P. Kinematic Synthesis and Analysis of the Rack and Pinion Mechanism for Planar Path Generation and Function Generation for Six Precision Conditions,M.M.T.,1987,22(6):563～568
[19] 叶仲和，齿轮连杆机构分析与分组运动分析法。福州大学学报，1991，19(3)：63～68
[20] 叶仲和，用杆组法作Ⅱ级齿轮连杆机构的运动分析。机械设计与研究，1992(4)：7～11
[21] 叶仲和，用杆轮分离法作高级齿轮连杆杆组运动分析。福州大学学报，1992，20(4)：45～50
[22] G.N. Sandor,etal:Kinematie Synthesis of Geared Linkages,Jnl.of Mechanisms,Vol.5,59-87,1970
[23] T. W .Lee ,E. Akbil: Kinematic Synthesis of Spherical Two-Gear Drives with Prescribed Entire—Motion Characteristics: Displacement Analysis and Dwell Characteristics,j .Mech.Trans.Auto.Design,Vol. 105,663—671,1983
[24] Gibson C G. On the Geometry of Geared 5- Bar Motion. Trans. of the ASME, 1990,(112):620～627
[25] Yoshiaki Yokoyama. Studies on the Geared Linkage Mechanisms. Bulletin of the JSME,1974,17(112):1332～1339
[26] Grashof, F. ,Theoretisehe Maschinenlehre ,Leipzig,1983.
[27] Harding,B.L.,"Derivation of Grashof's Law",Machine Design Bulletin,American Society of Engineering Education,April 1962,pp. 1-10.
[28] Paul,B. ,"A Reassessment of Grashof's Criterion",ASME Journal of Mechanical Design,July 1979,pp.515-518.
[29] Barker, C.R., and Jeng, Ywh-Ren, "Range of the Six Fundamental Position Angles in a Planar Four-Bar Mechanism", Mechanism and Machine Theory ,Vol.20,No.4,1985
[30] Barker, C. R.,"A Complete Classification of Planar Four-Bar Linkages", Mechanism and Machine Theory, Vol.20, No.6, 1985, pp.535-554.
[31] Midha, A.,Zhao,Z.L.,and Her, I., "Mobility Conditions for Planar Linkages Using Triangle Inequality and Graphical Interpretations", ASME JOURNAL OF MECHANISMS, TRANSMISSIONS AND AUTOMATION IN DES IGN,Vol. 107 ,No. 3,1983,pp394.
[32] Angeles, J., and Callejas, M.,"An Algebraic Formulation of Grashof's Mobility Criteria with Application to Linkage Optimization Using Gradient Dependent Methods", ASME JOURNAL OF MECHANISMS, TRANSMISSIONS AND AUTOMATION IN DESIGN, Vol.106,1984, pp.327-332．
[33] Williams, R.L., Ⅱ, and Reinholtz, C.F., "Proof of Grashof's Law Using Polynomial Discriminants", ASME JOURNAL OF MECHANISMS,TRANSMISSIONS,AND AUTOMATION IN DESIGN, Dec.l986,pp.562-564
[34] Gupta ,K.C.,"A General Theory for Synthesizing Crank-Type Four-Bar Function Generator With Transmission Angle Control", ASME JOURNAL OF APPLIED MECHANICS,Vol.45,l978,pp.415-421．
[35] Freudenstein, F., and Primrose, E.J.F., 1963a,"Geared Five-Bar Motion Parti-Gear Retia Minus One", ASME Journal of Engineering for Industry .pp. 11-16．
[36] Roth,B., and Freudenstein,F.,1963,"Synthesis of Path-generating Mechanisms by Numerical Methods", ASME Journal of Engineering for Industry ,pp.298-306．
[37] Sandor, G. N., and Erdman, A. G., 1984, Advanced Mechanism Design: Analysis and Synthesis, Vol.2, Prentice Hall, Englewood Cliffs, NJ.
[38] Kramer, S. N., and Sandor, G.N., 1970． "Kinematic Synthesis of a Cycloidal Crank Mechanism for Function Generation." ASME JOURNAL OF ENGINEERING for Industry.Vol.92． No.3, pp.531-536．
[39] Starns,G,K.,and Flugard,D.R.,1990,"Five-Bar Path Generation Synthesis by Continuation Methods.", ASME Mechanisms Analysis and Synthesis,DE-Vol.25,pp.353-359．
[40] Dhingra, A.K., and Mani, N.K., 1993． "Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing."ASME JOURNAL OF MECHANICAL DESIGN, pp.5620-567．
[41] Duffyj., 1980,Analysis of Mechanisms and Robot Manipulators John Wiley and Sons, New York
[42] T. W. Lee and F. Freudenstein, Mech. Mach. Theory 13,235(1978) .
[43] A. H. Soni and A. Shirkodaire, Proc, 9th OSU Applied Mechanisms Conf. Kansas City, Mo., Paper No. Ⅷ-Ⅳ(1985) .
[44] Midha, J.A., Zhou. Z. L., and Her, I., 1985,"Mobility Conditions for Planar
Linkages Using Triangle Inequality and Graphical Interpretation". ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN, Vol. 107, pp.394-400.
[45] White, R.J., 1987,"Solution Rectification for a Stephenson Ⅲ Motion Generator", Master thesis, University of Minnesota.
[46] Mirth,J.A.,and Chase,T.R.,1992,"Circuit Analysis For Four Precision Position Synthesis of Stephenson Six-bar Linkages.DE-Vol.46,ASME Mechanism Design and Synthesis,pp.359-366.
[47] Mirth.J.A.,and Chase,T.R.,1990,"Circuit Analysis of Watt Chain Six-bar Mechanisms,"ASME Mechanism Synthesis and Analysis ,DE-Vol.25.
[48] Ting, K, L., 1994,"Mobility Criteria of Geared Five-Bar Linkage", Mechanism and Machine Theory .Vol.29.No.2, pp.251-264.
[49] Ting, K. L., Mobility Criteria of Single Loop N-bar Linkage. Journal of Mechanisms, Transmission and Automation in Design. 1989, Vol.111:32-38.
[50] Ting, K.L.,"Five-bar Grashof Criteria",ASME JOURNAL OF MECHANISMS,TRANSMISSIONS,AND AUTOMATION IN DESIGN,Dec, 1986,pp.451-427.
[51] Ting, K. L., and Liu, Y. w., "Rotatability Laws for N-bar Kinematic Chains and Their Proof", ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN, Vol, 113, pp.394-400.
[52] 周双林、邹慧君、姚燕安、郭为忠，混合输入五杆机构构形的分析 上海交通大学学报 Vol．33，No．7 2001．7
[53] 周井玲、沈世德、程海正，五杆机构的混沌运动，南通工学院学报 Vol．12， 2001
[2] 葛文杰，陈作模 齿轮—五杆机构的轨迹特性研究，西北工业大学学报，1997，11
[3] 吕传毅，曹维庆齿轮连杆机构研究进展，中国机械工程，1996，5
[4] 曹维庆，褚金奎，严天宏，吕传毅齿轮连杆机构结构分析的研究，西安理工大学学报，Vol．14 No．3，1998
[5] 褚金奎、严天宏、曹维庆齿轮连杆机构的通用运动分析算法及程序设计，西安理工大学学报，Vol．3，1999
[6] 吕传毅，曹维庆齿轮连杆机构运动分析广义型转化法的基本理论。机械科学与技术，1995(6)：13～18
[7] 吕传毅，曹维庆齿轮连杆机构运动分析广义型转化法的实现。机械科学与技术，1996(1)：75～80
[8] 李团结、曹惟庆、褚金奎，齿轮—五杆机构轨迹综合的连续法 西安理工大学学报Vol．15 No14 1999
[9] 褚金奎、郭晓宁，连杆机构的装配构形于机构拓扑结构的关系研究—平面连杆机构装配构形分析 机械科学与技术Vol．20，No．2 2001．3
[10] 田汉民、张策、张新华，二自由度平面五杆机构的双曲柄存在条件 机械设计 2001．3
[11] 褚金奎 五杆双输入机构的输出特性图谱及输出特性分析 机械科学与技术 1995．
[12] 胡继强 实现近似平行直线轨迹差动推送的齿轮—五杆机构包装工程Vol．18 No．(2．3)1997
[13] 孔向东、董平、杨基厚，平面四杆曲柄摇杆机构连杆曲线形状分部规律的研究机械科学与技术1994．2
[14] 张旭滨、刘葆旗，类四杆五杆机构连杆曲线的变化规律 机械设计1997．7
[15] 洪笃利，常用齿轮连杆机构的分组运动分析—常用齿轮连杆机构的分组方法。第七届机构学术讨论会论文集，秦皇岛，1990
[16] Ananthasuresh G K .Kinematic Symhesis and Analysis of the Rack and Pinion Multi—Purpose Mechanism .Trans. of the ASME, 1992,114:428～432
[17] Dan Gibson. Kinematic Design and Analysis of the Rack—and—Gear
Mechanism for Function Generation. M.M.T,1984,19(3):369～375
[18] Duschl P. Kinematic Synthesis and Analysis of the Rack and Pinion Mechanism for Planar Path Generation and Function Generation for Six Precision Conditions,M.M.T.,1987,22(6):563～568
[19] 叶仲和，齿轮连杆机构分析与分组运动分析法。福州大学学报，1991，19(3)：63～68
[20] 叶仲和，用杆组法作Ⅱ级齿轮连杆机构的运动分析。机械设计与研究，1992(4)：7～11
[21] 叶仲和，用杆轮分离法作高级齿轮连杆杆组运动分析。福州大学学报，1992，20(4)：45～50
[22] G.N. Sandor,etal:Kinematie Synthesis of Geared Linkages,Jnl.of Mechanisms,Vol.5,59-87,1970
[23] T. W .Lee ,E. Akbil: Kinematic Synthesis of Spherical Two-Gear Drives with Prescribed Entire—Motion Characteristics: Displacement Analysis and Dwell Characteristics,j .Mech.Trans.Auto.Design,Vol. 105,663—671,1983
[24] Gibson C G. On the Geometry of Geared 5- Bar Motion. Trans. of the ASME, 1990,(112):620～627
[25] Yoshiaki Yokoyama. Studies on the Geared Linkage Mechanisms. Bulletin of the JSME,1974,17(112):1332～1339
[26] Grashof, F. ,Theoretisehe Maschinenlehre ,Leipzig,1983.
[27] Harding,B.L.,"Derivation of Grashof's Law",Machine Design Bulletin,American Society of Engineering Education,April 1962,pp. 1-10.
[28] Paul,B. ,"A Reassessment of Grashof's Criterion",ASME Journal of Mechanical Design,July 1979,pp.515-518.
[29] Barker, C.R., and Jeng, Ywh-Ren, "Range of the Six Fundamental Position Angles in a Planar Four-Bar Mechanism", Mechanism and Machine Theory ,Vol.20,No.4,1985
[30] Barker, C. R.,"A Complete Classification of Planar Four-Bar Linkages", Mechanism and Machine Theory, Vol.20, No.6, 1985, pp.535-554.
[31] Midha, A.,Zhao,Z.L.,and Her, I., "Mobility Conditions for Planar Linkages Using Triangle Inequality and Graphical Interpretations", ASME JOURNAL OF MECHANISMS, TRANSMISSIONS AND AUTOMATION IN DES IGN,Vol. 107 ,No. 3,1983,pp394.
[32] Angeles, J., and Callejas, M.,"An Algebraic Formulation of Grashof's Mobility Criteria with Application to Linkage Optimization Using Gradient Dependent Methods", ASME JOURNAL OF MECHANISMS, TRANSMISSIONS AND AUTOMATION IN DESIGN, Vol.106,1984, pp.327-332．
[33] Williams, R.L., Ⅱ, and Reinholtz, C.F., "Proof of Grashof's Law Using Polynomial Discriminants", ASME JOURNAL OF MECHANISMS,TRANSMISSIONS,AND AUTOMATION IN DESIGN, Dec.l986,pp.562-564
[34] Gupta ,K.C.,"A General Theory for Synthesizing Crank-Type Four-Bar Function Generator With Transmission Angle Control", ASME JOURNAL OF APPLIED MECHANICS,Vol.45,l978,pp.415-421．
[35] Freudenstein, F., and Primrose, E.J.F., 1963a,"Geared Five-Bar Motion Parti-Gear Retia Minus One", ASME Journal of Engineering for Industry .pp. 11-16．
[36] Roth,B., and Freudenstein,F.,1963,"Synthesis of Path-generating Mechanisms by Numerical Methods", ASME Journal of Engineering for Industry ,pp.298-306．
[37] Sandor, G. N., and Erdman, A. G., 1984, Advanced Mechanism Design: Analysis and Synthesis, Vol.2, Prentice Hall, Englewood Cliffs, NJ.
[38] Kramer, S. N., and Sandor, G.N., 1970． "Kinematic Synthesis of a Cycloidal Crank Mechanism for Function Generation." ASME JOURNAL OF ENGINEERING for Industry.Vol.92． No.3, pp.531-536．
[39] Starns,G,K.,and Flugard,D.R.,1990,"Five-Bar Path Generation Synthesis by Continuation Methods.", ASME Mechanisms Analysis and Synthesis,DE-Vol.25,pp.353-359．
[40] Dhingra, A.K., and Mani, N.K., 1993． "Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing."ASME JOURNAL OF MECHANICAL DESIGN, pp.5620-567．
[41] Duffyj., 1980,Analysis of Mechanisms and Robot Manipulators John Wiley and Sons, New York
[42] T. W. Lee and F. Freudenstein, Mech. Mach. Theory 13,235(1978) .
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