On the Programmed Kinematics Computation of Crank Rocker Mechanism Based on the Kinematics Bifurcation Position Analysis

YIN Xiaoli; LI Chunming

doi:10.21656/1000-0887.400173

Volume 41 Issue 4

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YIN Xiaoli, LI Chunming. On the Programmed Kinematics Computation of Crank Rocker Mechanism Based on the Kinematics Bifurcation Position Analysis[J]. Applied Mathematics and Mechanics, 2020, 41(4): 367-375. doi: 10.21656/1000-0887.400173

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On the Programmed Kinematics Computation of Crank Rocker Mechanism Based on the Kinematics Bifurcation Position Analysis

doi: 10.21656/1000-0887.400173

YIN Xiaoli^1,2,
LI Chunming^1,2

¹Shengli College of China University of Petroleum, China University of Petroleum (East China), Dongying, Shandong 257061, P.R.China;²College of Mechanical and Electronic Engineering, China University of Petroleum(East China), Qingdao, Shandong 266580, P.R.China

Received Date: 2019-05-16
Rev Recd Date: 2020-03-20
Publish Date: 2020-04-01

Abstract

Abstract

The crankrocker mechanism is a typical planar quabody mechanism. When the crank is a driven part, there is a kinematics bifurcation position (stuck position or dead point) with the collinear crank and rod. So it is difficult to achieve accurate programmed research. With the crank as the driving part, the same higher derivatives of the driven part position angles were obtained through differentiation of the vector projection equations and the angular velocity formula several times. With the rocker as the driving part, based on the L’Hopital’s rule, the derivative multiplication law, the chain derivative law and the vector equation graphic method, the kinematics parameters of 0/0 indefinites at the stuck position were obtained. The calculation formula was derived. So the foundation for accurate kinematics programmed simulation was made. The example shows that, 1) the order of derivation and solution of the vector projection equation system does not influence the final result; 2) the driven crank keeps the continuity of motion without impact at the stuck position.
- mechanism kinematics,
- dead point,
- stuck position,
- kinematics bifurcation position,
- graphic method,
- L’Hopital’s rule

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References(12)

References

[1]	VINOGRADOV O. Fundamentals of Kinematics and Dynamics of Machines and Mechanisms [M]. Boca Raton: CRC Press, 2000.
[2]	EDWARD J H. Computer Aided Analysis and Optimization of Mechanical System Dynamics [M]. Berlin: Springer, 1984.
[3]	PARVIZ E N. Computer-Aided Analysis of Mechanical Systems [M]. New Jersey: Prentice Hall, 1988.
[4]	李学荣, 吴培芳. ALT法设计曲柄摇杆机构[J]. 齐齐哈尔轻工学院学报, 1988,4(3): 47-52.(LI Xuerong, WU Peifang. The ALT means of designing oscillation-crank mechansis[J]. Journal of Qiqihaer Institute of Light Industry,1988,4(3): 47-52.(in Chinese))
[5]	游晓燕. 常规式游梁抽油机改造成斜井抽油机分析[J]. 机械设计与制造工程, 2002,31(3): 82-83.(YOU Xiaoyan. Reconstruct ion of the pump with inclined oil well from the common beam-moving one[J]. Mechanical Design and Manufacturing Engineering,2002,31(3): 82-83.(in Chinese))
[6]	李春明. 闭环结构的降维违约修正方法[J]. 中国石油大学学报(自然科学版), 2008,32(2): 93-96.(LI Chunming. Reduced dimension constraint violation correction method for multibody system with loop[J]. Journal of the China University of Petroleum(Edition of Natural Science),2008,32(2): 93-96.(in Chinese))
[7]	李春明, 尹晓丽, 贠平利, 等. 某机械曲柄滑块机构的动力学及相关问题研究[J]. 德州学院学报, 2019,35(6): 40-46.(LI Chunming, YIN Xiaoli, YUN Pingli, et al. Crank slider mechanism dynamics and its related problem of a machine[J]. Journal of Dezhou University,2019,35(6): 40-46.(in Chinese))
[8]	李春明, 李万腾, 刘庆, 等. 受弯矩作用中心轮的受力分析方法[J]. 德州学院学报, 2017,33(4): 50-53.(LI Chunming, LI Wanteng, LIU Qing, et al. Force analysis method of the center wheel with bending moment load[J]. Journal of Dezhou University,2017,33(4): 50-53.(in Chinese))
[9]	李岩汀, 徐绩青, 许锡宾, 等. 结构动力响应中急动度的计算[J]. 应用数学和力学, 2017,38(8): 922-931.(LI Yanting, XU Jiqing, XU Xibin, et al. A numerical method for calculation of structural jerk responses[J]. Applied Mathematics and Mechanics,2017,38(8): 922-931.(in Chinese))
[10]	刘晓昂, 上官文斌, 吕兆平. 三缸发动机悬置系统设计方法的研究[J]. 振动工程学报, 2016,29(5): 804-813.(LIU Xiaoang, SHANGGUAN Wenbin, L Zhaoping. Design methods of the powertrain mounting system with three cylinders engine[J]. Journal of Vibration Engineering,2016,29(5): 804-813.(in Chinese))
[11]	李春明. 摩擦力分类及压杆失效的新概念[J]. 制造业自动化, 2015,37(23): 85-86, 91.(LI Chunming. The new conception of the friction classification and the stressed pole failure[J]. Manufacturing Automation,2015,37(23): 85-86, 91.(in Chinese))
[12]	赵雪芬, 李星. 一维六方准晶非周期半平面的有限摩擦接触问题[J]. 应用力学学报, 2018,35(1): 8-14, 223.(ZHAO Xuefen, LI Xing. The frictional contact problem for aperiodical half-plane in one-dimensional hexagonal quasicrystals[J]. Chinese Journal of Applied Mechanics,2018,35(1): 8-14, 223.(in Chinese))