平面五杆机构计时轨迹综合的代数求解

doi:10.13190/j.jbupt.2017.01.003

北京邮电大学学报 ›› 2017, Vol. 40 ›› Issue (1): 23-27.doi: 10.13190/j.jbupt.2017.01.003

平面五杆机构计时轨迹综合的代数求解

李学刚^1,2, 魏世民¹, 廖启征¹, 张英¹

1. 北京邮电大学自动化学院, 北京 100876;
2. 华北理工大学研究生学院, 河北唐山 063009

收稿日期:2016-06-15 出版日期:2017-02-28 发布日期:2017-03-14
作者简介:李学刚(1979-),男,博士生,E-mail:hblgyjs@126.com;魏世民(1965-),男,教授,博士生导师.
基金资助:
国家自然科学基金项目（51375059）；中央高校基本科研业务费专项资金资助项目（2016RC28）

The Algebraic Solution for Path Synthesis of Planar Five-Bar Linkages with Timing

LI Xue-gang^1,2, WEI Shi-min¹, LIAO Qi-zheng¹, ZHANG Ying¹

1. School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2. Graduate School, North China University of Science and Technology, Hebei Tangshan 063009, China

Received:2016-06-15 Online:2017-02-28 Published:2017-03-14

摘要/Abstract

摘要： 提出了一种基于傅氏级数的平面五杆机构计时轨迹综合的代数求解新方法。通过将平面五杆机构拆分为左右2个二杆组，对轨迹综合设计变量进行了解耦。在此基础上，分析得到机构尺寸与连杆曲线谐波参数间的函数关系，并依据这一关系建立了不同传动比条件下平面五杆机构轨迹综合设计方程，通过析配消元法进一步将方程化简为一元四次方程，求解得到了平面五杆机构轨迹综合设计参数计算的通用公式。利用该公式分别计算得到左右2个二杆组的设计参数，进而得到完整机构设计参数。给出了2个数值实例，验证了该方法的有效性和可行性。

关键词: 五杆机构, 轨迹综合, 傅氏级数, 代数法

Abstract: A novel analytical approach is presented to solve path synthesis problems for planar five-bar linkages with timing. Firstly, the planar five-bar linkage is decomposed into two dyads for the purpose of decoupling the design parameters of the linkage. The relationship between the design parameters of the linkage and the harmonic parameters of the path is obtained, based on which, the new synthesis equations with different transmission ration for planar five-bar linkages are established. A quartic equation is obtained by dialytic elimination. As a result, a general formula is derived for calculation of the design parameters of a planar five-bar linkage. The design parameters of two dyads are obtained with the general formula respectively. At last, all design parameters of the planar five-bar linkage are obtained. Two numerical examples are provided to verify the effectiveness of the proposed algorithm.

Key words: five-bar linkages, path synthesis, Fourier series, analytical approach

中图分类号:

TH112

李学刚, 魏世民, 廖启征, 张英. 平面五杆机构计时轨迹综合的代数求解[J]. 北京邮电大学学报, 2017, 40(1): 23-27.

LI Xue-gang, WEI Shi-min, LIAO Qi-zheng, ZHANG Ying. The Algebraic Solution for Path Synthesis of Planar Five-Bar Linkages with Timing[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2017, 40(1): 23-27.

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[2]	黄昔光，廖启征，魏世民，徐强. 基于代数法的平面四杆机构五精确点轨迹综合[J]. 北京邮电大学学报, 2008, 31(2): 1-4.
[3]	韩林廖启征梁崇高. 一种6杆平面三级组运动分析 [J]. 北京邮电大学学报, 1998, 21(3): 56-60.

平面五杆机构计时轨迹综合的代数求解

The Algebraic Solution for Path Synthesis of Planar Five-Bar Linkages with Timing

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