Stephenson-Ⅲ型平面六杆机构五精确点轨迹综合代数求解  

The Algebraic Solution for Five Precision Points Path Synthesis of Stephenson-Ⅲ Planar Six-Bar Linkage

作　　者：魏锋[1,2] 魏世民[1] 张英[1] 廖启征[1] 

机构地区：[1]北京邮电大学自动化学院,北京100876 [2]河南理工大学机械与动力工程学院,河南焦作454000

出　　处：《北京邮电大学学报》2015年第5期104-108,共5页Journal of Beijing University of Posts and Telecommunications

基　　金：国家自然科学基金项目(51375059);国家高新技术研究与发展计划项目(2011AA040203);北京市自然科学基金项目(4132032);粮食公益性行业科研专项(201313009-06);国家科技支撑计划课题(2013BAD17B06)

摘　　要：提出Stephenson-Ⅲ型平面六杆机构五精确点轨迹综合代数求解方法.将Stephenson-Ⅲ型平面六杆机构拆分为一个二级杆组和一个四杆机构,先对二级杆组五精确点综合,再对四杆机构进行精确点综合.采用矩阵约束法建立该问题的数学模型,使用Groebner基和Sylvester结式(GS法)相结合的代数方法进行求解,最终获得一元高次方程及其全部封闭解析解.通过数值实例,并使用Solidworks和SAM软件对计算结果进行仿真,结果表明该方法的正确性.该方法为进一步采用代数法对其他类型平面六杆机构轨迹综合问题的研究提供了参考.An algebraic solution for five precision points path synthesis of Stephenson-Ⅲ planar six-bar linkage was presented. The Stephenson-Ⅲ planar six-bar linkage is decomposed into two parts： a dyad and a four-bar linkage. To synthesize the two parts,the dyad first then the four-bar linkage,the kinematic constraint equations are formulated based on displacement matrix. The equations are solved with the Groebner-Sylvester（ GS） hybrid approach in which a high degree univariate equation together with all its closed form solution is obtained finally. A numerical example was provided to validate the algorithm and the solutions are verified by Solidworks and SAM. The method given in this article can also be used to solve other types of synthesis problem concerning planar six-bar linkage.

关 键 词：轨迹综合 六杆机构 代数法 GROEBNER基 Sylvester结式 

分 类 号：TH112[机械工程—机械设计及理论]