Journal of Petrochemical Universities

Journal of Petrochemical Universities ›› 2010, Vol. 23 ›› Issue (2): 84-88.

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Research on the Singularity of Parallel Machine Tools

  

  1. School of Mechanical Engineering, Liaoning Shihua University, Fushun Liaoning 113001, P.R.China
  • Received:2009-11-17 Published:2010-06-25 Online:2010-06-25

并联机床的奇异性研究

王传强,赵恒华   

  1. 辽宁石油化工大学机械工程学院, 辽宁抚顺113001
  • 作者简介:王传强(1985 -), 男, 山东临沂市, 在读硕士
  • 基金资助:
    辽宁省自然科学基金(20052211);辽宁省教育厅科学研究计划(05L231)

Abstract:

The singularity of parallel machine tools was researched, which was based on the research objects of the speed matrix determinant, Jacobian matrix determinant det([WTHX]J[WTBZ]) and operability W respectively. The researches provided a basis for the design of the structural parameters about parallel machine tools.The singularity of bodies about parallel machine tools can be divided into three categories when the speed matrix determinant was put as the research object. Parallel machine tools can be judged at the singularity when det([WTHX]J[WTBZ])=0 or the operability was zero.The singularity was researched for a new type of 3-legged 3-DOF parallel machine tool when det([WTHX]J[WTBZ]) and the operability W were [KG*4]put as the research objects. The mathematical model of the [KG*4]machine [KG*4]tool [KG*4]was [KG*4]established. The [KG*4]Jacobian [KG*4]matrix [KG*4]of [KG*4]the [KG*4]machine [KG*4]tool [KG*4]were [KG*4]derived. [KG*4]The [KG*4]expressions [KG*4]of [KG*4]|det([WTHX]J[WTBZ])| and the operability W about the machine tool by Matlab had been worked out. |det([WTHX]J[WTBZ])|=W>0 and |det([WTHX]J[WTBZ])|=W≠∞ were obtained by the analysis. That is, there is no singularity about the machine tool. Besides, the machine tool has good operability. The stationarity of the machine tool was researched in the environment of Matlab. The simulation results show that the machine tool has good stationarity.

Key words:

摘要: 分别以速度矩阵行列式、雅可比矩阵行列式det(J)和可操作度为研究对象研究了并联机床的奇异
性, 为并联机床结构参数设计提供依据。当以速度矩阵行列式为研究对象时, 可将并联机床的机构奇异分为3 类;当
det(J)或可操作度为零时, 可判断并联机床处于奇异形位。以det(J)和可操作度W 为研究对象研究新型三杆三自
由度并联机床的奇异性, 建立了该机床的数学模型, 推导出了该机床的雅可比矩阵, 运用Ma tlab 软件计算出了该机
床雅可比矩阵行列式的绝对值表达式 de t(J) 及其可操作度W 的表达式, 经分析得出其 det(J) =W>0 且 det
(J) =W ≠∞, 即该机床不存在奇异形位, 具有较好的可操作性;在Matlab 环境下研究了该机床的平稳性, 仿真结果
表明该机床运动时的平稳性较好。

关键词: 并联机床 , 雅可比矩阵 , 奇异性 , 平稳性

Cite this article

WANG Chuan-qiang, ZHAO Heng-hua. Research on the Singularity of Parallel Machine Tools[J]. Journal of Petrochemical Universities, 2010, 23(2): 84-88.

王传强,赵恒华. 并联机床的奇异性研究[J]. 石油化工高等学校学报, 2010, 23(2): 84-88.

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