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Type synthesis of 4-DOF parallel kinematic mechanisms based on Grassmann line geometry and atlas method

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Abstract

Many methods are proposed to deal with the type synthesis of parallel kinematic mechanisms(PKMs), but most of them are less intuitive to some extent. Thus, to propose a concise and intuitive type synthesis method for engineering application is a very challenging issue, which should be further studied in the field. Grassmann line geometry, which can investigate the dimensions of spatial line-clusters in a concise way, is taken as the mathematic foundation. Atlas method is introduced to visually describe the degrees of freedom(DOFs) and constraints of a mechanism, and the dual rule is brought in to realize the mutual conversion of the freedom-space and constraint-space. Consequently, a systematic method based on Grassmann line geometry and Atlas method is generated and the entire type synthesis process is presented. Three type 4-DOF PKMs, i.e., 1T3R, 2T2R and 3T1R(T: translational DOF; R: rotational DOF), are classified according to the different combinations of the translational DOFs and rotational DOFs. The type synthesis of 4-DOF PKMs is carried out and the possible configurations are thoroughly investigated. Some new PKMs with useful functions are generated during this procedure. The type synthesis method based on Grassmann line geometry and Atlas method is intuitive and concise, and can reduce the complexity of the PKMs’ type synthesis. Moreover, this method can provide theoretical guidance for other PKMs’ type synthesis and engineering application. A novel type synthesis method is proposed, which solves the existing methods’ problems in terms of complicated, not intuitive and unsuitable for practical application.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Fugui Xie, Tiemin Li & Xinjun Liu

  2. Department of Precision Instruments, Tsinghua University, Beijing, 100084, China

    Fugui Xie

  3. Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Beijing, 100084, China

    Tiemin Li & Xinjun Liu

Authors
  1. Fugui Xie
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  2. Tiemin Li
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  3. Xinjun Liu
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Corresponding author

Correspondence to Fugui Xie.

Additional information

This project is supported by National Natural Science Foundation of China(Grant No. 51135008), National Basic Research Program of China(973 Program, Grant No. 2013CB035400), and China Postdoctoral Science Foundation(Grant Nos. 2012M520256, 2013T60107)

XIE Fugui, born in 1982, is currently a postdoctoral fellow at Department of Precision Instruments, Department of Mechanical Engineering, Tsinghua University, China. He received his PhD degree from Tsinghua University, China, in 2012, and received his bachelor degree from Tongji University, China, in 2005. His research interests include parallel mechanisms and hybrid machine tools.

LI Tiemin, born in 1971, is currently an associate professor and a PhD candidate supervisor at Beijing Key Lab of Precision/ Ultra-Precision Manufacturing Equipment and Control, Department of Mechanical Engineering, Tsinghua University, China. He received his PhD degree from Tsinghua University, Beijing, China, in 2000. His research interests include parallel kinematic machines and numerical control machines. He patented more than 20 inventions and published around 80 papers.

LIU Xinjun, born in 1971, is currently a professor and a PhD candidate supervisor at Beijing Key Lab of Precision/Ultra-Precision Manufacturing Equipment and Control, Department of Mechanical Engineering, Tsinghua University, China. He received his PhD degree from Yanshan University, Qinhuangdao China, in 1999. His research interests include parallel mechanisms, parallel kinematic machines and advanced manufacturing equipments. He patented more than 40 inventions and published around 110 papers.

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Xie, F., Li, T. & Liu, X. Type synthesis of 4-DOF parallel kinematic mechanisms based on Grassmann line geometry and atlas method. Chin. J. Mech. Eng. 26, 1073–1081 (2013). https://doi.org/10.3901/CJME.2013.06.1073

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  • DOI: https://doi.org/10.3901/CJME.2013.06.1073

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