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Mathematical Problems in Engineering
Volume 2013, Article ID 206181, 12 pages
Research Article

Type Synthesis and Typical Application of 1T2R-Type Parallel Robotic Mechanisms

1Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
2Department of Precision Instruments, Tsinghua University, Beijing 100084, China
3Beijing Key Lab of Precision/Ultra-Precision Manufacturing Equipments and Control, Tsinghua University, Beijing 100084, China

Received 2 July 2013; Accepted 20 August 2013

Academic Editor: Marcelo Moreira Cavalcanti

Copyright © 2013 Fugui Xie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper focuses on the 1T2R-type (T: translational DOF; R: rotational DOF) parallel robotic mechanisms (PKMs) and discusses their type synthesis and typical application in five-axis machine tools. Based on Grassmann line geometry and atlas method, a systematic method dealing with the type synthesis of lower mobility PKMs is introduced. The Blanding rules and generalized Blanding rules, which are the criterions in realizing the mutual conversion between the freedom-space atlas and the constraint-space atlas, are summarized and discussed in detail. Thereafter, the entire procedure of the type synthesis is presented, and the type synthesis of 1T2R PKMs is carried out. Based on the synthesis results, a five-axis hybrid mechanism is proposed and a machine tool is developed consequently. The type synthesis method presented in this paper is intuitive and concise and can be used in the type synthesis of other lower mobility PKMs.