Type synthesis of 2T1R-type parallel kinematic mechanisms and the application in manufacturing

This paper investigates the type synthesis of 2T1R-type (T: translational degree of freedom (DoF) and R: rotational DoF) parallel kinematic mechanisms (PKMs). A type synthesis method based on Grassmann Line Geometry and Line-graph Method is introduced. Some basic criterions of Grassmann Line Geometry are briefly summarized, and the Line-graph Method is presented sequentially. In order to uncover the relationship between DoF-line graph and constraint-line graph, the dual rule is brought in and explained in detail. Based on these foundations, the technological process of the type synthesis is given. Thereafter, the type synthesis of 2T1R-type PKMs is carried out and the results are listed. Taken as an application example, a synthesized 3-DoF mechanism is chosen as the parallel module of a five-axis hybrid machine tool, which is capable of five-face machining in one setup. The developed prototype is introduced and applied into the machining of a part with freeform surfaces. The presented type synthesis method is concise and can be used in the type synthesis of other PKMs. (C) 2013 Elsevier Ltd. All rights reserved.