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

•A type synthesis method based on Grassmann Line Geometry and atlas method is introduced.•The type synthesis of 2T1R-type parallel kinematic mechanisms is investigated and carried out.•A 3-DoF PKM whose rotational capability can achieve more than 90° is taken as the parallel module of a hybrid machine tool.•The developed machine tool is capable of five-face machining and is applied to the machining of a part with freeform surfaces.

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.