Type Synthesis of 4-DOF Parallel Kinematic Mechanisms Based on Grassmann Line Geometry and Atlas Method

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.