In this paper, a novel parallel kinematic mechanism (PKM) with Schönflies motion has been proposed under the guidance of a graphical type synthesis method. This PKM is composed of four identical arms and a single platform and has high rotational capability. The single-platform structure used in the proposed PKM can reduce structural complexity, increase dynamic response. In addition, the composite parallelogram structure in each arm brings in better limb stiffness. Based on the proposed concept, optimal design is carried out to make the PKM realize its high rotational potential. In this process, an input transmission index (ITI) and an output transmission index (OTI) (the two indices can be used to numerically evaluate motion and force transmission performance of PKMs, respectively) are taken as the performance evaluation criteria. On this basis, some other indices are defined and the corresponding performance atlases are also plotted to investigate the potential workspace. Consequently, dimensional parameters of the discussed PKM are derived on the precondition that the rotational capability should reach at least ±90 deg, and the workspace has also been identified. Based on these foundations, a parallel robot X4 has been developed which can realize high-speed pick-and-place manipulation in industrial lines.

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.