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.

Reciprocal Screw Theory Based Singularity Analysis of a Novel 3-DOF Parallel Manipulator

Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.