Degrees Of Freedom Less Degree Of Freedom Parallel Mechanism Analysis Of Some Key Problems In The Research

Mobility is an intrinsic property of a parallel mechanism. Mobility analysis has been a basic problem in theory for parallel mechanism. However, study on mobility of parallel mechanism requires much more than the number of degrees of freedom and motion pattern. Supported by NSFC project“Type synthesis and dynamic analysis of binary hyper redundant robot (No.50605055)”and“Type synthesis and parasitic motion index of rank-deficient parallel mechanism based on topology property (No. 50905167)”, this paper focuses on the rotation axis distribution of incomplete rotational degrees of freedom, mobility bifurcation and constraint singularity. The main contributions are as follows:(1) Rotational axis of 3-PRS parallel mechanism under different geometrical layout of limb chains is studied systematically. The 3-PRS parallel mechanism are classified into four categories and seven sub-categories. Four new types of 3-PRS parallel mechanism belonging to the third categories and the fourth categories are proposed. Using screw theory, rotational axis of 3-PRS parallel mechanism is identified. It is shown that the existence of finite rotational axis depends on the geometrical condition of limb planes and spherical joint centers. The research results help to clarify some fuzzy description of the mobility of 3-PRS parallel mechanism.(2) Type synthesis of 4-DOF parallel mechanism with Schoenflies bifurcation is studied systematically. Geometrical layout condition, limb displacement manifold and corresponding limb chains are presented. Various new parallel mechanism with Schoenflies bifurcation are obtained.(3) Constraint singularity of several typical parallel mechanism with Schoenflies bifurcation is studied using screw theory. It is shown that the initial configuration in which the moving platform is parallel to the base is a constraint singularity. From the initial configuration, the moving platform can perform two kinds of Schoenflies motion.(4) Constraint singularity of general 3-~vP~vR~wR~vR~vR translational parallel mechanism is studied systematically. It is shown that there are two types of constraint singularities. In the first constraint singularity, the moving platform has four instantaneous degrees of freedom; in the second constraint singularity, the moving platform has five instantaneous degrees of freedom. In order to avoid constraint singularity, an orthogonal 3-~vP~vR~wR~vR~vR translational parallel mechanism is proposed. The orthogonal 3-~vP~vR~wR~vR~vR translational parallel mechanism has no constraint singularity as well as kinematic singularity, being fully-isotopic. In addition, three base-fixed-prismatic pairs can be actuated, which shows good potential in application.(5) Using the mobility property of parallel mechanism with three rotational DOFs and two translational DOFs or with three rotational DOFs and one translational DOF, redundant information of Jacobian of limb chains can be removed and a 5×5 non-singular Jacobian of limb chain can be constructed. Further, the total Jacobian of the mechanism can be established. This method is simple and easy to use, providing a powerful tool for performance analysis and kinematic design. It is can also be applicable to other types of parallel mechanism.