Singularity Analysis Of Stewart Parallel Manipulator Using The Kinematics Method

Singular configuration of parallel manipulator is a crucial issue in a context of design and control. This issue has attracted the attention of many researchers, but hasn't been yet solved, since Hunt published his paper on it in 1983. People often use the manipulator's Jacobian matrix or Grassmann geometry to analyze the singularities of parallel manipulator. However, both methods are mathematical ones, and can't find the kinematics reason and universal condition that leads to singular configuration. In this dissertation, a new method is presented to determine the singularities of Stewart parallel manipulator, and termed the kinematics method.At first, the kinematics principle is strictly proved that leads to the singularities of 3-Stewart parallel manipulator in theory, and called the sufficient and necessary condition of singularities. Linear-complex singularity of Stewart manipulator is defined on the basis of the conception of linear complex. According to the pitch of instantaneous screw motion in singular configuration, all singularities of Stewart mechanism are classified into three different kinds. Based on the maximal independent line vectors for different geometrical conditions and the kinematics principle, seven singularity types of 3-6 Stewart manipulator are analyzed and derived, including geometrical and kinematic properties in the singular configurations of these types. The singularity loci and distribution characteristics of 3-6 Stewart manipulator for a given orientation of the mobile are studied in a oblique plane and in three-dimensional space. We also analyze the singularities of Stewart parallel manipulators with irregular triangle moving platform or spherical basic platform simply. The conclusion above is important to determine the workspace section of parallel manipulator and plan its trajectory accurately.At last, this dissertation presents another simple method to determine the singularity of parallel mechanism-equivalent mechanism method. The method is used to study the singularity distributions for different orientations of the mobile in a oblique plane. By parallel translation of the oblique plane, the singularity distributions are derived in three-dimensional space.