On Singular Configurations Of Six Degrees Of Freedom Of Parallel Manipulators

Singular configuration, i.e. special configuration, is an intrinsic property ofmechanisms which is also one of the important problems in robot kinematics of parallelmechanisms. It has great effects on performances of parallel mechanisms such as themotion ability, forces, control and accuracy etc. In order to reduce and eliminate effectsof singular configurations, improve performances of parallel mechanisms and promotepracticalization and productization of parallel mechanisms, it is indispensable that furtherresearch on singular configurations of parallel mechanisms should be maid. Thisdissertation will systematically and fully investigate singular configurations of SixDegrees of Freedom (DoF) parallel manipulators, the main contributions of the paper areas follows:An overview of fundamental theories on singularity of parallel mechanisms isintroduced. The definition of singular configuration is established at first which clearlyreveals physical meanings of parallel mechanisms in singular configurations, then themain approaches to analyze singularities, methods of the singularity classification, andthe kinematic principle of singular configuration of parallel mechanisms are presented.Finally, methods of solving the instantaneous motion screw when mechanism is singularare researched in detail.Properties of the distribution and structure of singularity loci of 3/6-SPS Gough-Stewart manipulators in three-dimensional space are further addressed in this dissertation.An analytic polynomial expression, which represents the constant-orientation singularitylocus of the manipulator in three-dimensional space, is derived, then a method calledsingularity-equivalent-mechanism is proposed, an analytic polynomial expressionrepresenting the position-singularity locus of the manipulator in θ -plane for generalorientations is derived by using this method and the property of the distribution andstructure of singularity loci of the manipulator in parallel θ -planes is identified. Finally,properties of the distribution and structure of singularity loci of the manipulator inthree-dimensional space for all orientations are summarized.Properties of the distribution and structure of singularity loci of 6/6-SPS Gough-Stewart manipulators in three-dimensional space are further researched in thisdissertation as well. An analytic polynomial expression representing the constant-orientation singularity locus of the manipulator in three-dimensional space is derived.Based on this analytic expression, an analytic polynomial expression representing theposition-singularity locus of the manipulator in the principal-plane is derived and theproperty of the distribution and structure of singularity loci of the manipulator in parallelprincipal-planes is identified. Finally, properties of the distribution and structure ofsingularity loci of the manipulator in three-dimensional space are summarized. For thefirst time, it is shown that for the 6/6-SPS Gough-Stewart manipulator's singularity, italso has some special cases in which six lines associated with six extensible links of themanipulator can intersect one common line, and even for the same orientation of themanipulator, there are two and more positions of the manipulator where six lines of themanipulator all intersect one common line simultaneously.The orientation-singularity and orientation capability analyses of 6/6-SPS Gough-Stewart manipulators are also presented in this paper. A polynomial expression, whichrepresents the orientation-singularity locus of the manipulator at a fixed position, isderived. Then, for the first time, a performance index, i.e. orientation capability, isproposed. Finally, effects of the geometry configuration of the moving platform, the ratioof the moving platform to the base one and the position of the moving platform on theorientation capability of the manipulator from the orientation-singularity point of vieware also presented. The analysis of the orientation capability of 6/6-SPS Gough-Stewartmanipulators provides very important theoretical guidance for the optimum design of themanipulator.Finally, this paper also addresses the orientation-workspace analysis of 6/6-SPSGough-Stewart manipulators. A discretization algorithm is proposed for computing theorientation-workspace of the manipulator, then concepts, i.e. nonsingular orientation-workspace, practical orientation-workspace, and corresponding discretization algorithmsare presented for computing the nonsingular orientation-workspace and the practicalorientation-workspace of the manipulator, respectively. Examples of a 6/6-SPS Gough-Stewart manipulator are given to demonstrate these theoretical results.