Singularity Analysis Of Six Degrees Of Freedom Of Parallel Manipulators Using Geometric Algebra

The Stewart parallel manipulator is a kind of typical 6-DOF parallel mechanical system.This kind of mechanical system has the advantages of high rigidity,rapid dynamic response and so on.It is widely used in many industries,such as virtual axes,micro-displacement mechanism,flight simulator and so forth.One inherent characteristic of parallel manipulators is its singularity.When it is in the singular position,the manipulator would lose its rigidity and become uncontrollable.Therefore,we must avoid singularities in motion control and path planning.This paper use geometric algebra method to analyze two typical classes of Stewart parallel mechanical systems.The main content is organized as follows:The singular polynomial is obtained based on the condition of singulairty in geometric algebra framework.The singular loci can be classified into the position-singularity locus and the orientation-singularity locus for analyzing the distribution rule of the singular loci.Given the orientation parameters,the position-singularity locus is quite complex in 3D space.However,the singular locus on the ‘Z-plane' is a quadratic curve with obvious geometric property.This paper develops a singularity model on the Z-planes.and briefly analyzes the instantaneous kinematic property of the mechanism.For the position-singularity,this paper finds the three-dimensional singularity path and studies the properties of position planes given the position space.it is found that there exist three special planes and the singularity paths are symmetric about the original.There are infinite numbers of pairs of symmetries.Once the position parameters are fixed,there always exists a nonsingular orientation region around the orientation origin.The radius of the minimal inscribed sphere of the orientation-singularity surface is defined as the orientation-capability which can be regarded as the measurement of the singularity-free void size.This paper provides theoretical guidance for the design,path planning and motion control of this type of Stewart parallel manipulator.