Principle of Singularity

determination of maximal singularity free zones in the workspace of parallel manipulator

due to the limiting workspace of parallel manipulator and regarding to finding the trajectory planning of singularity free at workspace is difficult, so finding a best solution that can develop a technique to determine the singularity-free zones in the workspace of parallel manipulators is highly important. in this thesis a simple and new technique are presented to determine the maximal singula...

The Principle Describing Possible Combinations of Singularities in Deformations of a Fixed Singularity

This is a review of my recent work. What kinds of combinations of singularities can appear in small deformation fibers of a fixed singularity? We consider this problem for hypersurface singularities on complex analytic spaces of dimension 2. Recall first that a connected Dynkin graph of type A, D or E corresponds to a surface singularity called a rational double point. (Durfee [3].) When the fi...

Orbital Normal Forms for a family of-zero Singularity

Consider a Dynamical system x'=F(x,µ) such that its linear part has a pair of imaginary eigenvalues and one zero eigenvalue (Hopf zero singularity). Recently, the simplest normal form for this singular system has been obtained by sl(2) Lie algebra theory and the decomposition of space into three invariant subspaces. The normal form of this singular system is divided into three general cases. In...

COORDINATE INFLUENCE ON SINGULARITY OF A 3-UPS PARALLEL MANIPULATOR

This paper shows the coordinates influence on singularity of a three degree-of-freedom structure, namely, three-Universal-Prismatic-Spherical (3-UPS) parallel manipulator. Rotational coordinates, which are chosen to define the orientation of the platform, affect the singularity of the manipulator. Euler parameters, which don't have any inherent geometrical singularity are utilized, however they...

The singularity of pluralism.