A region-specific feature-space transformation for speaker adaptation and singularity analysis of jacobian matrix

SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

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Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

Volume 2: 29th Design Automation Conference, Parts A and B ◽

10.1115/detc2003/dac-48822 ◽

2003 ◽

Cited By ~ 4

Author(s):

Hee-Byoung Choi ◽

Atsushi Konno ◽

Masaru Uchiyama

Keyword(s):

Closed Loop ◽

Jacobian Matrix ◽

Screw Theory ◽

Parallel Robot ◽

Singularity Analysis ◽

Loop Structure ◽

Singular Configurations ◽

Planning And Control ◽

Kinematic Singularities ◽

And Control

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

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Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures

Journal of Mechanisms and Robotics ◽

10.1115/1.4005336 ◽

2012 ◽

Vol 4 (1) ◽

Cited By ~ 40

Author(s):

Semaan Amine ◽

Mehdi Tale Masouleh ◽

Stéphane Caro ◽

Philippe Wenger ◽

Clément Gosselin

Keyword(s):

Parallel Manipulator ◽

Jacobian Matrix ◽

Parallel Manipulators ◽

Singularity Analysis ◽

Type Synthesis ◽

Constraint Analysis ◽

Fixed Direction ◽

Geometric Singularity ◽

Grassmann Geometry ◽

Grassmann Cayley Algebra

This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction (3T1R). Eleven architectures obtained from a recent type synthesis of such manipulators are analyzed. The constraint analysis shows that these architectures are all overconstrained and share some common properties between the actuation and the constraint wrenches. The singularities of such manipulators are examined through the singularity analysis of the 4-RUU parallel manipulator. A wrench graph representing the constraint wrenches and the actuation forces of the manipulator is introduced to formulate its superbracket. Grassmann–Cayley Algebra is used to obtain geometric singularity conditions. Based on the concept of wrench graph, Grassmann geometry is used to show the rank deficiency of the Jacobian matrix for the singularity conditions. Finally, this paper shows the general aspect of the obtained singularity conditions and their validity for 3T1R parallel manipulators with identical limb structures.

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Singularity Analysis of a Plane-Symmetry 3-RPS Parallel Robot Based on Translational/Rotational Jacobian Matrices

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.121-126.1590 ◽

2011 ◽

Vol 121-126 ◽

pp. 1590-1594

Author(s):

Yan Shi ◽

Hong Xin Yue ◽

Yi Lu ◽

Lian He Guo

Keyword(s):

Jacobian Matrix ◽

Parallel Robot ◽

Singularity Analysis ◽

Parallel Robots ◽

New Method ◽

Plane Symmetry ◽

Jacobian Matrices ◽

Different Types

Firstly, 3-DOF parallel robots were classified into different types from the view of moving form. A new method of analyzing the singularity of 3-DOF parallel robots was introduced, which is based on translational Jacobian matrix and rotational Jacobian matrix. The singularity of parallel robots with pure translational form and pure rotational form was introduced summarily. Secondly, the process of solving the plane-symmetry 3-RPS parallel robot with combined moving forms was focused on, through which translational Jacobian matrix and rotational Jacobian matrix were adopted. Finally, the solving results were compared with the axis-symmetry 3-RPS parallel robot, which showed more general singularity can be solved through the new method.

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Statics, Instantaneous Kinematics and Singularity Analysis of Planar Parallel Manipulators via Grassmann-Cayley Algebra

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.532.378 ◽

2014 ◽

Vol 532 ◽

pp. 378-381 ◽

Cited By ~ 2

Author(s):

Ke Fei Wen ◽

Jeh Won Lee

Keyword(s):

Jacobian Matrix ◽

Parallel Manipulators ◽

Singularity Analysis ◽

New Approach ◽

Coordinate Method ◽

Cayley Algebra ◽

Symbolic Formula ◽

Grassmann Cayley Algebra ◽

Planar Parallel Manipulators

The wrench Jacobian matrix plays an important role in statics and singularity analysis of planar parallel manipulators (PPMs). It is easy to obtain this matrix based on plücker coordinate method. In this paper, a new approach is proposed to the analysis of the forward and inverse wrench Jacobian matrix used by Grassmann-Cayley algebra (GCA). A symbolic formula for the inverse statics and a coordinate free formula for the singularity analysis are obtained based on this Jacobian. As an example, this approach is implemented for the 3-RPR PPMs.

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