Analysis of Singularities of a 3DOF Parallel Manipulator Based on a Novel Geometrical Method

2006 ◽  
Author(s):  
Hodjat Pendar ◽  
Hajir Roozbehani ◽  
Hoda Sadeghian ◽  
Hassan Zohoor
Keyword(s):  
Angular Velocity ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
The Novel ◽  
Geometrical Method ◽  
Novel Method ◽  
Grassmann Geometry ◽  
Constraint Plane ◽  
Definition Of

In this article singular points of a parallel manipulator are obtained based on a novel geometrical method. Here we introduce the constrained plain method (CPM) and some of its application in parallel mechanism. Given the definition of constraint plane (CP) and infinite constraint plane (ICP) the dependency conditions of constraints is achieved with the use of a new theorem based on the Ceva geometrical theorem. The direction of angular velocity of a body is achieved by having three ICPs with the use of another theorem. Finally, with the use of the above two novel theorems singularities of the 3UPF_PU mechanism are obtained. It should be emphasized that this method is completely geometrical, involving no complex or massive calculations. In the previous methods based on the Grassmann Geometry, the mechanism needs to be statically analyzed at first, so that the Inverse Jacobian Matrix is achieved, and then the Plucker-Vector is derived. This task is somewhat inconvenient and in the end there are plenty of conditions remained to be pondered in order to obtain the singularity conditions, while the novel method introduced here, involves no tiring calculations neither the analysis of numerous conditions and yields the answer quickly.

Design and analysis of a totally decoupled 3-DOF spherical parallel manipulator

Robotica ◽  
2010 ◽  
Vol 29 (7) ◽  
pp. 1093-1100 ◽  
Author(s):  
Dan Zhang ◽  
Fan Zhang
Keyword(s):  
Physical Meaning ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Redundant Constraints ◽  
Rotational Motions ◽  
Spherical Parallel Manipulator

SUMMARYIn this paper, we propose a unique, decoupled 3 degree-of-freedom (DOF) parallel wrist. The condition required for synthesizing a fully isotropic parallel mechanism is obtained on the basis of the physical meaning of the row vector in the Jacobian matrix. Specifically, an over-constrained spherical 3-DOF parallel mechanism is presented and the modified structure, which avoids the redundant constraints, is also introduced. The proposed manipulator is capable of decoupled rotational motions around the x, y, and z axes and contains an output angle that is equal to the input angle. As this device is analyzed with the Jacobian matrix, the mechanism is free of singularity within its workspace and maintains homogenous stiffness over the entire workspace.

scholarly journals Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures

2012 ◽  
Vol 4 (1) ◽  
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.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism for Rehabilitation

2007 ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai
Keyword(s):  
Control System ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Control System Design ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Moving Platform

This paper presents the geometry and the kinematic analysis of a parallel manipulator developed for ankle rehabilitation, as the beginning of a control system design process. First the geometry of the parallel mechanism is described, secondly the equations for the inverse and the forward kinematics are obtained, then the forward kinematics is analyzed in order to define all the possible configurations of the moving platform. Finally the Jacobian matrix of the rig is obtained by differentiating the position equations and the singularities are investigated, comparing the non-redundant and redundant type of mechanism.

On the kinematics of a new parallel mechanism with Schoenflies motion

Robotica ◽  
2015 ◽  
Vol 34 (9) ◽  
pp. 2056-2070 ◽  
Author(s):  
Po-Chih Lee ◽  
Jyh-Jone Lee
Keyword(s):  
Closed Form ◽  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Matrix Algebra ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Pick And Place

SUMMARYThis paper investigates the kinematics of one new isoconstrained parallel manipulator with Schoenflies motion. This new manipulator has four degrees of freedom and two identical limbs, each having the topology of Cylindrical–Revolute–Prismatic–Helical (C–R–P–H). The kinematic equations are derived in closed-form using matrix algebra. The Jacobian matrix is then established and the singularities of the robot are investigated. The reachable workspaces and condition number of the manipulator are further studied. From the kinematic analysis, it can be shown that the manipulator is simple not only for its construction but also for its control. It is hoped that the results of the evaluation of the two-limb parallel mechanism can be useful for possible applications in industry where a pick-and-place motion is required.

Kinematics and Singularity Analyses of a 2-RPU&SPR Parallel Manipulator

2013 ◽  
Vol 441 ◽  
pp. 568-571
Author(s):  
Jian Hui Fan ◽  
Bin Li ◽  
Xin Hua Zhao
Keyword(s):  
Numerical Simulations ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Algebraic Method ◽  
Singularity Analysis

In this paper, kinematics and singularity of a 2-RPU&SPR parallel mechanism are analyzed by algebraic method. Firstly, the inverse kinematics of the parallel mechanism is derived. Secondly, the Jacobian matrix of the parallel mechanism is obtained and the singularity of the mechanism is analyzed. Finally, the correctness of singularity analysis of the mechanism is verified by numerical simulations.

Singularity Analysis of the 4-RUU Parallel Manipulator Based on Grassmann-Cayley Algebra and Grassmann Geometry

2011 ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Ste´phane Caro ◽  
Philippe Wenger ◽  
Cle´ment Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Graph Representation ◽  
Fixed Direction ◽  
Cayley Algebra ◽  
Geometric Singularity ◽  
Grassmann Geometry ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Scho¨nflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The study is developed through the singularity analysis of the 4-RUU parallel manipulator. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity, namely, two constraint moments, among its six Plu¨cker lines. The Grassmann-Cayley Algebra is used to obtain geometric singularity conditions. However, due to the presence of lines at infinity, the rank deficiency of the Jacobian matrix for the singularity conditions is not easy to grasp. Therefore, a wrench graph representation for some singularity conditions emphasizes the linear dependence of the Plu¨cker lines of the Jacobian matrix and highlights the correspondence between Grassmann-Cayley algebra and Grassmann geometry.

Non-equidistance DGM(1,1) Model Based on the Concave Sequence and Its Application to Predict the China’s Per Capita Natural Gas Consumption

2018 ◽  
Vol 6 (4) ◽  
pp. 376-384
Author(s):  
Xinhai Kong ◽  
Yong Zhao ◽  
Jiajia Chen
Keyword(s):  
Symmetry Transformation ◽  
The Novel ◽  
Model Based ◽  
Grey Forecasting ◽  
Convex Sequence ◽  
Direct Modeling ◽  
Gas Consumption ◽  
Novel Method ◽  
Natural Gas Consumption ◽  
Definition Of

Abstract Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved, such as for the DGM(1,1) model, based on a concave sequence, the modeling error will be larger. In this paper, firstly the definition of sequence convexity is given out, and it is proved that the output sequence of DGM(1,1) model is a convex sequence. Next, the residual change law of DGM(1,1) model based on the concave sequence is discussed, and the non-equidistance DGM(1,1) model is proposed. Finally, by introducing the symmetry transformation, a concave sequence is transformed into a convex sequence, called the symmetric sequence of the concave sequence, and then construct the non-equidistance DGM(1,1) model based on the convex sequence. The example results show that the novel method is more accurate than the direct modeling for a concave sequence.

On the Design of Singularity-Free Cable-Driven Parallel Mechanism Based on Grassmann Geometry

2012 ◽  
Author(s):  
Yu Zou ◽  
Yuru Zhang ◽  
Yaojun Zhang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Geometric Meaning ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Singular Configurations ◽  
Negative Effect ◽  
Grassmann Line Geometry ◽  
Grassmann Geometry

This paper deals with the design of singularity-free cable-driven parallel mechanism. Due to the negative effect on the performance, singularities should be avoided in the design. The singular configurations of mechanisms can be numerically determined by calculating the rank of its Jacobian matrix. However, this method is inefficient and non-intuitive. In this paper, we investigate the singularities of planar and spatial cable-driven parallel mechanisms using Grassmann line geometry. Considering cables as line vectors in projective space, the singularity conditions are identified with clear geometric meaning which results in useful method for singularity analysis of the cable-driven parallel mechanisms. The method is applied to 3-DOF planar and 6-DOF spatial cable-driven mechanisms to determine their singular configurations. The results show that the singularities of both mechanisms can be eliminated by changing the dimensions of the mechanisms or adding extra cables.

Kinematics of a planar slider-crank linkage in screw form

2021 ◽  
pp. 095440622110207
Author(s):  
Jing-Shan Zhao ◽  
Songtao Wei ◽  
Junjie Ji
Keyword(s):  
Angular Velocity ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Numerical Algorithms ◽  
Forward Kinematics ◽  
End Effector ◽  
First Order ◽  
Forward And Inverse Kinematics ◽  
Definition Of ◽  
Inverse Velocity

This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

scholarly journals Neural Network and Performance Analysis for a Novel Reconfigurable Parallel Manipulator Based on the Spatial Multiloop Overconstrained Mechanism

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Guanyu Huang ◽  
Dan Zhang ◽  
Qi Zou
Keyword(s):  
Neural Network ◽  
Bp Neural Network ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Structural Parameters ◽  
Kinematic Model ◽  
Industrial Area ◽  
And Performance ◽  
The Relationship

To meet the different requirements in the industrial area, a novel reconfigurable parallel mechanism is proposed based on the spatial multiloop overconstrained mechanism. The configurations can be changed by driving the low-DOF (degree-of-freedom) overconstrained mechanism. The mobility of this mechanism is investigated. And the kinematic model and Jacobian matrix are both established. Based on the Jacobian matrix, the workspace, stiffness, and conditional number are all analyzed. To focus on the application in the industrial area, this paper proposes a method to establish the relationship between the performance and the structural parameters by using the modified BP neural network. Based on this method, the structural parameters can be chosen by the requirements of the special task in the industrial area. Finally, some numerical examples are presented to verify the method.

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