Singularity analysis of a novel 3SPS+PS bionic parallel processing platform based on Grassmann line geometry

2010 ◽  
Author(s):  
Wei Gu ◽  
Gang Cheng ◽  
Yongjian Wan
Keyword(s):  
Parallel Processing ◽  
Singularity Analysis ◽  
Line Geometry ◽  
Grassmann Line Geometry ◽  
Processing Platform

Combinatorial Method for Characterizing Singular Configurations in Parallel Mechanisms

2015 ◽  
Author(s):  
Avshalom Sheffer ◽  
Offer Shai
Keyword(s):  
Singularity Analysis ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Combinatorial Method ◽  
Combinatorial Characterization ◽  
Singular Configurations ◽  
Grassmann Line Geometry ◽  
2D And 3D ◽  
Grassmann Cayley Algebra

The paper presents a method for finding the different singular configurations of several types of parallel mechanisms/robots using the combinatorial method. The main topics of the combinatorial method being used are: equimomental line/screw, self-stresses, Dual Kennedy theorem and circle, and various types of 2D and 3D Assur Graphs such as: triad, tetrad and double triad. The paper introduces combinatorial characterization of 3/6 SP and compares it to singularity analysis of 3/6 SP using Grassmann Line Geometry and Grassmann-Cayley Algebra. Finally, the proposed method is applied for characterizing the singular configurations of more complex parallel mechanisms such as 3D tetrad and 3D double-triad.

Development of a novel two-limbed parallel mechanism having Schönflies motion

2014 ◽  
Vol 229 (1) ◽  
pp. 136-154 ◽  
Author(s):  
Sung Mok Kim ◽  
Kyoosik Shin ◽  
Byung-Ju Yi ◽  
Wheekuk Kim
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Model ◽  
Singularity Analysis ◽  
Short Description ◽  
High Potential ◽  
Haptic Device ◽  
Line Geometry ◽  
Grassmann Line Geometry ◽  
Schönflies Motion ◽  
Very High

This paper introduces a novel parallel mechanism having Schönflies motion. The mechanism consists of only two RRPaR-type limbs. After a short description of its structure, its position analysis is conducted and its screw-based kinematic model is derived. Next, its singularity analysis is performed via Grassmann line geometry and then its optimal kinematic characteristics are examined with respect to workspace size and isotropy property. The results show that the proposed parallel mechanism has a very high potential to be used as a manipulator or a haptic device. A prototype of this mechanism was developed and tested to corroborate its performance.

Singularity Analysis of 5-RPRRR Parallel Mechanisms via Grassmann Line Geometry

2009 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Line Geometry ◽  
Singular Configurations ◽  
Highly Nonlinear ◽  
Grassmann Line Geometry

This paper investigates the singular configurations of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical legs of the RPUR type. The general mechanism was recently revealed by performing the type synthesis for symmetrical 5-DOF parallel mechanisms. In this study, some simplified designs are proposed for which the singular configurations can be predicted by means of the so-called Grassmann line geometry. This technique can be regarded as a powerful tool for analyzing the degeneration of the Plu¨cker screw set. The main focus of this contribution is to predict the actuation singularity, for a general and simplified design, without expanding the determinant of the inverse Jacobian matrix (actuated constraints system) which is highly nonlinear and difficult to analyze.

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.

Design of a new gravity balanced parallel mechanism with Schönflies motion

2016 ◽  
Vol 230 (17) ◽  
pp. 3111-3134 ◽  
Author(s):  
Long Kang ◽  
Se-Min Oh ◽  
Wheekuk Kim ◽  
Byung-Ju Yi
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Force Transmission ◽  
Kinematic Modeling ◽  
Potential Applications ◽  
Structure Description ◽  
Grassmann Line Geometry ◽  
Schönflies Motion ◽  
Forward Kinematic

In this paper, a new gravity-balanced 3T1R parallel mechanism is addressed. Firstly, structure description, inverse and forward kinematic modeling are performed in detail. Secondly, Jacobian derivation based on screw theory and singularity analysis using Grassmann Line Geometry is performed, and then optimal kinematic design with respect to workspace size, kinematic isotropy and maximum force transmission ratio are conducted. Thirdly, the gravity balancing design using both counterweights and springs is proposed and a prototype of this mechanism is also presented. Results of analysis show that the proposed mechanism has quite a few potential applications.

scholarly journals Kinematic Analysis and Verification of a New 5-DOF Parallel Mechanism

2021 ◽  
Vol 11 (17) ◽  
pp. 8157
Author(s):  
Yesong Wang ◽  
Changhuai Lyu ◽  
Jiang Liu
Keyword(s):  
Parallel Mechanism ◽  
Closed Loop ◽  
Three Dimensional ◽  
Line Geometry ◽  
Vector Method ◽  
Five Dimensions ◽  
Grassmann Line Geometry ◽  
Working Performance ◽  
Geometry Method ◽  
Unstable Problem

This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU, and then analyses its DOF by traditional Grubler–Kutzbach and motion spiral theory. It theoretically shows that the mechanism meets the requirement of five dimensions of freedoms including three-dimensional movement and two-dimensional rotation. Based on this, the real mechanism is built, but unfortunately it is found unstable in some positions. Grassmann line geometry method is applied to analyze its unstable problem caused by singular posture, and then an improving method is put forward to solve it. With the improved mechanism, closed loop vector method is employed to establish the inverse position equation of the parallel mechanism, and kinematics analysis is carried out to get the mapping relationships between position, speed, and acceleration of moving and fixed platform. Monte Carlo method is used to analyze the workspace of the mechanism, to explore the influencing factors of workspace, and then to get the better workspace. Finally, an experiment is designed to verify the mechanism working performance.

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