Singularity Analysis of a Three-Leg Six-Degree-of-Freedom Parallel Platform Mechanism Based on Grassmann Line Geometry

2001 ◽  
Vol 20 (4) ◽  
pp. 312-328 ◽  
Author(s):  
Bruno Monsarrat ◽  
Clément M. Gosselin
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin

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.


2009 ◽  
Vol 147-149 ◽  
pp. 1-6 ◽  
Author(s):  
Rafal Osypiuk ◽  
Torsten Kröger

This contribution presents a new force control concept for industrial six-degree of freedom (DOF) manipulators, which uses a Hexa platform that provides an active environmental stiffness for all six DOFs. The paper focuses on the Hexa platform and is split into two essential parts: (i) parallel platform construction, and (ii) application of force control with industrial manipulators using a six-DOF environmental stiffness. This mechatronic solution almost gives one hundred percent robustness for stiffness changes in the environment, what guaranties a significant shortening of execution time.


2019 ◽  
Vol 16 (3) ◽  
pp. 172988141985891
Author(s):  
Zhi-Hao Kang ◽  
Ching-An Cheng ◽  
Han-Pang Huang

In this article, we analyze the singularities of six-degree-of-freedom anthropomorphic manipulators and design a singularity handling algorithm that can smoothly go through singular regions. We show that the boundary singularity and the internal singularity points of six-degree-of-freedom anthropomorphic manipulators can be identified through a singularity analysis, although they do not possess the nice kinematic decoupling property as six-degree-of-freedom industrial manipulators. Based on this discovery, our algorithm adopts a switching strategy to handle these two cases. For boundary singularities, the algorithm modifies the control input to fold the manipulator back from the singular straight posture. For internal singularities, the algorithm controls the manipulator with null space motion. We show that this strategy allows a manipulator to move within singular regions and back to non-singular regions, so the usable workspace is increased compared with conventional approaches. The proposed algorithm is validated in simulations and real-time control experiments.


Author(s):  
Avshalom Sheffer ◽  
Offer Shai

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.


Author(s):  
Sung Mok Kim ◽  
Kyoosik Shin ◽  
Byung-Ju Yi ◽  
Wheekuk Kim

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.


Author(s):  
Yu Zou ◽  
Yuru Zhang ◽  
Yaojun Zhang

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.


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