Mobility and Singularity Analysis of a Class of 2-DOF Rotational Parallel Mechanisms Using a Visual Graphic Approach

2011 ◽  
Author(s):  
J. J. Yu ◽  
X. Dong ◽  
X. Pei ◽  
G. H. Zong ◽  
Xianwen Kong ◽  
...  
Keyword(s):  
System Theory ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Parallel Mechanisms ◽  
Two Degrees Of Freedom ◽  
Simple Rules ◽  
Study Case ◽  
Formula Derivation ◽  
Visual Graphic

In this paper, a simple and straightforward visual graphic approach for mobility and singularity analysis of mechanisms is introduced. Although the proposed method is established upon the reciprocal screw system theory, it needs no formula derivation instead knowing about a few simple rules. As a study case, mobility and singularity analysis for a class of two degrees-of-freedom (DOF) rotational parallel mechanisms i.e. well-know Omni-Wrist III with four limbs, and its two derived architectures with three limbs (named T-type and δ-type) is analyzed by the proposed method. As a result, a novel PKM derived from Omni-Wrist III is presented, which has the DOF and kinematics property close to Omni Wrist III.

Mobility and Singularity Analysis of a Class of Two Degrees of Freedom Rotational Parallel Mechanisms Using a Visual Graphic Approach

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Jingjun Yu ◽  
Xin Dong ◽  
Xu Pei ◽  
Xianwen Kong
Keyword(s):  
System Theory ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Parallel Mechanisms ◽  
Two Degrees Of Freedom ◽  
Simple Rules ◽  
Formula Derivation ◽  
Visual Graphic ◽  
Kinematic Properties

In this paper, a visual graphic approach is presented for the mobility and singularity analysis of mechanisms with no helical pair. The presented method is established upon the reciprocal screw system theory. Using the visual graphic approach, the mobility and singularity analysis mainly requires applying a few simple rules and involves into no formula derivation. As a case study, the mobility and singularity analysis is implemented for a class of two degrees of freedom (DOF) rotational parallel mechanisms (RPMs), including the Omni-Wrist III with four limbs and its two derived architectures with three limbs called the T-type and Δ-type RPMs. The Δ-type one is found to has kinematic properties close to the Omni-Wrist III.

Type Synthesis of Two Degrees-of-Freedom Rotational Parallel Mechanisms With a Fixed Center-of-Rotation Based on a Graphic Approach

2012 ◽  
Author(s):  
K. Wu ◽  
J. J. Yu ◽  
S. Z. Li ◽  
G. H. Zong ◽  
Xianwen Kong
Keyword(s):  
High Performance ◽  
Degrees Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Two Degrees Of Freedom ◽  
Center Of Rotation ◽  
Parasitic Motion ◽  
Performance Requirements ◽  
Rotary Stage ◽  
Fixed Center

Mechanisms usually have to be particularly designed to meet the high-performance requirements in terms of different applications. For instance, Two degrees of freedom (DOF) rotational parallel mechanisms (RPMs) with a fixed center-of-rotation can eliminate parasitic motion and could provide the rotary stage with excellent dynamic stability, good controllability and easy operation. Therefore, this paper mainly aims at synthesizing 2-DOF RPMs with fixed center-of-rotation, a class of special RPMs with potential excellent performances. A graphic approach based on freedom and constraint spaces is introduced firstly. The constraint spaces of a class of the existing 2-DOF RPMs are illustrated, and the corresponding type synthesis patterns are summarized by comparing the geometric properties of those spaces with the mechanism characteristic. After fully decomposing the four-dimensional constraint space into sub-constraint spaces, a general type synthesis procedure is proposed based on the freedom and constraint topology. Two novel 2-DOF RPMs with fixed center-of-rotation are constructed based on the proposed method and procedure. The proposed graphic approach proves to be effective and simple to synthesizing those parallel mechanisms with some special performance.

Design and Singularity Analysis for Nine-Bar Mechanism of Three Crank Hybrid Driven

2014 ◽  
Vol 496-500 ◽  
pp. 781-784
Author(s):  
Sheng Tao Song ◽  
Rui Qin Li ◽  
Yan Gao ◽  
Da Hai Li
Keyword(s):  
Mechanical Properties ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Mechanism Analysis ◽  
Analysis Method ◽  
Loop Analysis ◽  
Two Degrees Of Freedom ◽  
Long Rod ◽  
Existence Conditions

With two degrees of freedom five-bar linkage as the foundation, carry on the multiple loop coupling, built three crank controllable nine bar mechanism similar to that of the crank slider pressing, which can meet the controlled flexible output, and conform to the mechanical properties of crank slider pressing mechanism. We use the loop analysis method to analyze the singularity of the mechanism. Analysis through two steps, first of all analysis on three crank existence conditions and the entire organization singularity, it is concluded that the condition of mechanism dont have singularity, and according to the singular condition carrying on research of singularity position, the long rod assembly condition is obtained.

Singularity Analysis of Large Workspace 3RRRS Parallel Mechanism Using Line Geometry and Linear Complex Approximation

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Alon Wolf ◽  
Daniel Glozman
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Community Research ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Equilibrium Equations ◽  
Six Degrees Of Freedom ◽  
Singular Configurations

During the last 15 years, parallel mechanisms (robots) have become more and more popular among the robotics and mechanism community. Research done in this field revealed the significant advantage of these mechanisms for several specific tasks, such as those that require high rigidity, low inertia of the mechanism, and/or high accuracy. Consequently, parallel mechanisms have been widely investigated in the last few years. There are tens of proposed structures for parallel mechanisms, with some capable of six degrees of freedom and some less (normally three degrees of freedom). One of the major drawbacks of parallel mechanisms is their relatively limited workspace and their behavior near or at singular configurations. In this paper, we analyze the kinematics of a new architecture for a six degrees of freedom parallel mechanism composed of three identical kinematic limbs: revolute-revolute-revolute-spherical. We solve the inverse and show the forward kinematics of the mechanism and then use the screw theory to develop the Jacobian matrix of the manipulator. We demonstrate how to use screw and line geometry tools for the singularity analysis of the mechanism. Both Jacobian matrices developed by using screw theory and static equilibrium equations are similar. Forward and inverse kinematic solutions are given and solved, and the singularity map of the mechanism was generated. We then demonstrate and analyze three representative singular configurations of the mechanism. Finally, we generate the singularity-free workspace of the mechanism.

Singularity Analysis on a Special Class of Cable-Suspended Parallel Mechanisms With Pairwise Cable Arrangement and Actuation Redundancy

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Lewei Tang ◽  
Pengshuai Shi ◽  
Li Wu ◽  
Xiaoyu Wu ◽  
Xiaoqiang Tang
Keyword(s):  
Special Class ◽  
Degrees Of Freedom ◽  
Full Rank ◽  
Singularity Analysis ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Actuation Redundancy ◽  
Translational Movement ◽  
The Matrix ◽  
Redundant Actuators

Abstract This paper presents a singularity study on a special class of spatial cable-suspended parallel mechanisms (CSPMs) with merely three translational degrees of freedom using redundant actuators. This paper focuses on the CSPMs that have the capability to perform the purely translational movement with pairwise cables as parallelograms. There are two types of singularity to be discussed, which result from dynamic equations of CSPMs and the parallelogram constraint of pairwise cables. To ensure three-translational dofs without rotation of the end-effector, the matrix formed by normals of the planes based on each pairwise cables should maintain in full rank. In the case study, four typical designs of CSPMs with a planar end-effector and a spatial end-effector are discussed to clarify and conclude the singularity features of CSPMs with actuation redundancy. The results show that for some architectures there exist both types of singularity for redundantly actuated CSPMs with pairwise cables but for some other architectures the redundant actuation exerts no effect on the singularity issue.

A comparison study of two planar 2-DOF parallel mechanisms: one with 2-RRR and the other with 3-RRR structures

Robotica ◽  
2010 ◽  
Vol 28 (6) ◽  
pp. 937-942 ◽  
Author(s):  
Jun Wu ◽  
Jinsong Wang ◽  
Liping Wang
Keyword(s):  
Comparative Study ◽  
Similar Condition ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
The Other ◽  
Stiffness Index ◽  
Parallel Mechanisms ◽  
Comparison Study ◽  
Two Degrees Of Freedom ◽  
Fair Comparison

SUMMARYThis paper deals with a comparative study of two planar two degrees of freedom parallel mechanisms: one with 2-RRR and the other with 3-RRR structures. For a fair comparison, both 3-RRR and 2-RRR mechanisms are symmetrical. The kinematics and Jacobian matrix of the two mechanisms are studied. Conditioning index, stiffness index and payload index are proposed to compare the condition, stiffness and payload performance of the two mechanisms. The results show that the 2-RRR and 3-RRR mechanisms have the similar condition performance, and the planar 3-RRR mechanism has better payload and stiffness performance than the 2-RRR one.

On the Maximization of Joint Velocities and Generalized Reactions in the Workspace and Singularity Analysis of Parallel Mechanisms

Robotica ◽  
2018 ◽  
Vol 37 (4) ◽  
pp. 675-690 ◽  
Author(s):  
Pavel Laryushkin ◽  
Victor Glazunov ◽  
Ksenia Erastova
Keyword(s):  
Case Studies ◽  
External Load ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
State Of The Art ◽  
Singularity Analysis ◽  
The State ◽  
Parallel Mechanisms ◽  
Different Types

SummaryAn approach for calculating the maximum possible absolute values of joint velocities or generalized reactions in a leg of a parallel mechanism has been considered in this paper. The Jacobian analysis and the Screw theory-based methods have been used to acquire the result. These values are calculated for the “worst” directions of the external load or end-effector’s velocity for each leg. The feasibility of using these parameters as the measures of closeness to different types of parallel mechanism singularity is discussed. Further, how this approach is related to the state-of-the-art methods has been illustrated. The key aspect of the discussed approach is that the normalization of vectors or screws is carried out separately for angular and linear components. One possible advantage of such an approach is that it deals only with the kinematic and statics of the mechanism while still providing physically meaningful and practically applicable measures. Case studies of a 3-Degrees Of Freedom translational parallel mechanism and a planar parallel mechanism are presented for illustration and comparison.

Conceptual Design and Static Analysis of Novel Planar Spring-Loaded Cable-Loop-Driven Parallel Mechanisms

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Hanwei Liu ◽  
Clément Gosselin ◽  
Thierry Laliberté
Keyword(s):  
Numerical Simulations ◽  
Static Analysis ◽  
Conceptual Design ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Parallel Mechanisms ◽  
Design Issues ◽  
Two Degrees Of Freedom ◽  
Actuation Redundancy ◽  
Insight Into

Two novel architectures of planar spring-loaded cable-loop-driven parallel mechanisms that do not require actuation redundancy are introduced in this paper. In order to avoid redundancy in the cable-driven parallel mechanisms and require only N actuators to control N-DOF motion, a new spring-loaded cable-loop-driven mechanism is proposed. By attaching springs to the cable loops, two degrees of freedom can be controlled using only two actuators and spools are eliminated in this mechanism. Therefore, the control method can be simplified compared with conventional cable-driven mechanisms making use of spools and actuation redundancy. The mechanisms can be actuated using either linear sliders or rotary actuators driving the motion of a cable or belt loop. Kinematic and static analyses are presented for the new architectures. It is verified that the cables and springs can be kept in tension within a certain workspace. Results of numerical simulations are also given in order to provide insight into the design issues.

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