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.

Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed-Loop Subchains

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Kristan Marlow ◽  
Mats Isaksson ◽  
Jian S. Dai ◽  
Saeid Nahavandi
Keyword(s):  
Performance Measures ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Force Transmission ◽  
Six Degrees Of Freedom ◽  
Lower Mobility ◽  
Transmission Ability

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input–output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism.

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.

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.

Mobility Analysis of a Novel 3-5R Parallel Mechanism Family

2004 ◽  
Vol 126 (1) ◽  
pp. 79-82 ◽  
Author(s):  
Q. C. Li ◽  
Z. Huang
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

Mobility analysis of a novel 3-5R parallel mechanism family whose limb consists of a 2R and a 3R parallel subchain is performed by the aid of screw theory. A mobility criterion applicable to such 3-leg parallel mechanisms in which each kinematic chain contains five kinematic pairs is proposed. It is shown that under different structural conditions, the 3-5R parallel mechanism can have 3, 4, or 5 DOF (degrees of freedom). The structural conditions that guarantee the full-cycle mobility are analyzed. The analysis and the method presented in this paper will be helpful in using such a 3-5R parallel mechanism family and introduce new insights into the mobility analysis of parallel mechanisms.

Kinematically Redundant Planar Parallel Mechanisms for Optimal Singularity Avoidance

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Mats Isaksson
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Power Transmission ◽  
Load Capacity ◽  
Parallel Mechanisms ◽  
Kinematic Redundancy ◽  
Singularity Avoidance ◽  
Cycle Times ◽  
Singular Configurations ◽  
Redundant Mechanism

A parallel mechanism possesses several advantages compared to a similar-sized serial mechanism, including the potential for higher accuracy and reduced moving mass, the latter enabling increased load capacity and higher acceleration. One of the most important issues affecting a parallel mechanism is the potential of parallel singularities. Such configurations strongly affect the performance of a parallel mechanism, both in the actual singularity and in its vicinity. For example, both the stiffness of a mechanism and the efficiency of the power transmission to the tool platform are related to the closeness to singular configurations. A mechanism with a mobility larger than the mobility of its tool platform is referred to as a kinematically redundant mechanism. It is well known that introducing kinematic redundancy enables a mechanism to avoid singular configurations. In this paper, three novel kinematically redundant planar parallel mechanisms are proposed. All three mechanisms provide planar translations of the tool platform in two degrees-of-freedom, in addition to infinite rotation of the platform around an axis normal to the plane of the translations. The unique feature of the proposed mechanisms is that, with the appropriate inverse kinematics solutions, all configurations in the entire workspace feature optimal singularity avoidance. It is demonstrated how it is sufficient to employ five actuators to achieve this purpose. In addition, it is shown how including more than five actuators significantly reduces the required actuator motions for identical motions of the tool platform, thereby reducing the cycle times for typical applications.

Geometric synthesis of spatial parallel manipulators with fewer than six degrees of freedom

2002 ◽  
Vol 216 (12) ◽  
pp. 1175-1185 ◽  
Author(s):  
T S Zhao ◽  
J S Dai ◽  
Z Huang
Keyword(s):  
Mechanism Design ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Algebraic Approach ◽  
Structural Complexity ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Kinematic Pair ◽  
Type Synthesis ◽  
Six Degrees Of Freedom

Manipulators with fewer than six degrees of freedom meet specific tasks and have the advantage of reducing structural complexity, design redundancy and cost. In order to construct parallel manipulators for given tasks, this paper develops an algebraic approach to type synthesis of spatial parallel mechanisms with fewer than six degrees of freedom based on the screw theory. With the proposed steps (i.e. describing restraining screws, identifying basic kinematic pair (KP) screws reciprocal to the restraining screws, linearly transforming the basic KP screws to obtain equivalent serial limbs and allocating the serial limbs) new parallel mechanisms can be constructed. The approach converts a mechanism design into a screw algebra operation, in which screws describe kinematic pairs and constraints between links. As examples, synthesis procedures of parallel mechanisms with four degrees of freedom are given, from which five novel parallel mechanisms result.

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.

scholarly journals Positioning Accuracy Analysis of the Parallel Mechanism Near Singular Positions

2015 ◽  
Vol 20 (1) ◽  
pp. 5-18 ◽  
Author(s):  
J. Bałchanowski
Keyword(s):  
Numerical Modelling ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Accuracy Analysis ◽  
Parallel Mechanisms ◽  
Contact Interactions ◽  
Positioning Accuracy ◽  
Singular Configurations ◽  
Positioning Errors ◽  
Three Degrees Of Freedom

Abstract This paper presents a method of numerical modelling of parallel mechanisms with clearances in their kinematic pairs taken into account. The pairs with clearances are modelled as shape connections based on constraints in the form of contact interactions. Using the created models simulations were run to determine the positioning errors of the links in a parallel mechanism with three degrees of freedom (MR2120). In particular, the accuracy of positioning the links close to the mechanism singular configurations was studied.

scholarly journals Kinematic analysis of a novel 3-CRU translational parallel mechanism

2015 ◽  
Vol 6 (1) ◽  
pp. 57-64 ◽  
Author(s):  
B. Li ◽  
Y. M. Li ◽  
X. H. Zhao ◽  
W. M. Ge
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Structural Characteristics ◽  
Parallel Mechanisms ◽  
Reachable Workspace ◽  
Potential Applications ◽  
Moving Platform ◽  
And Performance

Abstract. In this paper, a modified 3-DOF (degrees of freedom) translational parallel mechanism (TPM) three-CRU (C, R, and U represent the cylindrical, revolute, and universal joints, respectively) structure is proposed. The architecture of the TPM is comprised of a moving platform attached to a base through three CRU jointed serial linkages. The prismatic motions of the cylindrical joints are considered to be actively actuated. Kinematics and performance of the TPM are studied systematically. Firstly, the structural characteristics of the mechanism are described, and then some comparisons are made with the existing 3-CRU parallel mechanisms. Although these two 3-CRU parallel mechanisms are both composed of the same CRU limbs, the types of freedoms are completely different due to the different arrangements of limbs. The DOFs of this TPM are analyzed by means of screw theory. Secondly, both the inverse and forward displacements are derived in closed form, and then these two problems are calculated directly in explicit form. Thereafter, the Jacobian matrix of the mechanism is derived, the performances of the mechanism are evaluated based on the conditioning index, and the performance of a 3-CRU TPM changing with the actuator layout angle is investigated. Thirdly, the workspace of the mechanism is obtained based on the forward position analysis, and the reachable workspace volume is derived when the actuator layout angle is changed. Finally, some conclusions are given and the potential applications of the mechanism are pointed out.

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.

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