Singularity analysis and avoidance of a planar parallel mechanism with kinematic redundancy under a fixed orientation

2020 ◽  
pp. 095440622097671
Author(s):  
Haibo Qu ◽  
Lanqing Hu ◽  
Sheng Guo
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Singularity Analysis ◽  
Kinematic Redundancy ◽  
Comparison Analysis ◽  
Singularity Avoidance ◽  
Singular Configurations ◽  
Fixed Orientation ◽  
Free Transition ◽  
Singular Configuration

In this paper, the singularity of a planar mechanism with kinematic redundancy is studied. First, the architecture of the mechanism and the concept schematic diagram for singularity avoidance are stated. Next, inverse kinematics model of the planar parallel mechanism with kinematic redundancy is established. For determining the unique inverse solution of the mechanism under certain initial installation configuration, a comparison analysis based on the strategy tree and the virtual prototype is performed. Then, based on the obtained Jacobian matrices and the singular condition, the workspace-singularity map and two singular configurations of the mechanism are drawn. Finally, with the obtained workspace-singularity map, a singularity-free transition layer and an aisle can be found to perform to singularity avoidance, even if the initial designed trajectory passing through the second kind of singularity. Three tasks are carried out to illustrate that the workspace boundary and singular configuration can be changed by adjusting the kinematic redundant actuated parameter.

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.

scholarly journals Optimum Seeking of Redundant Actuators for M-RCM 3-UPU Parallel Mechanism

2020 ◽  
Author(s):  
Chen Zhao ◽  
Jingke Song ◽  
Xuechan Chen ◽  
Ziming Chen ◽  
Huafeng Ding
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Universal Joint ◽  
Prismatic Joint ◽  
Transmission Index ◽  
Redundant Actuators ◽  
Force Transmissibility ◽  
Singular Configuration

Abstract This paper focuses on a 2R1T 3-UPU (U for universal joint and P for prismatic joint) parallel mechanism (PM) with two rotational and one translational (2R1T) degrees of freedom (DOFs) and the ability of multiple remote centers of motion (M-RCM). The singularity analysis based on the indexes of motion/force transmissibility and constraint shows that this PM has transmission singularity, constraint singularity, mixed singularity and limb singularity. To solve these singularproblems, the quantifiable redundancy transmission index (RTI) and the redundancy constraint index (RCI) are proposed for optimum seeking of redundant actuators for this PM. Then the appropriate redundant actuators are selected and the working scheme for redundant actuators near the corresponding singular configuration are given to help the PM go through the singularity.

Singularity Analysis of Serial Robot-Manipulators

1996 ◽  
Vol 118 (4) ◽  
pp. 520-525 ◽  
Author(s):  
A. Karger
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Singularity Analysis ◽  
Singular Set ◽  
Singular Configurations ◽  
Special Cases ◽  
Serial Robot ◽  
Singular Configuration ◽  
Actual Configuration

This paper is devoted to the description of the set of all singular configurations of serial robot-manipulators. For 6 degrees of freedom serial robot-manipulators we have developed a theory which allows to describe higher order singularities. By using Lie algebra properties of the screw space we give an algorithm, which determines the degree of a singularity from the knowledge of the actual configuration of axes of the robot-manipulator only. The local shape of the singular set in a neighbourhood of a singular configuration can be determined as well. We also solve the problem of escapement from a singular configuration. For serial robot-manipulators with the number of degrees of freedom different from six we show that up to certain exceptions singular configurations can be avoided by a small change of the motion of the end-effector. We also give an algorithm which allows to determine equations of the singular set for any serial robot-manipulator. We discuss some special cases and give examples of singular sets including PUMA 560.

scholarly journals Regularization of the Spatial Inverse Positioning Problem of Revolute Joint Manipulators

2017 ◽  
Vol 61 (3) ◽  
pp. 279
Author(s):  
Dániel András Drexler
Keyword(s):  
Inverse Kinematics ◽  
Closed Loop ◽  
Singular Values ◽  
Singular Configurations ◽  
Revolute Joints ◽  
Singular Direction ◽  
Inverse Kinematics Problem ◽  
Singular Configuration ◽  
Damped Least Squares ◽  
Kinematic Singularities

Inverse kinematics is a central problem in robotics, and its solution is burdened with kinematic singularities, i.e. the task Jacobian of the problem is singular. A subproblem of the general inverse kinematics problem, the inverse positioning problem is considered for spatial manipulators consisting of revolute joints, and a regularization method is proposed that results in a regular task Jacobian in singular configurations as well, provided that the manipulator’s geometry makes movement in singular directions possible. The conditions of regularizability are investigated, and bounds on the singular values of the regularized task Jacobian are given that can be used to create stable closed-loop inverse kinematics algorithms. The proposed method is demonstrated on the inverse positioning problem of an elbow manipulator and compared to the Damped Least Squares and the Levenberg-Marquardt methods, and it is shown that only the proposed method can leave the singular configuration in the singular direction.

scholarly journals Generalized Singularity Analysis of Snake-Like Robot

2018 ◽  
Vol 8 (10) ◽  
pp. 1873 ◽  
Author(s):  
Shunsuke Nansai ◽  
Masami Iwase ◽  
Hiroshi Itoh
Keyword(s):  
Singularity Analysis ◽  
Common Point ◽  
Analysis Method ◽  
Link Length ◽  
New Model ◽  
Singular Configurations ◽  
Singular Configuration ◽  
The One

The purpose of this paper is to elucidate a generalized singularity analysis of a snake-like robot. The generalized analysis is denoted as analysis of singularity of a model which defines all designable parameters such as the link length and/or the position of the passive wheel as arbitrary variables. The denotation is a key point for a novelty of this study. This paper addresses the above new model denotation, while previous studies have defined the designable parameters as unique one. This difference makes the singularity analysis difficult substantively. To overcome this issue, an analysis method using redundancy of the snake-like robot is proposed. The proposed method contributes to simplify singularity analysis concerned with the designable parameters. The singular configurations of both the model including side-slipping and the one with non side-slipping are analyzed. As the results of the analysis, we show two contributions. The first contribution is that a singular configuration depends on designable parameters such as link length as well as state values such as relative angles. The second contribution is that the singular configuration is characterized by the axials of the passive wheels of all non side-slipping link. This paper proves that the singular configuration is identified as following two conditions even if the designable parameters are chosen as different variables and the model includes side-slipping link. One is that the axials of passive wheels of all non side-slipping links intersect at a common point. Another one is that axials of passive wheels of all non side-slipping links are parallel.

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.

scholarly journals Singularity analysis and dexterity performance on a novel parallel mechanism with kinematic redundancy

2019 ◽  
Vol 16 (5) ◽  
pp. 172988141987264 ◽  
Author(s):  
Fuqun Zhao ◽  
Sheng Guo ◽  
Chengyu Zhang ◽  
Haibo Qu ◽  
Dian Li
Keyword(s):  
Parallel Mechanism ◽  
Large Range ◽  
Kinematic Model ◽  
Design Strategy ◽  
Singularity Analysis ◽  
Kinematic Redundancy ◽  
Spatial Parallel Mechanism ◽  
Virtual Plane ◽  
Kinematic Performance ◽  
Redundant Mechanism

This article presents a novel spatial parallel mechanism with kinematic redundancy. The design strategy and evolution of the proposed mechanism is introduced, and kinematic model of the mechanism is established. To simplify singularity analysis of this kind of mechanism, the virtual plane method which can separate the whole parallel mechanism into two parts is presented. The relative Jacobian matrices are established and illustrated with singularity configurations of three types. Kinematic performance is obtained to see redundancy effects on the mechanism. The orientational workspace is obtained by the regions of orientational angles with varied platform position. It shows the orientational workspace of the redundant mechanism is significantly larger. Evaluation of condition number demonstrates the proposed mechanism can clearly stay away from singularities with a large range of rotational angles. A trajectory example is conducted to further prove the proposed mechanism can produce a large range of rotational angles without meeting with singularities.

Constraint and Singularity Analysis of the Exechon Tripod

2012 ◽  
Author(s):  
Dimiter Zlatanov ◽  
Matteo Zoppi ◽  
Rezia Molfino
Keyword(s):  
Machine Tool ◽  
System Approach ◽  
Parallel Mechanism ◽  
Singularity Analysis ◽  
Geometric Interpretation ◽  
End Effector ◽  
Singular Configurations ◽  
Parallel Kinematic ◽  
Three Degree Of Freedom ◽  
Fixture System

The paper discusses mobility and singularities of the Exechon three-degree-of-freedom (dof) parallel mechanism (PM) on which a family of parallel kinematic machines is based. Exechon designs are used by a number of machine-tool makers. A new version of the manipulator has been developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. The PM has two UPR (4-dof) legs, constrained to move in a common rotating plane, and an SPR (5-dof) leg. The paper focuses on the constraint and singularity analysis of the mechanism. The screw systems of end-effector freedoms and constraints are identified. The singular configurations are classified in detail and their geometric interpretation is discussed. The velocity kinematics and the Jacobian operator are formulated via a screw-system approach. A fully parameterized package of Maple tools has been developed and used to visualize singularities and their consequences.

Singularity Analysis and Simulation of 3-PRRR Parallel Mechanism

2014 ◽  
Vol 556-562 ◽  
pp. 1226-1231
Author(s):  
Ya Ya Zhu ◽  
Tie Fu ◽  
Hong Sheng Ding ◽  
Yan Ming Wang ◽  
Yong Jie Wang
Keyword(s):  
Theoretical Basis ◽  
Parallel Mechanism ◽  
Singularity Analysis ◽  
Search Method ◽  
Kinematics Analysis ◽  
Analysis Model ◽  
Vector Method ◽  
Singular Configurations ◽  
Cylindrical Coordinate

A new 3-DOF parallel mechanism is presented and its kinematics analysis model was established based on the vector method. Based on the speed equations of the mechanism, its singular conditions and singular configurations were analyzed systematically. Moreover, a given mechanism’s singularity was simulated by using cylindrical coordinate search method based on its inverse displacement solutions. The results show that the workspace of mechanism with outset chains is much bigger than mechanism with inset chains. The analysis and simulation on singularity provide a theoretical basis for the dimension synthesis and optimization of this kind of parallel mechanism.

scholarly journals Some aspects of topology and kinematics of a 3DOF translational parallel mechanism

2014 ◽  
Vol 19 (1) ◽  
pp. 5-15 ◽  
Author(s):  
J. Bałchanowski
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Analytical Procedure ◽  
Method Of Determination ◽  
Fixed Orientation ◽  
Three Degrees Of Freedom ◽  
Selection Of

Abstract The paper presents elements of the topology, geometry and the kinematic analysis of a translational parallel mechanism with three degrees of freedom. In such mechanisms the selection of a proper structure and geometry ensures that the driven link maintains a fixed orientation relative to the base. The method of determination of the configuration of mechanisms using contour vector notation was elaborated in the paper. The equations for the analysis of the direct and inverse kinematics task are determined. An analytical procedure for determining the system’s singular positions is presented and illustrated with examples

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