Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy

Robotica ◽  
2009 ◽  
Vol 27 (1) ◽  
pp. 51-57 ◽  
Author(s):  
Jinsong Wang ◽  
Jun Wu ◽  
Tiemin Li ◽  
Xinjun Liu
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Actuation Redundancy ◽  
Hybrid Machine Tool ◽  
Planar Parallel Manipulator ◽  
Redundantly Actuated ◽  
Value Decomposition ◽  
The Relationship ◽  
Orientation Workspace

SUMMARYThis paper deals with the position workspace, orientation workspace, and singularity of a 3-degree-of-freedom (DOF) planar parallel manipulator with actuation redundancy, which is created by introducing a redundant link with active actuator to a 3-DOF nonredundant parallel manipulator. Based on the kinematic analysis, the position workspace and orientation workspace of the redundantly actuated parallel manipulator and its corresponding nonredundant parallel manipulator are analyzed, respectively. In the singularity analysis phase, the relationship between the generalized input velocity and the generalized output velocity is researched on the basis of the theory of singular value decomposition. Then a method to investigate the singularity of parallel manipulators is presented, which is used to determine the singularity of the redundantly actuated parallel manipulator. In contrast to the corresponding nonredundant parallel manipulator, the redundant one has larger orientation workspace and less singular configurations. The redundantly actuated parallel manipulator is incorporated into a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

Dexterity and stiffness analysis of a three-degree-of-freedom planar parallel manipulator with actuation redundancy

2007 ◽  
Vol 221 (8) ◽  
pp. 961-969 ◽  
Author(s):  
J Wu ◽  
J-S Wang ◽  
L-P Wang ◽  
T-M Li
Keyword(s):  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Minimum Eigenvalue ◽  
Stiffness Analysis ◽  
Actuation Redundancy ◽  
Hybrid Machine Tool ◽  
Planar Parallel Manipulator ◽  
Redundantly Actuated ◽  
Singular Configuration ◽  
Three Degree Of Freedom

The current paper deals with the dexterity and stiffness of a three-degree of freedom (DOF) planar parallel manipulator with actuation redundancy, which is a subpart of a four-DOF-hybrid machine tool. Based on the kinematics, the dexterity is analysed. The stiffness indices, which are the maximum deflection of the moving platform under the action of a unit force and the minimum eigenvalue of the stiffness matrix of the manipulator, are presented for investigating the stiffness. According to the minimum eigenvalue index, it is proved that actuation redundancy can improve the stiffness of the parallel manipulator. Moreover, the relationship between the singular configuration and the stiffness of the parallel manipulator is discussed. Compared with the corresponding non-redundant parallel manipulator without the redundant link, the redundantly actuated parallel manipulator has better dexterity and higher stiffness.

Path Tracking of Parallel Manipulators in the Presence of Force Singularity

2005 ◽  
Vol 127 (4) ◽  
pp. 550-563 ◽  
Author(s):  
C. K. Kevin Jui ◽  
Qiao Sun
Keyword(s):  
Motion Planning ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Manipulators ◽  
Path Tracking ◽  
Singularity Avoidance ◽  
Design Complexity ◽  
Actuation Redundancy ◽  
Planar Parallel Manipulator ◽  
Simulation Results

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

scholarly journals SINGULARITY ANALYSIS OF A 3-PRRR KINEMATICALLY REDUNDANT PLANAR PARALLEL MANIPULATOR

1970 ◽  
Vol 41 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Soheil Zarkandi
Keyword(s):  
Motion Control ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Redundant Manipulators ◽  
Static Behavior ◽  
Singular Configurations ◽  
Planar Parallel Manipulator ◽  
And Control ◽  
Planar Parallel Manipulators

Finding Singular configurations (singularities) is one of the mandatory steps during the design and control of mechanisms. Because, in these configurations, the instantaneous kinematics is locally undetermined that causes serious problems both to static behavior and to motion control of the mechanism. This paper addresses the problem of determining singularities of a 3-PRRR kinematically redundant planar parallel manipulator by use of an analytic technique. The technique leads to an input –output relationship that can be used to find all types of singularities occurring in this type of manipulators.Key Words: Planar parallel manipulators; Redundant manipulators; Singularity analysis; Jacobian matrices.DOI: 10.3329/jme.v41i1.5356Journal of Mechanical Engineering, Vol. ME 41, No. 1, June 2010 1-6

Optimal Kinematic Design and Application of a Redundantly Actuated 3DOF Planar Parallel Manipulator

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Jun Wu ◽  
Jinsong Wang ◽  
Liping Wang
Keyword(s):  
Machine Tool ◽  
Gas Turbines ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Performance Measure ◽  
Kinematic Design ◽  
Hybrid Machine Tool ◽  
Planar Parallel Manipulator ◽  
Redundantly Actuated ◽  
Design And Application

This paper addresses optimal kinematic design and application of a redundantly actuated parallel manipulator with 3DOFs. Based on the kinematic model, the Jacobian matrix is derived and then transferred to a uniform form such that the conditioning index has explicit physical meaning. Based on the task workspace, the width between two columns is determined. Then, a comprehensive performance index, which compromises the conflict between workspace utilization performance measure and conditioning index, is proposed for the optimum design. The parallel manipulator is incorporated into a 4DOF hybrid machine tool, which also includes a feed worktable. Furthermore, a 5DOF machine tool is created by combining the parallel manipulator with a 2DOF worktable to machine blades of gas turbines.

Force optimization of planar 2-DOF parallel manipulators with actuation redundancy considering deformation

2012 ◽  
Vol 227 (6) ◽  
pp. 1371-1377 ◽  
Author(s):  
Jun Wu ◽  
Tiemin Li ◽  
Boqiang Xu
Keyword(s):  
Parallel Manipulator ◽  
Driving Forces ◽  
Parallel Manipulators ◽  
Optimization Method ◽  
Internal Force ◽  
Actuation Redundancy ◽  
Force Optimization ◽  
Redundantly Actuated ◽  
Internal Forces ◽  
Novel Method

Internal force distribution is one of the most important issues for redundantly actuated parallel manipulators. This article presents a novel method for optimizing internal force to minimize the deformation of key components in a parallel manipulator. The dynamic model is first derived, and then an objective function is proposed by giving different weights on internal forces of different components based on its flexibility. The deformation of the component with big flexibility is minimized. A planar 2-DOF parallel manipulator with actuation redundancy is taken as an example to validate the force optimization method. The simulation results show that the deformation of the manipulator with the force optimization method proposed in this article is smaller than that with the traditional method to minimize the norm of driving forces. Thus, the manipulator precision can be improved.

scholarly journals Interior singularity analysis for a 2(3HUS+S) parallel manipulator with descending matrix rank method

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141982684
Author(s):  
Feng Guo ◽  
Gang Cheng ◽  
Zunzhong Zhao
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singular Locus ◽  
Singularity Analysis ◽  
Normal Operation ◽  
Motion Path ◽  
Moving Platforms ◽  
Singular Configuration ◽  
The Relationship ◽  
Interior Singularity

Singularity analysis is one of the basic problems for parallel manipulators. When a manipulator moves in a singular configuration, the motion and transmission performance are poor. In certain serious cases, the normal operation could be damaged. Based on the topology structure and kinematics analysis of a 2(3HUS+S) parallel manipulator, the Jacobian matrices were established. Then, the singular locus surface was obtained by numerical simulation. In addition, the relationship between the motion path curve and the singular locus surface was analyzed. In this study, α, β, and γ are the attitude angles that describe the motion of moving platforms. There is a nonsingular attitude space in singular locus surfaces, and the singular locus surface is a single surface in a small attitude angle range. The nonsingular attitude space increases as the absolute value of γ increases, and singularity could be avoided when γ is large. Furthermore, the motion path curve passes through the singular locus surface two times, and the two intersection points are consistent with the positions where the motion dexterity is equal to zero. This study provides new insights on the singularity analysis of parallel manipulators, particularly for the structure parameter optimization of the nonsingular attitude space.

Kinematic and dynamic equations of a planar parallel manipulator

2003 ◽  
Vol 217 (5) ◽  
pp. 525-531 ◽  
Author(s):  
L-P Wang ◽  
J-S Wang ◽  
Y-W Li ◽  
Y Lu
Keyword(s):  
Machine Tool ◽  
Parallel Manipulator ◽  
Driving Forces ◽  
Dynamic Modelling ◽  
Parallel Manipulators ◽  
Hybrid Machine Tool ◽  
Dynamic Formulation ◽  
Planar Parallel Manipulator ◽  
Hybrid Machine ◽  
Five Axis

This paper presents an inverse dynamic formulation using the Newton-Euler approach for a planar parallel manipulator, which is used in a new five-axis hybrid machine tool. The inverse kinematics of the manipulator is given and the velocity and the acceleration formulae are derived. The driving forces acting on the legs are determined according to the dynamic formulation. The formulation has been implemented in a program and has been used for some typical trajectories planned for a numerical simulation experiment. The simulation results reveal the nature of the variation of the driving forces in the hybrid machine tool and justify the dynamic control model. The dynamic modelling approach presented in this paper can also be applied to other parallel manipulators with less than six degrees of freedom.

A novel planar parallel manipulator with high orientation capability for a hybrid machine tool: kinematics, dimensional synthesis and performance evaluation

Robotica ◽  
2015 ◽  
Vol 35 (5) ◽  
pp. 1031-1053 ◽  
Author(s):  
Samy F. M. Assal
Keyword(s):  
Performance Evaluation ◽  
Machine Tool ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Design Parameters ◽  
Dimensional Synthesis ◽  
Hybrid Machine Tool ◽  
Planar Parallel Manipulator ◽  
Hybrid Machine ◽  
High Orientation

SUMMARYIn order to potentially realize the advantages of planar parallel manipulators to be used for hybrid machine tools, the inherently abundant singularities which diminish the usable workspace must be eliminated. Proper structure synthesis and dimensional synthesis can provide a good solution. So, a non-conventional architecture of a three-PPR planar parallel manipulator is proposed in this paper for a hybrid machine tool. The proposed architecture permits a large dexterous workspace with unlimited orientation capability and no singularities. It also provides partially decoupled motion which permits independent actuators control. The kinematic, singularity, orientation capability and workspace analyses of the proposed manipulator are studied to verify those advantages. Based on a non-dimensional design parameter space, the highly important indices for this application namely the workspace index (WI), the motion/force transmission index, the kinematic and dynamic dexterity indices and the stiffness index are selected to be maximized yielding proper dimensions of the design parameters. Those performance indices are proven to be uniform over all the workspace achieving highly important characteristics of uniform accuracy, acceleration characteristics, rigidity and force transmissibility. Performance evaluation is finally presented to verify the high performance of the proposed non-singular planar parallel manipulator with high orientation capability.

Singularity Analysis of Limited-DOF Parallel Manipulator Based on Jacobian Matrixes

2011 ◽  
Vol 141 ◽  
pp. 488-492
Author(s):  
Xin You Li ◽  
W.Y. Chen
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Machine ◽  
Singularity Analysis ◽  
Mechanical Analysis ◽  
Singular Problem ◽  
Velocity Analysis ◽  
Force Transformation ◽  
The Relationship

To analyze effects of singularity on parallel manipulator, the Jacobian matrixes were introduced as the indexes for analyzing the 3UPS/S parallel machine. The relationship between the velocity Jacobian matrix and the force-transformation matrix was established, and their equivalence was verified through the determinant and condition number’ reciprocal of the matrixes. Effects of singularity on motion accuracy, actuator forces and constrained forces were investigated within the nutation angle’range. The result showed that velocity analysis and mechanical analysis were consistent for 3UPS/S parallel machine in the aspect of singularity, and proved that the accuracy and actuator force properties were deteriorated when approach to singularity. The approach could be applied to other parallel manipulators in the research on singular problem as a reference.

Effect of links deformation on motion precision of parallel manipulator based on flexible dynamics

2017 ◽  
Vol 44 (6) ◽  
pp. 776-787 ◽  
Author(s):  
Chunxia Zhu ◽  
Jay Katupitiya ◽  
Jing Wang
Keyword(s):  
Parallel Manipulator ◽  
High Speed ◽  
Beam Theory ◽  
Parallel Manipulators ◽  
Dynamic Responses ◽  
Axial Deformation ◽  
Content Type ◽  
High Performing ◽  
Coupling Equations ◽  
The Relationship

Purpose Manipulator motion accuracy is a fundamental requirement for precision manufacturing equipment. Light weight manipulators in high speed motions are vulnerable to deformations. The purpose of this work is to analyze the effect of link deformation on the motion precision of parallel manipulators. Design/methodology/approach The flexible dynamics model of the links is first established by applying the Euler–Bernoulli beam theory and the assumed modal method. The rigid-flexible coupling equations of the parallel mechanism are further derived by using the Lagrange multiplier approach. The elastic energy resulting from spiral motion and link deformations are computed and analyzed. Motion errors of the 3-link torque-prismatic-torque parallel manipulator are then evaluated based on its inverse kinematics. The validation experiments are also conducted to verify the numerical results. Findings The lateral deformation and axial deformation are largest at the middle of the driven links. The axial deformation at the middle of the driven link is approximately one-tenth of the transversal deformation. However, the elastic potential energy of the transversal deformation is much smaller than the elastic force generated from axial deformation. Practical implications Knowledge on the relationship between link deformation and motion precision is useful in the design of parallel manipulators for high performing dynamic responses. Originality/value This work establishes the relationship between motion precision and the amount of link deformation in parallel manipulators.

Sign in / Sign up

Export Citation Format

Share Document