On Singularities of Planar Parallel Manipulators

1993 ◽  
Author(s):  
H. R. Mohammadi Daniali ◽  
P. J. Zsombor-Murray ◽  
Jorge Angeles
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Classification Scheme ◽  
Parallel Manipulators ◽  
The Other ◽  
Jacobian Matrices ◽  
General Classification ◽  
Three Degrees Of Freedom ◽  
Planar Parallel Manipulators

Abstract The singularities of the Jacobian matrices of two manipulator with three degrees of freedom are analyzed. One is a planar 3-legged manipulator; the other, a planar double-triangular manipulator. A general classification of parallel-manipulator singularities into three groups is described. The classification scheme relies on the properties of the Jacobian matrices of the manipulator. Finally, the three types of singularity are identified for the two manipulators.

Instantaneous Center of Rotation and Singularities of Planar Parallel Manipulators

2005 ◽  
Vol 33 (3) ◽  
pp. 251-259 ◽  
Author(s):  
H. R. Mohammadi Daniali
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Classification Scheme ◽  
Parallel Manipulators ◽  
Singular Configurations ◽  
Classification Of Singularities ◽  
Instantaneous Center ◽  
Three Degrees Of Freedom ◽  
Planar Parallel Manipulators

With regard to planar parallel manipulators, a general classification of singularities into three groups is given. The classification scheme relies on the properties of instantaneous centers of rotation. This method is very fast and can easily be applied to the manipulators under study. The method is applied to a planar three-degrees-of-freedom parallel manipulator and all its singular configurations are found.

A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Jun Wu ◽  
Binbin Zhang ◽  
Liping Wang
Keyword(s):  
Dynamic Model ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Maximum Acceleration ◽  
Virtual Work Principle ◽  
Joint Force ◽  
Joint Forces ◽  
Three Degrees Of Freedom

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.

Dexterity and Adaptive Control of Planar Parallel Manipulators With and Without Redundant Actuation

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Weiwei Shang ◽  
Shuang Cong
Keyword(s):  
Adaptive Control ◽  
Parallel Manipulator ◽  
Adaptive Controller ◽  
Parallel Manipulators ◽  
The Other ◽  
Experimental Comparison ◽  
Redundant Actuation ◽  
Tracking Accuracy ◽  
Planar Parallel Manipulator ◽  
Planar Parallel Manipulators

The objective of this paper is to determine whether a planar parallel manipulator with redundant actuation has better tracking accuracy than a planar parallel manipulator without redundant actuation. The effects of the redundant actuation on tracking accuracy of parallel manipulators are studied by using two different experimental platforms. The first platform is the planar five-bar parallel manipulator with normal actuation, and the other one is the planar parallel manipulator with redundant actuation. The dexterity pictures and the kinematic configurations of the two platforms validate the kinematic advantages from the redundant actuation. In order to study the dynamic advantages of the redundant actuation further, a nonlinear adaptive controller is presented for the two platforms. The experimental comparison is implemented on two actual parallel manipulator platforms, and from the experimental results, one can find the tracking accuracy of the parallel manipulator with redundant actuation can be improved above 38% than that of the five-bar parallel manipulator without redundant actuation.

A New Parallel Manipulator With Multiple Operation Modes

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Ramon Rodriguez-Castro
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Operation Modes ◽  
The Family ◽  
Multiple Operation ◽  
Three Degrees Of Freedom

In this work, a new parallel manipulator with multiple operation modes is introduced. The proposed robot is based on a three-degrees-of-freedom (3DOF) parallel manipulator endowed with a three-dof central kinematic chain, where by blocking some specific kinematic pairs, the robot can modify its mobility. Hence, the robot manipulator is able to assume the role of a limited-dof or a nonredundant parallel manipulator. Without loss of generality, the instantaneous kinematics of one member of the family of parallel manipulators generated by the reconfigurable parallel manipulator, the three-RPRRC + RRPRU nonredundant parallel manipulator with decoupled motions, is approached by means of the theory of screws. For the sake of completeness, the finite kinematics of the robot is also investigated. Numerical examples are included with the purpose to clarify the method of kinematic analysis.

Constraint Redundancy in Mobility of Parallel Manipulators

2008 ◽  
Author(s):  
Akhtar N. Malik ◽  
Jian S. Dai ◽  
Gordon R. Pennock
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Parallel Manipulators ◽  
The Other ◽  
Redundant Constraints ◽  
Parallel Platform ◽  
Number Synthesis ◽  
The Individual ◽  
Three Degree Of Freedom

This paper presents a systematic approach to obtain the degrees of freedom (DOF) of the platforms of parallel manipulators. The paper begins with general Kutzbach criterion for mobility. With simple mathematical transformations this criterion is modified to incorporate number of parallel legs used in the parallel platform-type mechanism and the number of joints in the legs. The theory of screws is used to study the freedom of the joints in the individual legs and the mobility of the platform. It is established that the general Kutzbach mobility criterion does not cater for situations where the freedom screws (or constraint screws) of the joints in a leg become dependent on the freedom screws (or constraint screws) of one or more of the other legs; thus, altering the mobility of the platform. The general modified Kutzbach mobility formula is further modified to resolve the problem of redundant constraints. The paper then provides a systematic approach towards the number synthesis of parallel platform-type mechanims. The paper includes three examples of such mechanisms analyzed by this approach. Results agree with the existing studies carried out on the mechanism used in the examples. A numerical example of a three-degree-of-freedom parallel manipulator with three legs is used to show the enumeration of all possible parallel manipulators. This includes cases with and without redundant constraints.

scholarly journals A Family of Kinematically Redundant Planar Parallel Manipulators

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Iman Ebrahimi ◽  
Juan A. Carretero ◽  
Roger Boudreau
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Redundant Manipulators ◽  
Kinematic Redundancy ◽  
Jacobian Matrices ◽  
Prismatic Joint ◽  
Different Types ◽  
High Payload ◽  
Planar Parallel Manipulators

Parallel manipulators feature relatively high payload and accuracy capabilities compared to their serial counterparts. However, they suffer from small workspace and low maneuverability. Kinematic redundancy for parallel manipulators can improve both of these characteristics. This paper presents a family of new kinematically redundant planar parallel manipulators with six actuated-joint degrees of freedom based on a 3-PṞRR architecture obtained by adding an active prismatic joint at the base of each limb of the 3-ṞRR manipulator. First, the inverse displacement of the manipulators is explained, then their reachable and dexterous workspaces are obtained. Comparing the proposed redundant manipulators to the original 3-ṞRR nonredundant manipulator, both reachable and dexterous workspaces are substantially larger. Next, the Jacobian matrices of the manipulators are derived, and different types of singularities are analyzed and demonstrated. It is shown that the vast majority of singularities can be avoided by using kinematic redundancy.

scholarly journals Pa<sup>2</sup> kinematic bond in translational parallel manipulators

2018 ◽  
Vol 9 (1) ◽  
pp. 25-39 ◽  
Author(s):  
Alfonso Hernández ◽  
Erik Macho ◽  
Mónica Urízar ◽  
Víctor Petuya ◽  
Zhen Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
The Other ◽  
Practical Application ◽  
Promising Alternative ◽  
Revolute Joints ◽  
Prismatic Joints

Abstract. The Pa2 pair is composed of two intertwined articulated parallelograms connecting in parallel two links of a kinematic chain. This pair has two translational degrees of freedom leading to a translational plane variable with the position. Currently, the Pa2 pair appears in conceptual designs presented in recent papers. However, its practical application is very limited. One of the reasons for this can be the high number of redundant constraints it has. But, it has to be considered that most of them can be eliminated by replacing wisely the revolute joints by spherical joints. On the other side, the structure of the Pa2 pair contributes to increase the global stiffness of the kinematic chain in which it is mounted. Also, its implementation is a promising alternative to the problematic passive prismatic joints. In this paper, the Pa2 pairs are used in the design of a 3 − P Pa2 parallel manipulator. The potentiality of this design is evaluated and proven after doing the following analyses: direct and inverse kinematics, singularity study, and workspace computation and assessment.

Computation of the safe working zones of Planar and Spatial Parallel Manipulators

Robotica ◽  
2019 ◽  
Vol 38 (5) ◽  
pp. 861-885 ◽  
Author(s):  
Murali K. Karnam ◽  
Aravind Baskar ◽  
Rangaprasad A. Srivatsan ◽  
Sandipan Bandyopadhyay
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Working Zone ◽  
Three Degrees Of Freedom ◽  
Safe Working Zone ◽  
Safe Working

SUMMARYThis paper presents the computation of the safe working zone (SWZ) of a parallel manipulator having three degrees of freedom. The SWZ is defined as a continuous subset of the workspace, wherein the manipulator does not suffer any singularity, and is also free from the issues of link interference and physical limits on its joints. The proposed theory is illustrated via application to two parallel manipulators: a planar 3-R̲RR manipulator and a spatial manipulator, namely, MaPaMan-I. It is also shown how the analyses can be applied to any parallel manipulator having three degrees of freedom, planar or spatial.

Mobility, Kinematic Analysis, and Dimensional Optimization of New Three-Degrees-of-Freedom Parallel Manipulator With Actuation Redundancy

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Lingmin Xu ◽  
Qinchuan Li ◽  
Ningbin Zhang ◽  
Qiaohong Chen
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Force Transmission ◽  
Transmission Index ◽  
Prismatic Joints ◽  
Redundantly Actuated ◽  
Force Transmissibility ◽  
Solution Velocity ◽  
Three Degrees Of Freedom

Parallel manipulators (PMs) with redundant actuation are attracting increasing research interest because they have demonstrated improved stiffness and fewer singularities. This paper proposes a new redundantly actuated parallel manipulator that has three degrees-of-freedom (DOFs) and four limbs. The proposed manipulator is a 2UPR-2PRU parallel manipulator (where P represents an actuated prismatic joint, R represents a revolute joint, and U represents a universal joint) that is actuated using four prismatic joints; two of these joints are mounted on the base to reduce the movable mass. Mobility analysis shows that the moving platform has two rotational DOFs and one translational DOF. First, the inverse displacement solution, velocity, and singularity analyses are discussed. Next, the local transmission index (LTI) and the good transmission workspace are used to evaluate the motion/force transmissibility of the 2UPR-2PRU parallel manipulator. Finally, the parameter-finiteness normalization method (PFNM) is used to produce an optimal design that considers the good transmission workspace. It is thus shown that the motion/force transmission of the proposed manipulator is improved by optimizing the link parameters.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

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