Position and Workspace Analyses of 3-SPR and 3-RPS Parallel Manipulators

2005 ◽  
Author(s):  
Yi Lu ◽  
Yonghe Zhao
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Analytic Formula ◽  
Analytic Approach ◽  
Work Space ◽  
Working Space ◽  
Computer Aided ◽  
Calculation Results ◽  
Position And Orientation ◽  
Orientation Workspace

An analytic approach and a simulation mechanism for solving position and the workspace of a 3-SPR parallel manipulator are proposed. First, a simulation mechanism of the 3-SPR parallel manipulator and a simulation mechanism of the 3-RPS parallel manipulator are created by using the computer aided geometry constraints and dimension-driving techniques. Second, some analytic formulas are derived for inverse and forward solving position and orientation of the 3-SPR parallel manipulator. Third, some available solutions from multi-solutions during deriving analytic formula are determined, and analytic inverse and forward solutions are verified by using simulation mechanisms. Finally, the workspace of the 3-SPR parallel manipulator is created and three key parameters for determining work space of two kinds of parallel manipulators are solved. Calculation results prove that the position working space of the 3-SPR parallel manipulator is much larger than that of the 3-RPS parallel manipulator, and the orientation workspace of the 3-SPR parallel manipulator is less than that of 3-RPS parallel manipulator.

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.

Orientation Workspace Analysis of a Novel 3SPS+1PS Symmetrical Parallel Manipulator Based on Unit Quaternion

2011 ◽  
Vol 201-203 ◽  
pp. 1849-1853
Author(s):  
Jing Li Yu ◽  
Gang Cheng ◽  
Shuai Zhang ◽  
De Kun Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Unit Quaternion ◽  
Structure Characteristics ◽  
Workspace Analysis ◽  
Moving Platform ◽  
Position And Orientation ◽  
4 Degrees Of Freedom ◽  
Orientation Workspace

For a novel 3SPS+1PS parallel manipulator with 4 degrees of freedom including three rotations and one translation, the formulae for solving the inverse kinematics equations are derived based on quaternion method. Unit quaternion is used to represent the position and orientation of moving platform, and the singularities caused by Euler angles are avoided. Combining the topological structure characteristics of the parallel manipulator, it only has three rotations when its moving platform is at a given translation position. Based on the inverse position/pose equations and the all the constraints of the parallel manipulator, the discrete algorithm for the orientation workspaces of 3SPS+1PS parallel manipulator where the moving platform is at some different given translation positions are designed. The research builds the theoretical basis for optimizing the orientation workspace with given position.

Forward Problem Singularities of Manipulators Which Become PS-2RS or 2PS-RS Structures When the Actuators Are Locked

2003 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Rigid Body ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
Forward Problem ◽  
End Effector ◽  
Kinematic Chains ◽  
Position And Orientation ◽  
Manipulator Design

The instantaneous forward problem (IFP) singularities of a parallel manipulator (PM) must be determined during the manipulator design and avoided during the manipulator operation, because they are configurations where the end-effector pose (position and orientation) cannot be controlled by acting on the actuators any longer, and the internal loads of some links become infinite. When the actuators are locked, PMs become structures consisting of one rigid body (platform) connected to another rigid body (base) by means of a number of kinematic chains (limbs). The geometries (singular geometries) of these structures where the platform can perform infinitesimal motion correspond to the IFP singularities of the PMs the structures derive from. This paper studies the singular geometries both of the PS-2RS structure and of the 2PS-RS structure. In particular, the singularity conditions of the two structures will be determined. Moreover, the geometric interpretation of their singularity conditions will be provided. Finally, the use of the obtained results in the design of parallel manipulators which become either PS-2RS or 2PS-RS structures, when the actuators are locked, will be illustrated.

A Three-DOF Rotational Parallel Manipulator Without Intersecting Axes

2010 ◽  
Author(s):  
Ziming Chen ◽  
Jingfang Liu ◽  
Zhen Huang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Revolute Joint ◽  
Rotational Motions ◽  
Orientation Workspace

It is difficult to manufacture parallel manipulators(PMs) with multiple revolute joint axes intersecting at one point. These types include the 3-DOF spherical parallel manipulators (SPMs), the 4-DOF 3R1T and 2R2T PMs, the 5-DOF 3R2T PMs. This problem makes it hard to achieve the expected mobility of these PMs. In this paper, a 3-RPS cubic PM is studied which has three rotational freedoms and no intersecting axes. The orientation workspace of this PM is analyzed. Some discussions about the differences between the traditional SPMs and this PM are proposed. The results show that the 3-RPS cubic PM can achieve three rotational motions and has no intersecting axes.

FORCE-UNCONSTRAINED POSES OF THE 3-PRR AND 4-PRR PLANAR PARALLEL MANIPULATORS

2005 ◽  
Vol 29 (4) ◽  
pp. 617-628 ◽  
Author(s):  
Flavio Firmani ◽  
Ron P. Podhorodeski
Keyword(s):  
Parallel Manipulator ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Task Space ◽  
Planar Parallel Manipulator ◽  
Order Polynomial ◽  
Position And Orientation ◽  
Planar Parallel Manipulators ◽  
Three Dimensional Space

Force-unconstrained (singular) poses of the 3-PRR planar parallel manipulator (PPM), where the underscore indicates the actuated joint, and the 4-PRR, a redundant PPM with an additional actuated branch, are presented. The solution of these problems is based upon concepts of reciprocal screw quantities and kinematic analysis. In general, non-redundant PPMs such as the 3-PRR are known to have two orders of infinity of force-unconstrained poses, i.e., a three-variable polynomial in terms of the task-space variables (position and orientation of the mobile platform). The inclusion of redundant branches eliminates one order of infinity of force-unconstrained configurations for every actuated branch beyond three. The geometric identification of force-unconstrained poses is carried out by assuming one variable for each order of infinity. In order to simplify the algebraic procedure of these problems, the assumed or “free” variables are considered to be joint displacements. For both manipulators, an effective elimination technique is adopted. For the 3-PRR, the roots of a 6th-order polynomial determine the force-unconstrained poses, i.e., surfaces in a three dimensional space defined by the task-space variables. For the 4-PRR, a 64th-order polynomial determines curves of force-unconstrained poses in the same dimensional space.

Kinematics and Workspace Analyses of 3/3-RRRS Parallel Manipulator

2012 ◽  
Vol 155-156 ◽  
pp. 1090-1095 ◽  
Author(s):  
Meng Si Liu ◽  
Yi Cao ◽  
Qiu Ju Zhang ◽  
Clément Gosselin ◽  
Jian Chun Sun ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Geometrical Method ◽  
Three Dimensional Model ◽  
Forward Displacement ◽  
Theoretical Results ◽  
Orientation Workspace ◽  
Forward Displacement Analysis ◽  
Equivalent Mechanism

It is known that two primary disadvantages of parallel manipulators are the complicated forward kinematics and limited workspace. This paper mainly addressed the kinematics and workspace analyses of a 3/3-RRRS 6-DOF parallel manipulator. After a brief introduction of the 3/3 -RRRS 6-DOF parallel manipulator, a three-dimensional model and its relevant structure diagram are constituted, the forward and inverse displacement analyses of the 3/3-RRRS parallel manipulator are discussed in detail, especially, a novel geometrical method referred as equivalent mechanism is proposed for the forward displacement analysis of the manipulator under consideration. Based on the displacement analyses of the manipulator, a discretization method is proposed for the computation of the reachable position/orientation workspace of the 3/3-RRRS parallel manipulator, respectively. Examples of a 3/3-RRRS parallel manipulator are given to demonstrate these theoretical results.

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.

Accuracy Analysis of Parallel Manipulators With Joint Clearance

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Jian Meng ◽  
Dongjun Zhang ◽  
Zexiang Li
Keyword(s):  
Parallel Manipulator ◽  
Optimization Problem ◽  
Parallel Manipulators ◽  
Joint Clearance ◽  
Error Prediction ◽  
Accuracy Analysis ◽  
Analysis Problem ◽  
Convex Optimization Problem ◽  
End Effector ◽  
Position And Orientation

Due to joint clearance, a parallel manipulator’s end-effector exhibits position and orientation (or collectively referred to as pose) errors of various degrees. This paper aims to provide a systematic study of the error analysis problem for a general parallel manipulator influenced by joint clearance. We propose an error prediction model that is applicable to planar or spatial parallel manipulators that are either overconstrained or nonoverconstrained. By formulating the problem as a standard convex optimization problem, the maximal pose error in a prescribed workspace can be efficiently computed. We present several numerical examples to show the applicability and the efficiency of the proposed method.

Evaluation of the Position Error of Four Non-Overconstrained Spherical Parallel Manipulators

2012 ◽  
Vol 162 ◽  
pp. 194-203
Author(s):  
A. Chaker ◽  
A. Mlika ◽  
M.A. Laribi ◽  
L. Romdhane ◽  
S. Zeghloul
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Position Error ◽  
Point Of View ◽  
Good Precision ◽  
End Effector ◽  
High Rigidity ◽  
Manufacturing Errors ◽  
Position And Orientation ◽  
Spherical Parallel Manipulator

The 3-RRR spherical parallel manipulator is known to be highly overconstrained, which causes several problems of mounting the mechanism, but has the advantage of having high rigidity thus a good precision. Several works in the literature proposed non-overconstrained versions of this mechanism. However, very few works dealt with the problem of the consequence of modifying an overconstrained mechanism into a non-overconstrained one, mainly from an accuracy point of view. In this work, we present an analysis of the accuracy of four different non-overconstrained SPMs, i.e., 3-RSR, 3-RCC, 3-RRS, and 3-RUU. These four SPM are then evaluated in translational and rotational accuracy due to manufacturing errors. The error on the position and orientation of the end-effector, due to manufacturing errors, are computed in 100 different configurations within their workspace. These SPMs are then compared among each other and we showed that the 3-RRS has the best compromise between the translational and rotational accuracy.

Accuracy of Four Parallel Manipulator

2013 ◽  
Vol 380-384 ◽  
pp. 567-571
Author(s):  
Shu Kui Han ◽  
Hua Li ◽  
Xu Dong
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Error Model ◽  
Mobile Platform ◽  
Position And Orientation ◽  
Source Errors

The Due to the error, parallel manipulators always exhibit some position and orientation errors at the mobile platform. The analysis of accuracy is carried out to find the source errors which affect the pose accuracy of the end-effecter in terms of the error model. The accuracy synthesis is implemented to obtain the geometry tolerance of the major parts affecting the uncompensable pose error. In order to finish these works, one method is proposed, which can also be used to handle the similar mechanism

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