Determination of the Workspace of 6-DOF Parallel Manipulators

1990 ◽  
Vol 112 (3) ◽  
pp. 331-336 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration in its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully parallel manipulator.

Determination of the Workspace of 6-DOF Parallel Manipulators

1989 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-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.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

An Efficient Algorithm for the Graphical Representation of the Three-Dimensional Workspace of Parallel Manipulators

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Eric Lavoie ◽  
Pierre Toutant
Keyword(s):  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Dimensional Representation ◽  
Efficient Procedure ◽  
Three Dimensional Representation ◽  
The Subject ◽  
Six Degree Of Freedom ◽  
Analytical Expressions

Abstract This paper presents an algorithm for the graphical representation of the three-dimensional workspace of six-degree-of-freedom parallel manipulators. In fact, the algorithm introduced here follows from previous work on the subject (Gosselin 1990). In the latter reference, an algorithm was developed to obtain analytical expressions of the boundaries of the workspace. However, the method was applicable to two-dimensional sections of the workspace only. Therefore, a three-dimensional representation of the workspace, i.e., the set of positions attainable with a given orientation of the platform, could only be obtained by discretization. The algorithm introduced here involves the determination of analytical expressions of the boundaries of the three-dimensional workspace. Hence, it results in a very efficient procedure which can be performed interactively, in a context of CAD. The algorithm is described in detail in this paper. Examples of results that have been obtained with this algorithm are also presented.

A New Method to Calculate the Force and Moment Workspaces of Actuation Redundant Spatial Parallel Manipulators

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Venus Garg ◽  
Juan A. Carretero ◽  
Scott B. Nokleby
Keyword(s):  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
New Method ◽  
Task Planning ◽  
Cartesian Space ◽  
Redundantly Actuated ◽  
Six Degree Of Freedom

A new method for obtaining the force and moment workspaces of spatial parallel manipulators (PMs) is presented. Force and moment workspaces are regions within which a manipulator can sustain/apply at least a certain value of force or moment in all directions. Here, the force and moment workspaces are found using a method, which explicitly sets the largest possible number of actuators to their maximum limits ensuring that the manipulator is performing at its best possible wrench capabilities. Two cases for obtaining these workspaces are used. The first gives the applicable/sustainable force with a prescribed moment whereas the second one gives the applicable/sustainable moment with a prescribed force. For illustration purposes, the method is applied to a six-degree-of-freedom (DOF) redundantly-actuated spatial PM, the 3-RRṞS. The results are represented graphically as the boundaries of the workspace in the three-dimensional Cartesian space. These workspaces can be used as a powerful tool for path/task planning and PM design.

Determination of the Workspace of Parallel Manipulators Using a CAD Software and the Concept of Virtual Chains

2013 ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Performance Indices ◽  
Workspace Analysis ◽  
Static Calculation

Development of a new parallel manipulator can be very time consuming due to the traditional method of producing kinematic, dynamic and static calculation models and then evaluating them to determine aspects of the manipulator’s performance indices such as the mechanism’s workspace and singularity analysis. By extending the virtual chain approach to the type synthesis of parallel manipulators, this paper proposes a virtual-chain approach to the workspace analysis of parallel manipulators. This method is illustrated by producing and evaluating the workspace of several parallel robots including the well known DELTA robot by utilising the three-dimensional CAD software SolidWorks to produce a virtual prototype of a manipulator with an embedded virtual chain. The virtual chain represents the motion pattern of a manipulator’s end-effector and is very useful in the production of a graphical representation of the workspace of the manipulator. Using this approach, the link interferences and transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

scholarly journals Classification of 3T1R Parallel Manipulators Based on Their Wrench Graph

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Semaan Amine ◽  
Ossama Mokhiamar ◽  
Stéphane Caro
Keyword(s):  
Projective Space ◽  
Parallel Manipulator ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Geometrical Properties ◽  
Cayley Algebra ◽  
Dimensional Projective Space ◽  
Grassmann Cayley Algebra

This paper presents a classification of 3T1R parallel manipulators (PMs) based on the wrench graph. By using the theory of reciprocal screws, the properties of the three-dimensional projective space, the wrench graph, and the superbracket decomposition of Grassmann–Cayley algebra, six typical wrench graphs for 3T1R parallel manipulators are obtained along with their singularity conditions. Furthermore, this paper shows a way in which each of the obtained typical wrench graphs can be used in order to synthesize new 3T1R parallel manipulator architectures with known singularity conditions and with an understanding of their geometrical properties and assembly conditions.

Optimization Design of a Spatial Six-Degree-of-Freedom Parallel Manipulator Based on Genetic Algorithms and Neural Networks

2008 ◽  
Author(s):  
Dan Zhang ◽  
Zhen Gao
Keyword(s):  
Neural Networks ◽  
Genetic Algorithms ◽  
Parallel Manipulator ◽  
Optimization Design ◽  
Optimal Solution ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Objective Functions ◽  
Kinetostatic Model ◽  
Six Degree Of Freedom

Optimizing the performances of parallel manipulators by adjusting the structure parameters can be a difficult and time-consuming exercise especially when the parameters are multifarious and the objective functions are too complex. Artificial intelligence approaches can be investigated as the effective criteria to address this issue. In this paper, genetic algorithms and artificial neural network are implemented as the intelligent optimization criteria of global stiffness and dexterity for spatial six degree-of-freedom (DOF) parallel manipulator. The objective functions of global stiffness and dexterity are calculated and deduced according to the kinetostatic model. Neural networks are utilized to model the solutions of performance indices. Multi-objective optimization is developed by Pareto-optimal solution. The effectiveness of the proposed methodology is proved by simulation.

Parallel Computational Algorithms for the Kinematics and Dynamics of Planar and Spatial Parallel Manipulators

1996 ◽  
Vol 118 (1) ◽  
pp. 22-28 ◽  
Author(s):  
C. M. Gosselin
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Novel Approach ◽  
Judicious Choice ◽  
Six Degree Of Freedom ◽  
Three Degree Of Freedom

This paper introduces a novel approach for the computation of the inverse dynamics of parallel manipulators. It is shown that, for this type of manipulator, the inverse kinematics and the inverse dynamics procedures can be easily parallelized. The result is a closed-form efficient algorithm using n processors, where n is the number of kinematic chains connecting the base to the end-effector. The dynamics computations are based on the Newton-Euler formalism. The parallel algorithm arises from a judicious choice of the coordinate frames attached to each of the legs, which allows the exploitation of the parallel nature of the mechanism itself. Examples of the application of the algorithm to a planar three-degree-of-freedom parallel manipulator and to a spatial six-degree-of-freedom parallel manipulator are presented.

Kinematics and dynamics of a six-degree-of-freedom parallel manipulator with revolute legs

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 385-394 ◽  
Author(s):  
Kourosh E. Zanganeh ◽  
Rosario Sinatra ◽  
Jorge Angeles
Keyword(s):  
Computer Simulation ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Displacement Velocity ◽  
Kinematics And Dynamics ◽  
Cartesian Space ◽  
Moving Platforms ◽  
Proposed Model ◽  
Six Degree Of Freedom

This paper presents the kinematics and dynamics of a six-degree-of-freedom platform-type parallel manipulator with six revolute legs, i.e. each leg consists of two links that are connected by a revolute joint. Moreover, each leg is connected, in turn, to the base and moving platforms by means of universal and spherical joints, respectively. We first introduce a kinematic model for the manipulator under study. Then, this model is used to derive the kinematics relations of the manipulator at the displacement, velocity and acceleration levels. Based on the proposed model, we develop the dynamics equations of the manipulator using the method of the natural orthogonal complement. The implementation of the model is illustrated by computer simulation and numerical results are presented for a sample trajectory in the Cartesian space.

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