On the Properties and the Determination of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms

2004 ◽  
Author(s):  
Marc Gouttefarde ◽  
Cle´ment M. Gosselin
Keyword(s):  
Detailed Analysis ◽  
Graphical Representation ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Conic Sections ◽  
Moving Platform ◽  
Three Degree Of Freedom ◽  
Disconnected Sets

This paper presents a detailed analysis of the constant-orientation wrench-closure workspace of planar three-degree-of-freedom parallel mechanisms driven by four cables. The constant-orientation wrench-closure workspace is defined as the subset of the plane wherein, for a given orientation of the moving platform, any planar wrench applied on the moving platform can be balanced by the cable-driven mechanism. Based on mathematical observations, this workspace is proved to be the union of two disconnected sets that may or may not exist. Moreover, if the constant-orientation wrench-closure workspace (WCW) exists, its boundary is shown to be composed of portions of conic sections. Then, an algorithm that determines the constant-orientation wrench-closure workspace by means of a graphical representation of its boundary is introduced. Several examples are also included.

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.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

WRENCH-CLOSURE WORKSPACE OF SIX-DOF PARALLEL MECHANISMS DRIVEN BY 7 CABLES

2005 ◽  
Vol 29 (4) ◽  
pp. 541-552 ◽  
Author(s):  
Marc Gouttefarde ◽  
Clément M. Gosselin
Keyword(s):  
Cross Sections ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Six Dof ◽  
Moving Platform ◽  
Six Degree Of Freedom

The wrench-closure workspace (WCW) of six-degree-of-freedom (DOF) parallel cable-driven mechanisms is defined as the set of poses of the moving platform of the mechanism for which any external wrench can be balanced by tension forces in the cables. This workspace is fundamental in order to analyze and design parallel cable-driven mechanisms. This paper deals with the class of six-DOF mechanisms driven by seven cables. Two theorems, which provide efficient means to test whether a given pose of the moving platform belongs to the WCW, are proposed. One of these two theorems reveals the nature of the boundary of the constant-orientation cross sections of the WCW. Moreover, some of the possible applications of these theorems are discussed and illustrated.

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.

Dynamic Balancing of Multi-Degree-of-Freedom Parallel Mechanisms With Multiple Legs

2004 ◽  
Author(s):  
Yangnian Wu ◽  
Cle´ment M. Gosselin
Keyword(s):  
Numerical Simulations ◽  
Degree Of Freedom ◽  
Effective Algorithm ◽  
Parallel Mechanisms ◽  
Dynamic Balancing ◽  
Dynamic Equivalence ◽  
Moving Platforms ◽  
Moving Platform

This paper systematically presents an effective algorithm for the dynamic balancing of multi-degree-of-freedom parallel mechanisms with multiple legs and the dynamic equivalence between point masses and arbitrary moving platforms. The mass and inertia of the moving platform are replaced by point masses located at the points of attachment of the legs to the platform and the mechanisms are balanced by considering each of the legs independently. The validity and feasibility of this algorithm is first verified both theoretically and using numerical simulations in ADAMS. Two, three and four point masses are respectively discussed for different cases. Finally, some reactionless planar and spatial multi-degree-of-freedom parallel mechanisms synthesized based on this algorithm are given.

A Family of Novel Lower-Mobility Decoupled Parallel Mechanisms

2007 ◽  
Author(s):  
Daxing Zeng ◽  
Sijun Zhu ◽  
Zhen Huang
Keyword(s):  
Real Time ◽  
Basic Feature ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Real Time Control ◽  
Motion Feature ◽  
Time Control ◽  
Fixed Base ◽  
Lower Mobility ◽  
Moving Platform

This paper presents a family of novel lower-mobility decoupled parallel mechanisms (DPMs), which consists of one 5-DOF (degree of freedom) DPM, two 4-DOF DPMs, three 3-DOF DPMs, and three 2-DOF DPMs. The basic feature of this family is that the moving platform and the fixed base of the DPMs are connected by two limbs and the motion of the moving platform is fully decoupled. Then the constraint screw method is used to analyze the motion feature of all DPMs presented in this paper. The mobility of these DPMs has also been calculated by the Modified Grubler-Kutzbach criterion. All the DPMs in this paper are simple and no computation is required for real-time control.

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