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.

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 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.

Inverse position analysis, workspace determination and position synthesis of parallel manipulators with 3-RSR topology

Robotica ◽  
2003 ◽  
Vol 21 (6) ◽  
pp. 627-632 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulators ◽  
End Effector ◽  
New Approach ◽  
Position Analysis ◽  
Starting Point ◽  
Inverse Position Analysis ◽  
The Common ◽  
Three Degree Of Freedom ◽  
Position Synthesis

Manipulators with 3-RSR topology are three-degree-of-freedom parallel manipulators that may be either spherical or mixed-motion manipulators. The inverse position analysis (IPA) and the workspace determination of 3-RSR manipulators are addressed by means of a new approach. The new approach is centered on a particular form of the closure equations called compatibility equations. The compatibility equations contain only the six coordinates (end-effector coordinates) which locates the end-effector pose (position and orientation) with respect to the frame, and the geometric constants of the manipulator. When the manipulator geometry is assigned, the common solutions of the compatibility equations are the end-effector coordinates which identify the end-effector poses belonging to the manipulator workspace. Moreover, they can be the starting point to easily solve the IPA. The presented compatibility equations can be also used to solve the position synthesis of the 3-RSR manipulator. This way of solving the position synthesis will demonstrate that only approximated solutions exist when more than eight end-effector poses are given.

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 Algorithm for the Determination of the Workspace of Complex Planar Kinematic Chains

1995 ◽  
Author(s):  
Pascal Lê-Huu ◽  
Clément M. Gosselin
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degree Of Freedom ◽  
Topological Graph ◽  
Kinematic Chains ◽  
Cartesian Space ◽  
Hybrid Manipulator ◽  
Three Degree Of Freedom ◽  
Two Degree Of Freedom

Abstract A new algorithm for the determination of the workspace of complex planar kinematic chains is presented in this paper. This algorithm is completely general since it can deal with any kind of topological graph and any set of parameters defined in a convention of notation. It uses the numerical solution of the inverse kinematics and is based on a wavefront expansion in the Cartesian space. Three examples are presented here, and lead to a dexterity mapping for two two-degree-of-freedom multi-loop manipulators and a three-degree-of-freedom hybrid manipulator.

Analytical Determination of Principal Twists and Singular Directions in Robot Manipulators

2003 ◽  
Author(s):  
Sandipan Bandyopadhyay ◽  
Ashitava Ghosal
Keyword(s):  
Degrees Of Freedom ◽  
Riemannian Metric ◽  
Degree Of Freedom ◽  
Body Motion ◽  
Inner Product ◽  
Analytical Determination ◽  
End Effector ◽  
Singular Configurations ◽  
Analytical Expressions

The identification of principal twists of the end-effector of a manipulator undergoing multi-degree-of-freedom motion is considered to be one of the central problems in kinematics. In this paper, we use dual velocity vectors to parameterize se(3), the space of twists, and define an inner product of two dual velocities as a dual number analog of a Riemannian metric on SE(3). We show that the principal twists can be obtained from the solution of an eigenvalue problem associated with this dual metric. It is shown that the computation of principal twists for any degree-of-freedom (DoF) of rigid-body motion, requires the solution of at most a cubic dual characteristic equation. Furthermore, the special nature of the coefficients yields simple analytical expressions for the roots of the dual cubic, and this in turn leads to compact analytical expressions for the principle twists. We also show that the method of computation allows us to separately identify the rotational and translational degrees-of-freedom lost or gained at singular configurations. The theory is applicable to serial, parallel, and hybrid manipulators, and is illustrated by obtaining the principal twists and singular directions for a 3-DoF parallel, and a hybrid 6-DoF manipulator.

Determination of singularities of some 4-DOF parallel manipulators by translational/rotational Jacobian matrices

Robotica ◽  
2009 ◽  
Vol 28 (6) ◽  
pp. 811-819 ◽  
Author(s):  
Yi Lu ◽  
Yan Shi ◽  
Jianping Yu
Keyword(s):  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Analytic Approach ◽  
Simple Process ◽  
Jacobian Matrices ◽  
Complicated Process

SUMMARYA novel analytic approach is proposed for determining the singularities of some four degree of freedom (DOF) parallel manipulators (PMs). First, the constraint and displacement of a general 4-DOF PM are analyzed. Second, a common 3 × 4 translational Jacobian matrix Jν and a common 3 × 4 rotational Jacobian matrix Jω are derived, and a 4 × 4 general Jacobian matrix J of the 4-DOF PMs is derived from Jν and Jω. Since a complicated process to determine singularities from the 4 × 6 Jacobian matrix is transformed into a simple process to determine singularity from J, the singularities of the some 4-DOF PMs with 3 translations and 1 rotation, or with 3 rotations and 1 translation, or with combined translation–rotations are analyzed and determined easily by this approach.

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.

Experimental Validation of a Three-Degree-of-Freedom Cable-Suspended Parallel Robot for Spatial Translation With Constant Orientation

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Dinh-Son Vu ◽  
Eric Barnett ◽  
Clément Gosselin
Keyword(s):  
Experimental Validation ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Proof Of Concept ◽  
Kinematic Modeling ◽  
End Effector ◽  
Cartesian Space ◽  
Positioning Errors ◽  
Kinematic Sensitivity ◽  
Three Degree Of Freedom

This paper shows an experimental validation for the design of a three-degree-of-freedom (DOF) cable-suspended parallel robot, which has six cables attached to the end-effector, arranged in three pairs, with each pair being driven by a single motor. For each pair, the moving platform attachment points and the winch cable guides on the fixed frame form a parallelogram, an arrangement that allows the end-effector to be positioned throughout its static workspace (SW) while maintaining a constant orientation. In this paper, the kinematic modeling of the robot is first described, along with its SW. Then, the robot's kinematic sensitivity is assessed in position and orientation such that an upper bound is found for the amplification of the cable positioning errors in Cartesian space. Finally, experimental results obtained using a proof-of-concept mechanism are described, which confirm the claim that the proposed design maintains a constant platform orientation in the SW.

Three-Degree-of-Freedom Parallel Robot Arm

2006 ◽  
Author(s):  
Martin Hosek ◽  
Michael Valasek ◽  
Jairo Moura
Keyword(s):  
Parallel Robot ◽  
Degree Of Freedom ◽  
Motion Path ◽  
Angular Orientation ◽  
Robot Arm ◽  
Flat Panel Display ◽  
End Effector ◽  
Cluster Tools ◽  
Manufacturing Applications ◽  
Three Degree Of Freedom

This paper presents single- and dual-end-effector configurations of a planar three-degree of freedom parallel robot arm designed for automated pick-place operations in vacuum cluster tools for semiconductor and flat-panel-display manufacturing applications. The basic single end-effector configuration of the arm consists of a pivoting base platform, two elbow platforms and a wrist platform, which are connected through two symmetric pairs of parallelogram mechanisms. The wrist platform carries an end-effector, the position and angular orientation of which can be controlled independently by three motors located at the base of the robot. The joints and links of the mechanism are arranged in a unique geometric configuration which provides a sufficient range of motion for typical vacuum cluster tools. The geometric properties of the mechanism are further optimized for a given motion path of the robot. In addition to the basic symmetric single end-effector configuration, an asymmetric costeffective version of the mechanism is derived, and two dual-end-effector alternatives for improved throughput performance are described. In contrast to prior attempts to control angular orientation of the end-effector(s) of the conventional arms employed currently in vacuum cluster tools, all of the motors that drive the arm can be located at the stationary base of the robot with no need for joint actuators carried by the arm or complicated belt arrangements running through the arm. As a result, the motors do not contribute to the mass and inertia properties of the moving parts of the arm, no power and signal wires through the arm are necessary, the reliability and maintenance aspects of operation are improved, and the level of undesirable particle generation is reduced. This is particularly beneficial for high-throughput applications in vacuum and particlesensitive environments.

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