A Geometric Constructive Approach for the Workspace Analysis of Symmetrical 5-PRUR Parallel Mechanisms (3T2R)

2010 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Mohammad Hossein Saadatzi ◽  
Cle´ment Gosselin ◽  
Hamid D. Taghirad
Keyword(s):  
Geometric Approach ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
End Effector ◽  
Workspace Analysis ◽  
Architecture Optimization ◽  
Insight Into ◽  
Orientation Workspace

This paper investigates an important kinematic property, the constant-orientation workspace, of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical limbs of the PRUR type. The general mechanism originates from the type synthesis performed for symmetrical 5-DOF parallel mechanism. In this study, the emphasis is placed on the determination of constant-orientation workspace using geometrical interpretation of the so-called vertex space, i.e., motion generated by a limb for a given orientation, rather than relying on classical recipes, such as discretization methods. For the sake of better understanding a CAD model is also provided for the vertex space. The constructive geometric approach presented in this paper provides some insight into the architecture optimization. Moreover, this approach facilitates the computation of the evolution of the volume of the constant-orientation workspace for different orientations of the end-effector.

Extending the workspace of parallel working mechanisms

2008 ◽  
Vol 222 (7) ◽  
pp. 1305-1313 ◽  
Author(s):  
H Alp ◽  
İ Özkol
Keyword(s):  
Material Processing ◽  
Flight Simulation ◽  
Parallel Mechanisms ◽  
Working Mechanism ◽  
Workspace Analysis ◽  
Cylindrical Coordinate ◽  
Robotic Applications ◽  
Orientation Workspace ◽  
Working Mechanisms

The aim of this study is to present a new model to extend the workspace of a parallel working machine in a chosen direction. Therefore, the existing mathematical models are combined and developed to represent the extension of the workspace of a 6° parallel working machine. For this purpose, the 6-3 Stewart platform mechanism (SPM), which is commonly used in robotic applications, material processing, and flight simulation, and the 6-4 SPM have been chosen. Although there are many studies on parallel mechanisms, the workspace analysis of a parallel working mechanism has not yet been generalized. This study determines the workspace of a parallel working mechanism in the direction perpendicular to the moving platform, which is the most workable direction. For these types of working mechanisms, i.e. mechanical tools used for material processing that is forced to move in a certain chosen direction, the determination of the point in that direction at which the workspace is maximum has to be outlined. After carrying out a kinematic analysis, the discretization method, which is based on Euler angles, is used to represent the orientation workspace of these parallel working mechanisms. Additionally, the orientation workspaces of the 6-3 SPM and the 6-4 SPM are compared. Results are presented in a cylindrical coordinate system.

An Optimization-Based Algorithm for Determination of Inclusive and Constant Orientation Workspace of Parallel Mechanisms

2009 ◽  
Author(s):  
Gholamreza Vossoughi ◽  
Soroosh Hassanpour ◽  
Amir Fazeli ◽  
Mehdi Paak
Keyword(s):  
Optimization Technique ◽  
Optimization Methods ◽  
Optimization Approach ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Boundary Determination ◽  
Spatial Parallel Mechanism ◽  
Forward Kinematic ◽  
Orientation Workspace

Workspace of a mechanism is generally defined as the region of space which end-effector of that mechanism can reach. Determination of workspace is an important task in the design of a mechanism. However, for parallel mechanisms, due to the complexity of solving the forward kinematic equations, determination of workspace is much more complicated than for serial mechanisms. In the literature, time-consuming numerical methods, such as point-by-point searching, are usually employed for this purpose. In this paper, an optimization-based algorithm is introduced for the boundary determination of inclusive and constant orientation workspaces of parallel mechanisms. In the proposed algorithm, thanks to applying the optimization approach along with point-by-point searching, the dimension of the point-by-point searched space (and hence, the consumed time) are significantly reduced. While different optimization methods can be used in the proposed algorithm, Particle Swarm Optimization is utilized as the optimization technique in this paper. The proposed algorithm is illustrated through its application to a planar and a spatial parallel mechanism.

Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system

Robotica ◽  
2014 ◽  
Vol 33 (08) ◽  
pp. 1686-1703 ◽  
Author(s):  
Mohammad Reza Chalak Qazani ◽  
Siamak Pedrammehr ◽  
Arash Rahmani ◽  
Behzad Danaei ◽  
Mir Mohammad Ettefagh ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
High Acceleration ◽  
Workspace Analysis ◽  
Rotation Symmetric ◽  
Cloud Of Points

SUMMARYParallel mechanisms possess several advantages such as the possibilities for high acceleration and high accuracy positioning of the end effector. However, most of the proposed parallel manipulators suffer from a limited workspace. In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced. Since parallel mechanisms have more workspace limitations compared to that of serial mechanisms, determination of the workspace in parallel manipulators is of the utmost importance. For finding position, angular velocity, and acceleration, in this paper, inverse and forward kinematics of the mechanism are studied and after presenting the workspace limitations, workspace analysis of the hexarot manipulator is performed by using MATLAB software. Next, using the obtained cloud of points from simulation, the overall borders of the workspace are illustrated. Finally, it is shown that this manipulator has the important benefits of combining a large positional workspace in relation to its footprint with a sizable range of platform rotations.

Determination of Maximal Singularity-Free Workspace of Parallel Mechanisms Using Constructive Geometric Approach

2013 ◽  
pp. 307-314
Author(s):  
Mohammad Hadi Farzaneh Kaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Behnam Mashhadi Gholamali
Keyword(s):  
Geometric Approach ◽  
Parallel Mechanisms ◽  
Maximal Singularity

Design and workspace analysis of a 3-degree-of-freedom parallel swivel head with large tilting capacity

2015 ◽  
Vol 231 (10) ◽  
pp. 1838-1849 ◽  
Author(s):  
Jiangzhen Guo ◽  
Dan Wang ◽  
Rui Fan ◽  
Wuyi Chen
Keyword(s):  
Machine Tool ◽  
Parallel Mechanism ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Spherical Joint ◽  
Hybrid Machine Tool ◽  
Tilting Angle ◽  
Workspace Analysis ◽  
Hybrid Machine ◽  
Orientation Workspace

Traditional parallel mechanisms are usually characterized by small tilting capability. To overcome this problem, a 3-degree-of-freedom parallel swivel head with large tilting capacity is proposed in this article. The proposed parallel swivel head, which is structurally developed from a conventional 3-PRS parallel mechanism, can achieve a large tilting capability by means of structural improvements. First, a modified spherical joint with a maximum tilting angle of ±120° is devised to diminish the physical restrictions on the orientation workspace. Second, a UPS typed leg is introduced for the sake of singularity elimination. The superiority of the proposed parallel swivel head is theoretically proved by investigations of singularity-free orientation workspace and then is experimentally validated using a prototype fabricated. The theoretical and experimental results illustrate that the proposed parallel swivel head has a large tilting capacity and thus can be used as swivel head for a hybrid machine tool which is designed to be capable of realizing both horizontal and vertical machining.

Kinematic Analysis and Design of Planar Parallel Mechanisms Actuated With Cables

2000 ◽  
Author(s):  
Guillaume Barrette ◽  
Clément M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Analysis And Design ◽  
Spring Mechanism

Abstract In this paper, we present a general and systematic analysis of planar parallel mechanisms actuated with cables. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is denned, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable sub-workspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Singularity Analysis of 5-RPRRR Parallel Mechanisms via Grassmann Line Geometry

2009 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Line Geometry ◽  
Singular Configurations ◽  
Highly Nonlinear ◽  
Grassmann Line Geometry

This paper investigates the singular configurations of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical legs of the RPUR type. The general mechanism was recently revealed by performing the type synthesis for symmetrical 5-DOF parallel mechanisms. In this study, some simplified designs are proposed for which the singular configurations can be predicted by means of the so-called Grassmann line geometry. This technique can be regarded as a powerful tool for analyzing the degeneration of the Plu¨cker screw set. The main focus of this contribution is to predict the actuation singularity, for a general and simplified design, without expanding the determinant of the inverse Jacobian matrix (actuated constraints system) which is highly nonlinear and difficult to analyze.

Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Guillaume Barrette ◽  
Cle´ment M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Two Dimensional ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Spring Mechanism

In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

On the Force Capabilities of Two-Degree-of-Freedom Planar Parallel Mechanisms Equipped With Torque Limiters

2013 ◽  
Author(s):  
Wei Chen ◽  
Clément Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Joint Torque ◽  
Design Stage ◽  
Parallel Mechanisms ◽  
Human Beings ◽  
Safety Index ◽  
End Effector ◽  
Two Degree Of Freedom ◽  
Insight Into

Safety is the most important issue that should be considered when designing collaborative robots that are intended to physically interact with humans. This paper investigates the force capabilities of two-degree-of-freedom planar parallel mechanisms that are equipped with torque limiters (safety clutches). Joint torque limiting devices are used in these mechanisms in order to limit the forces that the robot can apply to its environment. Such devices aim at ensuring the safety of the human beings interacting with the robot. However, because the torque-limiting devices are mounted at the joints of the robot, the end-effector force capabilities induced by these devices are dependent on the pose (Jacobian matrix) of the robot. Therefore, the characteristics of the torque limiting devices must be determined at the design stage in order to ensure safety and maximize effectiveness in all possible poses of the robot. Two types of planar two-degree-of-freedom parallel mechanisms are considered in this paper. Their architecture is first described. Then, the force capabilities are studied based on the Jacobian matrices. The maximum force that can be applied at the end-effector for given torque limits (safety index) is determined together with the maximum isotropic force (effectiveness) that can be produced. The ratio between these two forces, referred to as the force efficiency, can be considered as a performance index. Finally, some numerical results are proposed which can provide insight into the design of cooperation robots based on parallel architectures.

Design and Analysis of 3R2T and 3R3T Parallel Mechanisms With High Rotational Capability

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Congzhe Wang ◽  
Yuefa Fang ◽  
Sheng Guo
Keyword(s):  
Inverse Kinematics ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Velocity Analysis ◽  
Parallel Mechanisms ◽  
Workspace Analysis ◽  
Moving Platform ◽  
Displacement Theory ◽  
Lie Subgroup ◽  
Orientation Workspace

This paper describes the design, kinematics, and workspace analysis of 3R2T and 3R3T parallel mechanisms (PMs) with large rotational angles about three axes. Since the design of PMs with high rotational capability is still a challenge, we propose the use of a new nonrigid (or articulated) moving platform with passive joints in order to reduce the interference between limbs and the moving platform. According to the proposed nonrigid platform and Lie subgroup of displacement theory, several 3R2T and 3R3T PMs are presented. Subsequently, the inverse kinematics and velocity analysis of one of the proposed mechanisms are detailed. Based on the derived inverse kinematic model, the constant-orientation workspace is computed numerically. Then, the analysis of rotational capability about the three axes is performed. The result shows that even if interference and singularity are taken into account, the proposed mechanisms still reveal the high continuously rotational capability about the three axes, by means of actuation redundancy.

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