Optimum design of a 4-PSS-PU redundant parallel manipulator based on kinematics and dynamics

2015 ◽  
Vol 230 (13) ◽  
pp. 2273-2284 ◽  
Author(s):  
Liping Wang ◽  
Binbin Zhang ◽  
Jun Wu
Keyword(s):  
Optimum Design ◽  
Parallel Manipulator ◽  
Design Space ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Search Method ◽  
Kinematics And Dynamics ◽  
Performance Indices ◽  
Maximum Acceleration ◽  
High Acceleration

This paper presents an optimum design of a 4-PSS-PU redundant parallel manipulator by taking the workspace, conditioning performance, and acceleration into account. On the basis of rank of the Jacobian matrix, a method to directly find out the workspace is presented, rather than the search method. Based on the dynamic model, a maximum acceleration index is defined. The corresponding atlases of these performance indices are represented graphically in the established design space. Based on these atlases, the optimum design is performed and the optimum region is determined. It is expected to realize the high acceleration of parallel manipulators by using the optimum method.

Optimum design of 3-RRR planar parallel manipulators

2010 ◽  
Vol 224 (2) ◽  
pp. 411-418 ◽  
Author(s):  
Runliang Dou
Keyword(s):  
Optimum Design ◽  
Design Space ◽  
Jacobian Matrix ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Stiffness Index ◽  
Geometrical Parameters ◽  
Dimensional Parameter ◽  
Planar Parallel Manipulators

This article deals with the optimum design of 3-RRR planar parallel manipulators. Based on the kinematic model and Jacobian matrix, the global conditioning index, global velocity index and global stiffness index of 3-RRR parallel manipulators are investigated. The corresponding atlases are represented graphically in the established design space, and the geometrical parameters without dimension are determined. An example is presented to achieve the optimum dimensional parameter based on the optimum non-dimensional result. The result of this article is not only useful for the development of 3-RRR planar parallel manipulators, but also helpful for the optimum design of other parallel manipulators.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Jun Wu ◽  
Binbin Zhang ◽  
Liping Wang
Keyword(s):  
Dynamic Model ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Maximum Acceleration ◽  
Virtual Work Principle ◽  
Joint Force ◽  
Joint Forces ◽  
Three Degrees Of Freedom

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.

scholarly journals Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Clément Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Constraint Analysis ◽  
Fixed Direction ◽  
Geometric Singularity ◽  
Grassmann Geometry ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction (3T1R). Eleven architectures obtained from a recent type synthesis of such manipulators are analyzed. The constraint analysis shows that these architectures are all overconstrained and share some common properties between the actuation and the constraint wrenches. The singularities of such manipulators are examined through the singularity analysis of the 4-RUU parallel manipulator. A wrench graph representing the constraint wrenches and the actuation forces of the manipulator is introduced to formulate its superbracket. Grassmann–Cayley Algebra is used to obtain geometric singularity conditions. Based on the concept of wrench graph, Grassmann geometry is used to show the rank deficiency of the Jacobian matrix for the singularity conditions. Finally, this paper shows the general aspect of the obtained singularity conditions and their validity for 3T1R parallel manipulators with identical limb structures.

Unified Solving Jacobian∕Hessian Matrices of Some Parallel Manipulators With n SPS Active Legs and a Passive Constrained Leg

2006 ◽  
Vol 129 (11) ◽  
pp. 1161-1169 ◽  
Author(s):  
Yi Lu ◽  
Bo Hu
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Simple Approach ◽  
Spherical Joint ◽  
Load Bearing ◽  
Prismatic Joint ◽  
First Order ◽  
Partial Differentiation

Some parallel manipulators with n spherical joint-prismatic joint-spherical joint (SPS)-type active legs and a passive constrained leg possess a larger capability of load bearing and are simple in structure of the active leg. In this paper, a unified and simple approach is proposed for solving Jacobian∕Hessian matrices and inverse∕forward velocity and acceleration of this type of parallel manipulators. First, a general parallel manipulator with n SPS-type active legs and one passive constrained leg in various possible serial structure is synthesized, and some formulae for solving the poses of constrained force∕torque and active∕constrained force matrix are derived. Second, the formulae for solving extension of active legs, the auxiliary velocity∕acceleration equation are derived. Third, the formulae for solving inverse∕forward velocity and acceleration and a Jacobian matrix without the first-order partial differentiation and a Hessian matrix without the second-order partial differentiation are derived. Finally, the procedure is applied to three parallel manipulators with four and five SPS-type active legs and one passive constrained leg in different serial structures and to illustrate.

Two Natural Dexterity Indices for Parallel Manipulators: Angularity and Axiality

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
J. Jesús Cervantes-Sánchez ◽  
J. M. Rico-Martínez ◽  
V. H. Pérez-Muñoz
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Mobile Platform ◽  
Angular Velocity Vector ◽  
Motion Sensitivity ◽  
Physical Insight ◽  
Dimensionally Homogeneous Jacobian Matrix ◽  
The One ◽  
General Motion

This paper introduces two novel dexterity indices, namely, angularity and axiality, which are used to estimate the motion sensitivity of the mobile platform of a parallel manipulator undergoing a general motion involving translation and rotation. On the one hand, the angularity index can be used to measure the sensitivity of the mobile platform to change in rotation. On the other hand, the axiality index can be used to measure the sensitivity of the operation point (OP) of the mobile platform to change in translation. Since both indices were inspired by very fundamental concepts of classical kinematics (angular velocity vector and helicoidal velocity field), they offer a clear and simple physical insight, which is expected to be meaningful to the designer of parallel manipulators. Moreover, the proposed indices do not require obtaining a dimensionally homogeneous Jacobian matrix, nor do they depend on having similar types of actuators in each manipulator's leg. The details of the methodology are illustrated by considering a classical parallel manipulator.

An Effective Approach to Model Parallel Robots With Flexible Links

2021 ◽  
Author(s):  
Brillarelli Stefano ◽  
Matteo-Claudio Palpacelli
Keyword(s):  
Software Architecture ◽  
Parallel Manipulator ◽  
Path Following ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Flexible Links ◽  
Model Based Control ◽  
High Acceleration ◽  
Control Schemes ◽  
Pick And Place

Abstract This paper is focused on the development of an effective hardware and software architecture that is useful to improve the performance of slender parallel manipulators. The latter can perform high acceleration in fast pick and place applications, but their features can be also exploited in more advanced operations, where path following is a central issue. A simple and effective approach to model the elastodynamic behavior of flexible parallel manipulator is proposed, conceived to be fast and easy to implement in model-based control schemes. Moreover, a workbench architecture based on camera acquisitions is essential to calibrate the elastodynamic model and provide all the required information that are needed to improve path following of flexible mechanims.

Kinematics and Singularity Analysis of the Hexaglide Parallel Robot

2008 ◽  
Author(s):  
Mansour Abtahi ◽  
Hodjat Pendar ◽  
Aria Alasty ◽  
Gholamreza Vossoughi
Keyword(s):  
Machine Tools ◽  
Parallel Manipulator ◽  
High Speed ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
The Past ◽  
Different Types ◽  
Forward Kinematic

In the past few years, parallel manipulators have become increasingly popular in industry, especially, in the field of machine tools. Hexaglide is a 6 DOF parallel manipulator that can be used as a high speed milling machine. In this paper, the kinematics and singularity of Hexaglide parallel manipulator are studied systematically. At first, this robot has been modeled and its inverse and forward kinematic problems have been solved. Then, formulas for solving inverse velocity are derived and Jacobian matrix is obtained. After that, three different types of singularity for this type of robot have been investigated. Finally a numerical example is presented.

Singularity Elimination of Stewart Parallel Manipulator Based on Redundant Actuation

2010 ◽  
Vol 143-144 ◽  
pp. 308-312 ◽  
Author(s):  
Yi Cao ◽  
Hui Zhou ◽  
Bao Kun Li ◽  
Shen Long ◽  
Meng Si Liu
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Singular Value ◽  
Kinematics And Dynamics ◽  
Redundant Actuation ◽  
Numerical Examples ◽  
Singular Configurations ◽  
Parallel Platform ◽  
Singular Configuration

This paper mainly addresses the principle of the singularity elimination of the Stewart parallel platform. By adding appropriate redundant actuation, the rank of the Jacobian matrix of the parallel platform is always full, accordingly the singular value of the Jacobian matrix of the parallel platform is nonzero. Then the singular configuration of the parallel platform can be eliminated by adding one redundant actuation. Numerical examples are taken to illuminate the principle’s effectiveness. It is shown that not only singular configurations of the Stewart parallel platform can be eliminated, but also performances of kinematics and dynamics of the parallel platform can be greatly perfected by adding appropriate redundant actuation.

Sensitivity Analysis of Planar Parallel Manipulators

2008 ◽  
Author(s):  
Ste´phane Caro ◽  
Nicolas Binaud ◽  
Philippe Wenger
Keyword(s):  
Sensitivity Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Sensitivity Coefficients ◽  
Planar Parallel Manipulator ◽  
Moving Platform ◽  
Conditioning Number ◽  
Planar Parallel Manipulators

This paper deals with the sensitivity analysis of planar parallel manipulators. A methodology is introduced to derive the sensitivity coefficients by means of the study of 3-RPR manipulators. As a matter of fact, the sensitivity coefficients of the pose of its moving platform to variations in the geometric parameters are expressed algebraically, the variations being defined both in Polar and Cartesian coordinates. The dexterity of the manipulator is also studied by means of the conditioning number of its normalized kinematic Jacobian matrix. As an illustrative example, the sensitivity of a symmetrical planar parallel manipulator is analyzed in detail. Finally, the accuracy of the manipulator is compared with its dexterity.

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