scholarly journals On the Dynamic Properties of Flexible Parallel Manipulators in the Presence of Type 2 Singularities

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Sébastien Briot ◽  
Vigen Arakelian
Keyword(s):  
Optimal Control ◽  
Parallel Manipulator ◽  
Dynamic Properties ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Inverse Dynamic ◽  
Suggested Approach ◽  
Singular Configurations ◽  
Optimal Force

In the present paper, we expand information about the conditions for passing through Type 2 singular configurations of a parallel manipulator. It is shown that any parallel manipulator can cross the singular configurations via an optimal control permitting the favorable force distribution, i.e., the wrench applied on the end-effector by the legs and external efforts must be reciprocal to the twist along with the direction of the uncontrollable motion. The previous studies have proposed the optimal control conditions for the manipulators with rigid links and flexible actuated joints. The different polynomial laws have been obtained and validated for each examined case. The present study considers the conditions for passing through Type 2 singular configurations for the parallel manipulators with flexible links. By computing the inverse dynamic model of a general flexible parallel robot, the necessary conditions for passing through Type 2 singular configurations are deduced. The suggested approach is illustrated by a 5R parallel manipulator with flexible elements and joints. It is shown that a 16th order polynomial law is necessary for the optimal force generation. The obtained results are validated by numerical simulations carried out using the software ADAMS.

scholarly journals On the Dynamic Properties of Rigid-Link Flexible-Joint Parallel Manipulators in the Presence of Type 2 Singularities

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Sébastien Briot ◽  
Vigen Arakelian
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Dynamic Properties ◽  
Experimental Tests ◽  
Parallel Manipulators ◽  
Flexible Joints ◽  
Rigid Link ◽  
Pass Through

In our previous work (2008, “Optimal Force Generation in Parallel Manipulators for Passing through the Singular Positions,” Int. J. Robot. Res., 27(8), pp. 967–983), the dynamic properties of rigid-link parallel manipulators, in the presence of type 2 singularities, have been studied. It was shown that any parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts of the manipulator are orthogonal to the twist along the direction of the uncontrollable motion. This condition was obtained using the symbolic approach based on the inverse dynamics and the study of the Lagrangian of a general rigid-link parallel manipulator. It was validated by experimental tests carried out on the prototype of a four-degrees-of-freedom parallel manipulator. However, it is known that the flexibility of the mechanism may not always be neglected. Indeed, joint flexibility is the main source contributing to the overall manipulator flexibility and it leads to the trajectory distortion. Therefore, in this paper, the condition for passing through a type 2 singularity of parallel manipulators with flexible joints is studied. The suggested technique is illustrated by the example of a 5R parallel manipulator with flexible joints. It is shown that passing through singularity is possible if the 12th-order polynomial trajectory planning is applied. The obtained results are validated by the numerical simulations carried out using the ADAMS software.

scholarly journals On the Dynamic Properties of Flexible Parallel Manipulators in the Presence of Payload and Type 2 Singularities

2010 ◽  
Author(s):  
Sebastien Briot ◽  
Vigen Arakelian
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Dynamic Properties ◽  
Experimental Tests ◽  
Parallel Manipulators ◽  
Rigid Link ◽  
Singular Configuration ◽  
Pass Through

It is known that a parallel manipulator at a singular configuration can gain one or more degrees of freedom and become uncontrollable. In our recent work [1], the dynamic properties of rigid-link parallel manipulators, in the presence of Type 2 singularities, have been studied. It was shown that any parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts is orthogonal to the twist along the direction of the uncontrollable motion. This condition was obtained using symbolic approach based on the inverse dynamics and the study of the Lagrangian of a general rigid-link parallel manipulator. It was validated by experimental tests carried out on the prototype of a four-degrees-of-freedom parallel manipulator. However, it is known that the flexibility of the mechanism may not always been neglected. Indeed, for robots, joint flexibility can be the main source contributing to overall manipulator flexibility and can lead to trajectory distortion. Therefore, in our second paper [2], the condition of passing through a Type 2 singularity for parallel manipulators with flexible joints has been studied. In the present paper, we expand information about the dynamic properties of parallel manipulators in the presence of Type 2 singularity by including in the studied problem the link flexibility and the payload. The suggested technique is illustrated by a 5R parallel manipulator with flexible elements (actuated joints and moving links) and a payload. The obtained results are validated by numerical simulations carried out using the software ADAMS.

scholarly journals Internal redundancy: an approach to improve the dynamic parameters around sharp corners

2013 ◽  
Vol 4 (1) ◽  
pp. 233-242 ◽  
Author(s):  
S. S. Parsa ◽  
J. A. Carretero ◽  
R. Boudreau
Keyword(s):  
Parallel Manipulator ◽  
Dynamic Properties ◽  
Dynamic Performance ◽  
Parallel Manipulators ◽  
Variable Geometry ◽  
Centre Of Mass ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Planar Parallel Manipulator ◽  
Sharp Corners

Abstract. In recent years, redundancy in parallel manipulators has been studied broadly due to its capability of overcoming some of the drawbacks of parallel manipulators including small workspaces and singular configurations. Internal redundancy, first introduced for serial manipulators, refers to the concept of adding movable masses to some links so as to allow to control the location of the centre of mass and other dynamic properties of some links. This concept has also been referred to as variable geometry. This paper investigates the effects of internal redundancy on the dynamic properties of a planar parallel manipulator while performing a family of trajectories. More specifically, the 3-RRR planar manipulator, where a movable mass has been added to the distal link, is allowed to trace trajectories with rounded corners and different radii. The proposed method uses the manipulator's dynamic model to actively optimise the location of the redundant masses at every point along the trajectory to improve the dynamic performance of the manipulator. Numerical examples are shown to support the idea.

Improving Motion Stability of the Plane 3-RPR Parallel Manipulator at Singular Configuration

2018 ◽  
Author(s):  
Yu-Tong Li ◽  
Yu-Xin Wang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Angular Speed ◽  
Motion Stability ◽  
Singular Configurations ◽  
Movable Platform ◽  
Singular Configuration ◽  
Translation Type ◽  
External Forces ◽  
Gerschgorin Circle

Kinematic parameters have significant influences on the motion stability of parallel manipulators at singular configureations. Taking the plane 3-RPR parallel manipulator as an example, the motion stability at different types of singular configurations corresponding to the angular speed and velocity of the movable platform are investigated. At first, the second order of uncoupled dynamics equation for the 3-RPR parallel manipulator is established with the aid of the second class Lagrange approach. According to the Lyapunov first approximate stability criterion, the approximate conditions for the 3-RPR parallel manipulator with a stabile motion at singular configurations are determined based on the Gerschgorin circle theorem. Next, the exact Hurwitz criterion is utilized to study the motion stability and the load capability of the manipulator corresponding to the angular speed and velocity of the movable platform, as well as the directions of the external forces at two kinds of singular configurations: with a gained rotation-type DOF, and with a gained translation-type DOF, respectively. The results show that increasing both the angular speed and the velocity of the mass center of the movable platform can efficiently improve the motion stability of the 3-RPR parallel manipulator at singular configurations.

A new family of spherical parallel manipulators

Robotica ◽  
2002 ◽  
Vol 20 (4) ◽  
pp. 353-358 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
End Effector ◽  
Singular Configurations ◽  
New Family ◽  
Geometric Conditions ◽  
Singularity Locus ◽  
The Given ◽  
Spherical Parallel Manipulator ◽  
Spherical Motion

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

Study on the Parallel Modeling of Spatial Parallel Manipulator

2012 ◽  
Vol 472-475 ◽  
pp. 2096-2099
Author(s):  
Wen Jun Liu ◽  
Yu Feng Luo ◽  
Mei Tao Fu
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Modeling Approach

The modeling approach of spatial parallel manipulator has been extensively studied based on the SOC theory in this paper. According to the characteristics of the parallel robot mechanism’s , ideas and general methods of spatial parallel manipulator modeling in parallel has been proposed and typical spatial mechanism’s modeling has been performed. Study shows that the parallel modeling approach can dramatically increase the modeling and solving efficiency for parallel manipulators.

Dynamic Performance With Control of a 2DOF Parallel Robot

2012 ◽  
Author(s):  
Gianmarc Coppola ◽  
Dan Zhang ◽  
Kefu Liu ◽  
Zhen Gao
Keyword(s):  
Dynamic Model ◽  
Performance Index ◽  
Parallel Manipulator ◽  
Dynamic Performance ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Performance Study ◽  
Linear Controller ◽  
Reachable Workspace ◽  
And Control

In this work the dynamic performance and control of a 2DOF parallel robot is conducted. The study is partly motivated by large variations in dynamic performance and control within the reachable workspace of many parallel manipulators. The forward dynamic model of the robot is derived in detail. The connection method is directly utilized for this derivation. Subsequently, a dynamic performance study is undertaken. This reveals important information whilst using a forward dynamic model. A performance index is proposed to determine the variability of performance of the parallel manipulator. Then a trajectory-tracking scenario is undertaken using a linear controller. By means of control, the simulations illustrate the validity of the proposed index for parallel manipulators.

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-Free Taskspace Optimization of 6-RSS Mechanisms

2009 ◽  
Author(s):  
Hao Li ◽  
Yuru Zhang ◽  
Yi Yang
Keyword(s):  
Design Of Experiment ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Optimization Process ◽  
Singular Configurations ◽  
Reachable Workspace ◽  
Design Variables ◽  
Structured Optimization

A method to calculate the volume of constant-orientation taskspace of parallel manipulators is developed and applied on the 6-RSS mechanism as an example. The taskspace is defined as a singularity-free reachable workspace. Quasi-singularity measure is used to measure the closeness to singular configurations and construct the quasi-singularity zone. Analyzed by DOE (Design of Experiment), effect weighs of design variables of a parallel manipulator are revealed and experiment results are applied in the optimization process. In order to obtain the maximum taskspace, the volume of the constant-orientation taskspace is optimized by a structured optimization process aided by iSIGHT-FD software. Finally, constant-orientation taskspace of greater volume is obtained.

Dynamic Modeling of Parallel Manipulators

1996 ◽  
Author(s):  
Ivan J. Baiges ◽  
Joseph Duffy
Keyword(s):  
Dynamic Response ◽  
Parallel Manipulator ◽  
Coupling Effect ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
High Degree ◽  
Degree Of Coupling ◽  
Explicit Equations Of Motion

Abstract The dynamic response is an important consideration when designing and controlling manipulators. This dynamic response can be better understood with the explicit equations of motion. This paper presents the derivation of the explicit equations of motion for a parallel manipulator using Kane’s Method. These equations illustrate the high degree of coupling existing in this type of manipulator. A simulation program is developed with the equations of motion and used for the inverse dynamic analysis of the system. The results of the tests indicate that the most important coupling effect is caused by gravity.

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