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.

Jacobian Analysis of a Fully Decoupled Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Central Point ◽  
Special Structure ◽  
Jacobian Matrices ◽  
Singular Configurations ◽  
Reachable Workspace

This paper presents the Jacobian analysis of a parallel manipulator that has a fully decoupled 4-DOF remote center-of-motion for application in minimally invasive surgery. Owing to the special structure of the manipulator, the Jacobian matrix of the manipulator is expressed as a combination of three special Jacobian matrices, namely the Jacobian of motion space, Jacobian of constraints, and Jacobian of actuations. Based on these Jacobian matrices, the singular configurations of the manipulator are then identified. It shows that the configuration singularity only exists at the central point and the boundary of the reachable workspace of the manipulator.

scholarly journals Workspace Delineation of Cable-Actuated Parallel Manipulators

2004 ◽  
Author(s):  
Ethan Stump ◽  
Vijay Kumar
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Extensive Literature ◽  
Reachable Workspace ◽  
Planar Parallel Manipulator ◽  
Analytic Expressions

While there is extensive literature available on parallel manipulators in general, there has been much less attention given to cable-driven parallel manipulators. In this paper, we address the problem of analyzing the reachable workspace using the tools of semi-definite programming. We build on earlier work [1, 2] done using similar techniques by deriving limiting conditions that allow us to compute analytic expressions for the boundary of the reachable workspace. We illustrate this computation for a planar parallel manipulator with four actuators.

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.

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.

Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator

1999 ◽  
Vol 122 (4) ◽  
pp. 439-446 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Sameer Joshi
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Structural Characteristics ◽  
Translational Motion ◽  
Parallel Manipulators ◽  
Condition Index ◽  
Mirror Image ◽  
Geometric Conditions ◽  
Design Variables ◽  
Opposite Limb

The structural characteristics associated with parallel manipulators are investigated. Using these characteristics a class of 3 degree-of-freedom parallel manipulators are enumerated. Several parallel manipulators with only translational degrees of freedom are identified and the 3-UPU parallel manipulator is chosen for design analysis and optimization. The kinematics of this 3-UPU parallel manipulator is studied. Two geometric conditions that lead to pure translational motion of the moving platform are described. Due to the simple kinematic structure, the inverse kinematics yields two equal and opposite limb lengths whereas the direct kinematics produces two possible manipulator postures with one being the mirror image of the other. The Jacobian matrix is derived and several singular conditions are discussed. Furthermore the conditions for existence of an isotropic point within the workspace are discussed and equations to compute the isotropic configurations of a 3-UPU manipulator are derived. Finally, we undertake architecture optimization and show that certain values of design variables maximize the global condition index of the 3-UPU manipulator. [S1050-0472(00)01404-5]

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.

scholarly journals SINGULARITY ANALYSIS OF A 3-PRRR KINEMATICALLY REDUNDANT PLANAR PARALLEL MANIPULATOR

1970 ◽  
Vol 41 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Soheil Zarkandi
Keyword(s):  
Motion Control ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Redundant Manipulators ◽  
Static Behavior ◽  
Singular Configurations ◽  
Planar Parallel Manipulator ◽  
And Control ◽  
Planar Parallel Manipulators

Finding Singular configurations (singularities) is one of the mandatory steps during the design and control of mechanisms. Because, in these configurations, the instantaneous kinematics is locally undetermined that causes serious problems both to static behavior and to motion control of the mechanism. This paper addresses the problem of determining singularities of a 3-PRRR kinematically redundant planar parallel manipulator by use of an analytic technique. The technique leads to an input –output relationship that can be used to find all types of singularities occurring in this type of manipulators.Key Words: Planar parallel manipulators; Redundant manipulators; Singularity analysis; Jacobian matrices.DOI: 10.3329/jme.v41i1.5356Journal of Mechanical Engineering, Vol. ME 41, No. 1, June 2010 1-6

Direct Singular Positions of 3RPS Parallel Manipulators

2004 ◽  
Vol 126 (6) ◽  
pp. 1006-1016 ◽  
Author(s):  
C. H. Liu ◽  
Shengchia Cheng
Keyword(s):  
Circular Cylinder ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Second Step ◽  
Horizontal Position ◽  
Solid Cylinder ◽  
Singular Configurations ◽  
Solid Circular Cylinder ◽  
Moving Platform

In this study a procedure to obtain direct singular positions of a 3RPS parallel manipulator is presented. If the heights of three spherical joints, denoted by d1n,d2n, and d3n respectively, are used as coordinate axes, then the workspace of the moving platform may be represented as an inclined solid cylinder in this coordinate system. The location of a point on the solid circular cylinder determines a configuration of the manipulator’s moving platform. The procedure to locate direct singular positions consists of two steps, the orientation of the moving platform is assumed first, from which the horizontal position of the moving platform may be obtained. Then in the second step the heights that make determinant of the Jacobian matrix vanish may always be determined. Results show that unless the moving platform is normal to the base, in which case there exist only one or two singular configurations, otherwise there are always three singular configurations corresponding to a moving platform’s orientation.

A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Xin-Jun Liu ◽  
Chao Wu ◽  
Jinsong Wang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Challenging Problem ◽  
Performance Indices ◽  
New Approach ◽  
Singular Configurations ◽  
Different Types ◽  
Force Transmissibility ◽  
Singular Configuration

Singularity analysis is one of the most important issues in the field of parallel manipulators. An approach for singularity analysis should be able to not only identify all possible singularities but also explain their physical meanings. Since a parallel manipulator is always out of control at a singularity and its neighborhood, it should work far from singular configurations. However, how to measure the closeness between a pose and a singular configuration is still a challenging problem. This paper presents a new approach for singularity analysis of parallel manipulators by taking into account motion/force transmissibility. Several performance indices are introduced to measure the closeness to singularities. By using these indices, a uniform “metric” can be found to represent the closeness to singularities for different types of nonredundant parallel manipulators.

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