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.

Direct Singular Positions of 3RPS Parallel Manipulators

2004 ◽  
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 3 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 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.

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.

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.

Dimensionally Homogeneous Jacobian and Condition Number

2016 ◽  
Vol 836 ◽  
pp. 42-47 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Performance Analysis ◽  
Condition Number ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Moving Platform ◽  
Conditioning Number

This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f ≤6) parallel manipulators having coupled rotational and translational motions. By using the f independent coordinates to define the permitted motions and (6-f) independent coordinates to define the restricted motions of the moving platform, the 6×6 dimensionally homogeneous extended Jacobian matrix is derived for non-redundant parallel manipulators. The conditioning number of the parallel manipulators is computed to evaluate the homogeneous extended Jacobian matrix, the homogeneous actuation wrench matrix, and the homogeneous constraint wrench matrix to evaluate the performance of the parallel manipulators. By using these indices, the closeness of a pose to different singularities can be detected. An illustrative example with the 3-RPS parallel manipulator is provided to highlight the effectiveness of the approach and the proposed indices.

Design and analysis of CICABOT: a novel translational parallel manipulator based on two 5-bar mechanisms

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 449-456 ◽  
Author(s):  
M. F. Ruiz-Torres ◽  
E. Castillo-Castaneda ◽  
J. A. Briones-Leon
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Geometric Analysis ◽  
Vector Equation ◽  
Prismatic Joints ◽  
Hollow Cylinders ◽  
Moving Platform ◽  
Direct Kinematics

SUMMARYThis work presents the CICABOT, a novel 3-DOF translational parallel manipulator (TPM) with large workspace. The manipulator consists of two 5-bar mechanisms connected by two prismatic joints; the moving platform is on the union of these prismatic joints; each 5-bar mechanism has two legs. The mobility of the proposed mechanism, based on Gogu approach, is also presented. The inverse and direct kinematics are solved from geometric analysis. The manipulator's Jacobian is developed from the vector equation of the robot legs; the singularities can be easily derived from Jacobian matrix. The manipulator workspace is determined from analysis of a 5-bar mechanism; the resulting workspace is the intersection of two hollow cylinders that is much larger than other TPM with similar dimensions.

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.

Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator

2006 ◽  
Vol 129 (6) ◽  
pp. 611-616 ◽  
Author(s):  
Pierre-Luc Richard ◽  
Clément M. Gosselin ◽  
Xianwen Kong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Quadratic Equation ◽  
Design Stage ◽  
Forward Displacement ◽  
Singular Configurations ◽  
The Family ◽  
Moving Platform ◽  
Forward Displacement Analysis

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Schönflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations, and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.

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 geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 511-520 ◽  
Author(s):  
Kefei Wen ◽  
TaeWon Seo ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Singular Configurations ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

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