Constraint Singularities of Force Transmission in Nonredundant Parallel Robots With Less Than Six Degrees of Freedom

2003 ◽  
Vol 125 (3) ◽  
pp. 557-563 ◽  
Author(s):  
Matteo Zoppi ◽  
Luca E. Bruzzone ◽  
Rezia M. Molfino ◽  
Rinaldo C. Michelini
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Robots ◽  
Numerical Results ◽  
Structural Behavior ◽  
Force Transmission ◽  
Constraint Force ◽  
Six Degrees Of Freedom ◽  
Local Properties ◽  
Delta Robot

The analysis of the workspace singularities is one of the fundamental aspects in the design of parallel robots. The architecture singularities are generally studied analysing the local properties of the Jacobian matrix. Nevertheless, for limited-DOF parallel robots, there is a category of singularities (constraint or constructive singularities), relating to the constraint force transmission, which are not described by this matrix. This paper deals with a general approach to the analysis of these singularities, used in the synthesis of a Linear Delta robot to suitably modify its geometry, remarkably improving the structural behavior. Details and numerical results are provided.

Dynamic Analysis of a Biglide Parallel Grinder

2005 ◽  
Vol 291-292 ◽  
pp. 495-500
Author(s):  
Ping Zou
Keyword(s):  
Machine Tool ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Lagrangian Formulation ◽  
Dynamic Equations ◽  
Six Degrees Of Freedom ◽  
Moving Platform ◽  
Drill Point ◽  
Joint Velocity

In this paper, the moving platform of the biglide parallel grinder with six degrees of freedom will keep moving horizontally at any time using parallelograms. Besides grinding the helical drill point, this grinder also can work as drilling and welding machine tool as well as a CMM. The joint-velocity Jacobian matrix is calculated. Moreover, the dynamic equations are derived by applying the Lagrangian formulation.

Experimental identification of the dynamics model for 6-DOF parallel manipulators

Robotica ◽  
2009 ◽  
Vol 28 (3) ◽  
pp. 359-368 ◽  
Author(s):  
Houssem Abdellatif ◽  
Bodo Heimann
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Automatic Tuning ◽  
Data Filtering ◽  
Dynamics Model ◽  
Likelihood Estimator ◽  
Six Degrees Of Freedom ◽  
Experimental Identification ◽  
Dynamics Identification

SUMMARYThe paper presents a self-contained approach for the dynamics identification of six degrees of freedom (DOF) parallel robots. Major feature is the consequent consideration of structural properties of such machines to provide an experimentally adequate identification method. The known periodic excitation is modified and enhanced to take the actuator coupling as well as the numerical solution of the direct kinematics into account. The benefits of explicit frequency-domain data filtering are demonstrated. Additionally, a new implementation of the maximum-likelihood estimator allows for automatic tuning of the data filter. The issue of optimal input experiment design is also discussed and substantiated with extensive experiments.

Gateway Configuration for Rapid Pick-and-Place Operations of 2-Degrees-of-Freedom Parallel Robots

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Andrea Martin-Parra ◽  
David Rodriguez-Rosa ◽  
Sergio Juarez-Perez ◽  
Guillermo Rubio-Gomez ◽  
Antonio Gonzalez-Rodriguez ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Robots ◽  
End Effector ◽  
Joint Coordinates ◽  
Pick And Place ◽  
Low Energy Consumption ◽  
Simulation Results ◽  
The Difference

Abstract This article presents a new assembling for 2 degrees-of-freedom (DOFs) parallel robots for executing rapid pick-and-place operations with low energy consumption. A conventional design of 2-DOF parallel robots is based on five-bar mechanisms. Collisions between links are highly possible, restricting the end-effector workspace and/or increasing the trajectory time to avoid collisions. In this article, an alternative assembling for preventing collisions is presented. This novel assembling allows exploring the difference between the four five-bar mechanism configurations for the same position of the end-effector. Some of these configurations yield to lower time and/or lower energy consumption for the same motorization. First, a dynamic model of the robot has been developed using matlab® and simulink® and validated by comparison with the results obtained by adams® software. A robust cascade PD regulator for controlling joint coordinates has been tuned providing a high accurate end-effector positioning. Finally, simulation results of four configurations are presented for executing controlled maneuvers. The obtained results demonstrate that the conventional configuration is the worst one in terms of trajectory time or energy consumption and, conversely, the best one corresponds to an uncommonly used configuration. A workspace map where all configurations provide faster maneuvers has been obtained in terms of Jacobian matrix and mechanism elbows distance. The results presented here allow designing a rapid manipulator for pick-and-place operations.

Fully-Isotropic T1R2-Type Parallel Robots With Three Degrees of Freedom

2005 ◽  
Author(s):  
Grigore Gogu
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Velocity Space ◽  
Linear Transformations ◽  
Matrix Mapping ◽  
Joint Velocity ◽  
First Time ◽  
Three Degrees Of Freedom

The paper presents singularity-free fully-isotropic T1R2-type parallel manipulators (PMs) with three degrees of freedom. The mobile platform has one independent translation (T1) and two rotations (R2). A method is proposed for structural synthesis of fully-isotropic T1R2-type PMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic T1R2-type PMs presented in this paper is the 3x3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, this paper presents for the first time in the literature solutions of singularity-free T1R2-type PMs with decoupled an uncoupled motions, along with the fully-isotropic solutions.

Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed-Loop Subchains

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Kristan Marlow ◽  
Mats Isaksson ◽  
Jian S. Dai ◽  
Saeid Nahavandi
Keyword(s):  
Performance Measures ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Force Transmission ◽  
Six Degrees Of Freedom ◽  
Lower Mobility ◽  
Transmission Ability

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input–output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism.

Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot

Robotica ◽  
2012 ◽  
Vol 31 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Yongjie Zhao
Keyword(s):  
Performance Evaluation ◽  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
End Effector ◽  
Transmission Index ◽  
Delta Robot ◽  
Singular Configuration ◽  
Velocity Transmission

SUMMARYPerformance evaluation of a parallel robot is a multicriteria problem. By taking Delta robot as an object of study, this paper presents the kinematic performance evaluation of a three translational degrees-of-freedom parallel robot from the viewpoint of singularity, isotropy, and velocity transmission. It is shown that the determinant of a Jacobian matrix cannot measure the distance from the singular configuration due to the existing inverse kinematic singularity of a Delta robot. The determinants of inverse and direct kinematic Jacobian matrices are adopted for the measurement of distance from the singular configuration based on the theory of numerical linear dependence. The denominator of the Jacobian matrix will be lost in the computation of the condition number when the end-effector is on the centerline of the workspace, so the Delta robot may also be nearly at a singular configuration when the condition number of the Jacobian matrix is equal to 1. The velocity transmission index whose physical meaning is the maximum input angular velocity when the end-effector translates in the unit velocity is presented. The evaluation of singularity, isotropy, and velocity transmission of a Delta robot is investigated by simulation. The velocity transmission index can also be used for the velocity transmission evaluation of a parallel robot with pure rotational degrees-of-freedom based on the principle of similarity. The physical meaning is modified to be the maximum input velocity when the end-effector rotates in the unit angular velocity.

Six degrees of freedom parallel robots with C5 links

Robotica ◽  
1992 ◽  
Vol 10 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Y. Amirat ◽  
F. Artigue ◽  
J. Pontnau
Keyword(s):  
Automotive Industry ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Parallel Architecture ◽  
Parallel Robot ◽  
Parallel Architectures ◽  
Parallel Robots ◽  
Left Hand ◽  
Six Degrees Of Freedom ◽  
Assembly Tasks

SummaryThis paper presents at first a static and kinematic analysis of closed chains mechanisms which permits to deduce different possible fully parallel architectures. Then we focus on a particular parallel architecture with C5 links designed to perform precise assembly tasks. A general modeling of this C5 parallel robot is presented. Two typical assembly tasks in the automotive industry are also proposed; the first one uses the C5 links parallel robot as a left-hand device, while the second one uses it as the terminal tool of a sequential manipulator.

scholarly journals Geometric Interpretation of the Derivatives of Parallel Robots’ Jacobian Matrix With Application to Stiffness Control

2003 ◽  
Vol 125 (1) ◽  
pp. 33-42 ◽  
Author(s):  
N. Simaan ◽  
M. Shoham
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Geometric Interpretation ◽  
Parallel Robots ◽  
Redundant Robot ◽  
Moving Platforms ◽  
Stiffness Control ◽  
Derivatives Of ◽  
Direct Kinematics

This paper presents a closed-form formulation and geometrical interpretation of the derivatives of the Jacobian matrix of fully parallel robots with respect to the moving platforms’ position/orientation variables. Similar to the Jacobian matrix, these derivatives are proven to be also groups of lines that together with the lines of the instantaneous direct kinematics matrix govern the singularities of the active stiffness control. This geometric interpretation is utilized in an example of a planar 3 degrees-of-freedom redundant robot to determine its active stiffness control singularity.

Jacobian Analysis of Limited-DOF Parallel Manipulators

2002 ◽  
Vol 124 (2) ◽  
pp. 254-258 ◽  
Author(s):  
Sameer A. Joshi ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Six Degrees Of Freedom

This paper presents a methodology for the Jacobian analysis of limited degrees-of-freedom (DOF) parallel manipulators. A limited-DOF parallel manipulator is a spatial parallel manipulator which has less than six degrees-of-freedom. It is shown that a 6×6 Jacobian matrix, which provides information about both architecture and constraint singularities, can be derived by making use of the theory of reciprocal screws. The 3-UPU and 3-RPS parallel manipulators are used as examples to demonstrate the methodology.

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