On the Singularities of DELTA Parallel Robots

2015 ◽  
Vol 762 ◽  
pp. 125-130
Author(s):  
Luciana Cristina Dudici ◽  
Ion Simionescu
Keyword(s):  
Jacobian Matrix ◽  
Equation System ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Jacobian Determinant ◽  
Transformation Matrices ◽  
Geometric Conditions ◽  
Major Disadvantage ◽  
Analysis Equation

The major disadvantage of the parallel robot is that the singular positions are comprised into the work space. The singular positions are the particular poses for parallel robot DELTA where the mobility of the structure is not longer zero when the actuators are locked. Present analysis is focused on the determinant value of the Jacobian matrix of the kinematic analysis equation system, written using Denavit – Hartenberg transformation matrices. The kinematic equations possess the algebraic and trigonometric character, so that the inverse singularity analysis can be formulated. By instantaneous mobility analysis of the moving platform of the parallel robots, the geometric conditions for the forward singularity configurations are identified. Finally, a numerical example is solved in order to illustrate the variation of the Jacobian determinant in the proximity of a singular position.

Singularity Analysis of a Plane-Symmetry 3-RPS Parallel Robot Based on Translational/Rotational Jacobian Matrices

2011 ◽  
Vol 121-126 ◽  
pp. 1590-1594
Author(s):  
Yan Shi ◽  
Hong Xin Yue ◽  
Yi Lu ◽  
Lian He Guo
Keyword(s):  
Jacobian Matrix ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
New Method ◽  
Plane Symmetry ◽  
Jacobian Matrices ◽  
Different Types

Firstly, 3-DOF parallel robots were classified into different types from the view of moving form. A new method of analyzing the singularity of 3-DOF parallel robots was introduced, which is based on translational Jacobian matrix and rotational Jacobian matrix. The singularity of parallel robots with pure translational form and pure rotational form was introduced summarily. Secondly, the process of solving the plane-symmetry 3-RPS parallel robot with combined moving forms was focused on, through which translational Jacobian matrix and rotational Jacobian matrix were adopted. Finally, the solving results were compared with the axis-symmetry 3-RPS parallel robot, which showed more general singularity can be solved through the new method.

Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

2003 ◽  
Author(s):  
Hee-Byoung Choi ◽  
Atsushi Konno ◽  
Masaru Uchiyama
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Loop Structure ◽  
Singular Configurations ◽  
Planning And Control ◽  
Kinematic Singularities ◽  
And Control

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

scholarly journals Design and Analysis of a Novel Schönflies Motion Parallel Robot with Full Cycle Rotation

2021 ◽  
Author(s):  
Luquan Li ◽  
Yuefa Fang ◽  
Lin Wang ◽  
Jiaqiang Yao
Keyword(s):  
Complex Dynamics ◽  
Virtual Work ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
The Novel ◽  
Scara Robot ◽  
Pick And Place ◽  
Place Task ◽  
Schönflies Motion

Abstract Due to the complex structures of multi-limbed parallel robots, conventional parallel robots generally have limited workspace, complex kinematics, and complex dynamics, which increases the application difficulty of parallel robot in industrial engineering. To solve the above problems, this paper proposes a single-loop Schönflies motion parallel robot with full cycle rotation, the robot can generate Schönflies motion by the most simplified structure. The novel Schönflies motion parallel robot is a two-limb parallel mechanism with least links and joints, and each limb is driven by a 2-degree of freedom (DOF) cylindrical driver (C-driver). The full cycle rotation of the output link is achieved by “…R-H…” structure, where the revolute (R) and helical (H) joints are coaxial. Mobility, kinematics, workspace and singularity analysis of novel Schönflies motion parallel robot are analyzed. Then, dynamic model is formulated based on the principle of virtual work. Moreover, a pick-and-place task is implemented by proposed Schönflies motion parallel robot and a serial SCARA robot, respectively. The simulation results verify the correctness of the theoretical model. Furthermore, dynamics performances of Schönflies motion parallel robot and serial SCARA robot are compared, which reveal the performance merits of proposed Schönflies motion parallel robot.

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.

scholarly journals Kinematics, Workspace, and Singularity Analysis of a Parallel Robot With Five Operation Modes

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Damien Chablat ◽  
Xianwen Kong ◽  
Chengwei Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Rotation Axis ◽  
Operation Mode ◽  
Parallel Robot ◽  
Joint Space ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Operation Modes ◽  
Serial Chain ◽  
Kinematic Study

Most multimode parallel robots can change operation modes by passing through constraint singularities. This paper deals with a comprehensive kinematic study of a three degrees-of-freedom (DOF) multimode three-PRPiR parallel robot developed at Heriot-watt University. This robot is able to reach several operation modes without crossing any constraint singularity by using lockable Pi and R joints. Here, a Pi joint may act as a 1DOF planar parallelogram if its lockable P (prismatic) joint is locked or a 2DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation mode and four 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation mode are dealt with in detail. The joint space and workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. It is shown that the robot is able to change assembly mode in one operation mode by passing through another operation mode.

High-order singularities of 5R planar parallel robots

Robotica ◽  
2018 ◽  
Vol 37 (2) ◽  
pp. 233-245 ◽  
Author(s):  
Mustafa Özdemir
Keyword(s):  
Time Derivative ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Research Field ◽  
Parallel Robots ◽  
High Order ◽  
Inverse Dynamic ◽  
Active Research ◽  
Order Parallel

SUMMARYSingularity analysis of parallel manipulators is an active research field in robotics. The present article derives for the first time in the literature a condition under which a five-bar parallel robot encounters high-order parallel singularities. In this regard, by focusing on the planar 5R mechanism, a theorem is given in terms of the slope of its coupler curve at the parallel singular configurations. At high-order parallel singularities, the associated determinant vanishes simultaneously with at least its first-order time derivative. The determination of such singularities is quite important since in their presence, some special conditions should be satisfied for bounded inverse dynamic solutions.

Numerical Framework and Design Optimization of an Intrinsically Compliant 3-DOF Parallel Robot

2020 ◽  
Vol 21 (2) ◽  
Author(s):  
Shahid Hussain ◽  
Prashant K. Jamwal ◽  
Akim Kapsalyamov ◽  
Mergen H. Ghayesh
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Simultaneous Optimization ◽  
Design Synthesis ◽  
Pneumatic Muscle ◽  
Nonlinear Motion ◽  
Strength Pareto Evolutionary Algorithm ◽  
Muscle Actuators

Abstract Parallel robots are multiple degrees of freedom (DOFs) systems that are typically used in applications characterized by enhanced accuracy, rigidity, and large force requirements within a compact workspace. In the present research, an intrinsically compliant parallel robot with 3-DOFs, actuated using four pneumatic muscle actuators (PMA), is conceptualized, developed, and analyzed. Despite many benefits, parallel robots also offer certain challenges that arise from the highly coupled and nonlinear motion of their actuators. The small workspace of parallel robots has many singularities and solving a closed-form forward kinematics (FK) for its end-effector motion is complicated. The PMAs can provide intrinsically compliant robotic motions, however, since they are flexible, their unilateral actuation also poses constraints on the achievable DOFs. The present research focuses on analyzing kinematics and dynamics of the developed parallel robot incorporating the stiffness together with force closure analyses besides suggesting design improvements as a consequence of the singularity analysis. Design synthesis and multi-criteria optimization have been performed to obtain a robot design which may provide higher accuracies (near unity condition number), quick response to external wrench (stiffness and rigidity), and reduced actuator force requirements. SPEA2 (Improved Strength Pareto Evolutionary Algorithm) has been implemented to carry out the simultaneous optimization of design objectives and provide Pareto optimal design solutions.

One Novel Isoconstrained Parallel Robot With Schoenflies-Motion

2013 ◽  
Author(s):  
Po-Chih Lee
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Point Of View ◽  
Universal Joint ◽  
Small Motion ◽  
Robot Architecture ◽  
Pick And Place ◽  
Pick And Place Operation

The coupling between two opposite bars of the hinged parallelogram produces relative 1-DoF circular translation and the opposite bars can move but remain parallel. From the point of view of kinematics, a hinged parallelogram is equivalent to a prismatic pair for a small motion. On the basis of a special parallel mechanism with the limb architecture of type CPUh (C and P denote cylindrical and prismatic pairs; Uh indicates the pseudo-universal-joint having one revolute and one screw pairs with the intersecting axes), we provide one novel Schoenflies-motion isoconstrained CPaUh//CPaUh robot with only two limbs having the hinged parallelograms for the fast pick-and-place operation of the assembly and packaging applications. This type of robot is compact for not only its structure but also its actuation. The robot architecture and kinematics including inverse and forward solutions are studied. In addition, Jacobian matrix, singularity analysis and workspace are further discussed. It is hoped that the evaluations of such two-limb parallel mechanism can be useful for possible application in industry where pick-and-place motion and higher accuracy are required.

Kinematic Design of a New Four Degree-of-Freedom Parallel Robot for Knee Rehabilitation

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Jokin Aginaga ◽  
Xabier Iriarte ◽  
Aitor Plaza ◽  
Vicente Mata
Keyword(s):  
Vertical Plane ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Degree Of Freedom ◽  
Mobile Platform ◽  
Rehabilitation Robots ◽  
Knee Rehabilitation ◽  
Wide Range ◽  
Lower Mobility

Rehabilitation robots are increasingly being developed in order to be used by injured people to perform exercise and training. As these exercises do not need wide range movements, some parallel robots with lower mobility architecture can be an ideal solution for this purpose. This paper presents the design of a new four degree-of-freedom (DOF) parallel robot for knee rehabilitation. The required four DOFs are two translations in a vertical plane and two rotations, one of them around an axis perpendicular to the vertical plane and the other one with respect to a vector normal to the instantaneous orientation of the mobile platform. These four DOFs are reached by means of two RPRR limbs and two UPS limbs linked to an articulated mobile platform with an internal DOF. Kinematics of the new mechanism are solved and the direct Jacobian is calculated. A singularity analysis is carried out and the gained DOFs of the direct singularities are calculated. Some of the singularities can be avoided by selecting suitable values of the geometric parameters of the robot. Moreover, among the found singularities, one of them can be used in order to fold up the mechanism for its transportation. It is concluded that the proposed mechanism reaches the desired output movements in order to carry out rehabilitation maneuvers in a singularity-free portion of its workspace.

scholarly journals Kinematics, Workspace and Singularity Analysis of a Multi-Mode Parallel Robot

2017 ◽  
Author(s):  
Damien Chablat ◽  
Xianwen Kong ◽  
Chengwei Zhang
Keyword(s):  
Rotation Axis ◽  
Operation Mode ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Revolute Joints ◽  
Operation Modes ◽  
Serial Chain ◽  
Motion Modes ◽  
Workspace Analysis

A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity analysis of a 3-PRPiR parallel robot involving lockable Pi and R (revolute) joints. Here a Pi joint may act as a 1-DOF planar parallelogram if its lockable P (prismatic) joint is locked or a 2-DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation modes to three 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation modes are dealt with in detail. The workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. A prototype built at Heriot-Watt University is used to illustrate the results of this work.

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