scholarly journals Optimal Design and Singularity Analysis of a Spatial Parallel Manipulator

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 551 ◽  
Author(s):  
Xiaoyong Wu
Keyword(s):  
Optimal Design ◽  
Mechanism Design ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Kinematic Model ◽  
Singularity Analysis ◽  
Singular Configurations ◽  
Simulation Results ◽  
Optimal Configurations

Optimal design and singularity analysis are two important aspects of mechanism design, and they are discussed within a spatial parallel manipulator in this work. Resorting to matrix transformation, the parametric kinematic model is established, upon which the inverse position and Jacobian are analyzed. As for optimal design, dexterity and payload indices are taken into consideration. From the simulation results, two optimal configurations are obtained, namely, the star-shaped one and the T-shaped one, and they respectively own the best payload performance and the best dexterity performance. Moreover, the concept of shape singularity is introduced and generalized, which is a special type of singularity that will lead to the singularity in all configurations. The shape singularity of the proposed manipulator is indicated by dexterity index and identified by screw theory. A case study is presented to demonstrate the implication of the shape singularity. Both optimal and singular configurations are useful, and new devices can thus be envisaged for this type of application.

Kinematic analysis of a novel 2(3-RUS) parallel manipulator

Robotica ◽  
2015 ◽  
Vol 34 (10) ◽  
pp. 2241-2256 ◽  
Author(s):  
Róger E. Sánchez-Alonso ◽  
José-Joel González-Barbosa ◽  
Eduardo Castillo-Castaneda ◽  
Jaime Gallardo-Alvarado
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Analytical Form ◽  
Planar Geometry ◽  
Moving Platform

SUMMARYThis paper introduces a novel 6-DOF parallel manipulator, which is composed of two 3-RUS parallel manipulators that share a common three-dimensional moving platform. Semi-analytical form solutions are easily obtained to solve the forward displacement analysis of the robot using the non-planar geometry of the moving platform, whereas the velocity, acceleration, and singularity analyses are performed using screw theory. A case study is included to show the application of the kinematic model, which is verified with the aid of a commercially available software. Simple kinematic analysis and reduced singular regions are the main benefits of the proposed parallel manipulator.

Optimal Design of the Three-Degree-of-Freedom Parallel Manipulator in a Spray-Painting Equipment

Robotica ◽  
2019 ◽  
Vol 38 (6) ◽  
pp. 1064-1081
Author(s):  
Guang Yu ◽  
Jun Wu ◽  
Liping Wang ◽  
Ying Gao
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
Optimization Design ◽  
Virtual Work ◽  
Kinematic Model ◽  
Geometrical Parameters ◽  
Parallel Mechanisms ◽  
Spray Painting ◽  
Conditioning Performance ◽  
Accuracy Performance

SUMMARYSpray-painting equipments are important for the automatic spraying of long conical objects such as rocket fairing. This paper proposes a spray-painting equipment that consists of a feed worktable, a gantry frame and two serial–parallel mechanisms and investigates the optimal design of PRR–PRR parallel manipulator in serial–parallel mechanisms. Based on the kinematic model of the parallel manipulator, the conditioning performance, workspace and accuracy performance indices are defined. The dynamic model is derived using virtual work principle and dynamic evaluation index is defined. The conditioning performance, workspace, accuracy performance and dynamic performance are involved in multi-objective optimization design to determine the optimal geometrical parameters of the parallel manipulator. Furthermore, the geometrical parameters of the gantry frame are optimized. An example is given to show how to determine these parameters by taking a long object with conical surface as painted object.

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.

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.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

Simplified Kinematics for a Parallel Manipulator Generator of the Schönflies Motion

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mohammad H. Abedinnasab ◽  
Daniel Lichtblau
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Kinematic Chain ◽  
Singularity Analysis ◽  
Input Output ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Novel Method ◽  
Schönflies Motion

This work is devoted to simplify the inverse–forward kinematics of a parallel manipulator generator of the 3T1R motion. The closure equations of the displacement analysis are formulated based on the coordinates of two points embedded in the moving platform. Afterward, five quadratic equations are solved by means of a novel method based on Gröbner bases endowed with first-order perturbation and local stability of parameters. Meanwhile, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that concern, the inclusion of pseudokinematic pairs connecting the limbs to the fixed platform and a passive kinematic chain to the robot manipulator allows to avoid the handling of rank-deficient Jacobian matrices. The workspace of the robot is determined by using a discretized method associated to its inverse–forward displacement analysis, whereas the singularity analysis is approached based on the input–output equation of velocity. Numerical examples are provided with the purpose to show the application of the method.

scholarly journals A Five-Bar Planar Parallel Manipulator with Two End-Effectors

2018 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Ramon Rodriguez-Castro ◽  
Luciano Perez-Gonzalez ◽  
Carlos R. Aguilar-Najera ◽  
Alvaro Sanchez-Rodriguez
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Intermediate Step ◽  
Euclidean Group ◽  
Planar Parallel Manipulator ◽  
Special Software ◽  
End Effectors ◽  
Klein Form

Parallel manipulators with multiple end-effectors bring us interesting advantages over conventional parallel manipulators such as improved manipulability, workspace and avoidance of singularities. In this work the kinematics of a five-bar planar parallel manipulator equipped with two end-effectors is approached by means of the theory of screws. As an intermediate step the displacement analysis of the robot is also investigated. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that regard the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) plays a central role. In order to exemplify the method of kinematic analysis, a case study is included. Furthermore, the numerical results obtained by means of the theory of screws are confirmed with the aid of special software like ADAMS.TM

Geometrical method to determine the reciprocal screws and applications to parallel manipulators

Robotica ◽  
2009 ◽  
Vol 27 (6) ◽  
pp. 929-940 ◽  
Author(s):  
Jianguo Zhao ◽  
Bing Li ◽  
Xiaojun Yang ◽  
Hongjian Yu
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Algebraic Manipulation ◽  
Robot Kinematics ◽  
Geometrical Approach ◽  
New Approach ◽  
Geometrical Relation ◽  
Manipulator Design

SUMMARYScrew theory has demonstrated its wide applications in robot kinematics and statics. We aim to propose an intuitive geometrical approach to obtain the reciprocal screws for a given screw system. Compared with the traditional Plücker coordinate method, the new approach is free from algebraic manipulation and can be used to obtain the reciprocal screws just by inspecting the structure of manipulator. The approach is based on three observations that describe the geometrical relation for zero pitch screw and infinite pitch screw. Based on the observations, the reciprocal screw systems of several common kinematic elements are analyzed, including usual kinematic pairs and chains. We also demonstrate usefulness of the geometrical approach by a variety of applications in mobility analysis, Jacobian formulation, and singularity analysis for parallel manipulator. This new approach can facilitate the parallel manipulator design process and provide sufficient insights for existing manipulators.

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