Performance Analysis and Optimal Design of a 3-DOF 3-PRUR Parallel Mechanism

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Daxing Zeng ◽  
Zhen Huang ◽  
Wenjuan Lu
Keyword(s):  
Optimal Design ◽  
Performance Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Performance Indices ◽  
Geometrical Characteristics

In this paper, a 3-DOF 3-PRUR parallel mechanism (PM) is chosen for performance analysis and optimal design. First, the mobility of the PM is analyzed by using screw theory. Then, the kinematics of this PM is studied based on the geometrical characteristics and the Jacobian matrix is derived. Furthermore, we research some performance indices with respect to the Jacobian matrix over the whole workspace and nondimensional parameters when the input is given, and their performance atlases are obtained with different inputs. Finally, the optimal design of the PM is determined according to the performance atlases, and some examples are presented.

Singularity-Free Workspace Aimed Optimal Design of a 2T2R Parallel Mechanism for Automated Fiber Placement

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Rehan Umer ◽  
Lakmal Seneviratne
Keyword(s):  
Optimal Design ◽  
Condition Number ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Forward Kinematics ◽  
Test Bed ◽  
Fiber Placement ◽  
Automated Fiber Placement ◽  
System Requirements

This paper introduces a new concept of applying a parallel mechanism in automated fiber placement (AFP) for aerospace part manufacturing. By investigating the system requirements, a 4DOF parallel mechanism consisting of two revolute–prismatic–spherical joints (2RPS) and two universal–prismatic–spherical joints (2UPS) limbs with two rotational (2R) and two translational (2T) motions is proposed. Both inverse and forward kinematics models are obtained and solved analytically. Based on the overall Jacobian matrix in screw theory, singularity loci are presented and the singularity-free workspace is correspondingly illustrated. To maximize the singularity-free workspace, locations of the 2UPS limbs with the platform and base sizes are used in the optimization which gives a new design of a 4DOF parallel mechanism. A dimensionless Jacobian matrix is also defined and its condition number is used for optimizing the kinematics performance in the optimization process. A numerical example is presented with physical constraint considerations of a test bed design for AFP.

Evaluation of the Kinematic Performance of a 3-RRS Parallel Mechanism

Robotica ◽  
2020 ◽  
pp. 1-12
Author(s):  
Manxin Wang ◽  
Qiusheng Chen ◽  
Haitao Liu ◽  
Tian Huang ◽  
Hutian Feng ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Mean Value ◽  
Spherical Joint ◽  
Performance Indices ◽  
Active Joint ◽  
Strongly Coupled ◽  
The Mean ◽  
Kinematic Performance

SUMMARY This paper proposes a set of novel indices for evaluating the kinematic performance of a 3-RRS (R and S denote revolute and spherical joint respectively, R denotes active joint.), parallel mechanism whose translational and rotational movements are strongly coupled. First, the indices are formulated using the decoupled overall Jacobian matrix, which is developed using coordinate transformation. Then, the influences of the homogeneous dimensionless parameters on these indices are investigated. In addition, the dimension synthesis of the 3-RRS parallel mechanism is carried out by minimizing the mean value of the kinematic performance indices and their standard deviation. The results demonstrate that the established approach facilitates good global kinematic performance of the parallel mechanism.

Optimal Design of 6-UPU Parallel Mechanism

2011 ◽  
Vol 480-481 ◽  
pp. 1055-1060
Author(s):  
Guang Hua Wu ◽  
Lie Hang Gong ◽  
Xin Wei Ji ◽  
Zhong Jun Wu ◽  
Yong Jun Gai
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimal Design ◽  
Objective Function ◽  
Parallel Mechanism ◽  
Design Space ◽  
Jacobian Matrix ◽  
Optimal Model ◽  
The Real ◽  
Universal Joints

The methodology of the optimal design for the 6-UPU parallel mechanism (PM) is presented based on genetic algorithms. The optimal index which expressed by Jacobian matrix of the PM is first deduced. An optimal model is established, in which the kinematic dexterity of a parallel mechanism is considered as the objective function. The design space, the limiting length of the electric actuators and the limit angles of universal joints are taken as constraints. The real-encoding genetic algorithm is applied to the optimal design of a parallel mechanism, which is proved the validity and advantage for the optimal design of a similar mechanism.

scholarly journals Performance Analysis of Gough Stewart Platform with 6 Limbs

2020 ◽  
Vol 22 (1) ◽  
pp. 133-142
Author(s):  
A. Chandrashekhar ◽  
G. Satish Babu
Keyword(s):  
Optimal Design ◽  
Performance Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Stewart Platform ◽  
Stiffness Index ◽  
Important Criterion ◽  
Transmission Index ◽  
Application Fields ◽  
Optimal Designing

AbstractThis paper concentrates on widespread study of parallel manipulator. It focuses on optimal designing of manipulator which has a large number of application fields. Optimal design is an important criterion to improve the accuracy of a robot. Through optimal design a robot can achieve isotropic configurations where the condition number of its jacobian matrix equals one. In this we are also concentrating on transmission index and stiffness index along with their plots, which can affect the kinetostatic performance of the robot. In this the singularity of Gough Stewart platform is also studied.

Optimal Design of a Metamorphic Parallel Mechanism With Reconfigurable 1T2R and 3R Motion Based on Unified Motion/Force Transmissibility

2016 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Optimal Design ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Rotation Axis ◽  
Geometric Constraint ◽  
Transmission Performance ◽  
Trade Off ◽  
Pure Rotation ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism which can switch its motion between one translation and two rotation (1T2R) motion and pure rotation (3R) motion. This feature stems from a reconfigurable revolute (rR) joint of which the rotation axis can be altered freely. Screw based geometric constraint is used to demonstrate the reconfiguration and mobility. Unified inverse kinematics, Jacobian matrix and motion/force transmissibility are provided using screws. Based on those, singularity loci are illustrated and optimal design of some key parameters are conducted considering both the 1T2R and 3R phases. Trade-off can be made between the maximum singularity-free workspace and transmission performance based on the optimal design results in this paper for specific applications requiring 1T2R and 3R motion.

Design and Kinematics Analysis of a Novel Planar Parallel Mechanism

2014 ◽  
Vol 568-570 ◽  
pp. 904-910
Author(s):  
Yan Bin Zhang ◽  
Hui Ping Wang
Keyword(s):  
Condition Number ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Kinematics Analysis ◽  
Moving Platform ◽  
One To One ◽  
Actuated Joints

A novel 3-dof planar parallel mechanism, which is composed by three different limbs, is designed. The moving platform can translate along two directions and rotate around one axis with respect to the base. Mobility of the mechanism is discussed and calculated based on the screw theory. The forward and the inverse analytical position equations are derived and the veloctiy analysis is addressed too. The Jacobian matrix is an identical one, so there exists one-to-one corresponding linear controlling relationship between one of the actuated joints and one of the outputs of the platform. Moreover, the condition number of the Jacobian matrix is constantly equal to one and the mechanism shows fully-isotropic throughout entire workspace.

A novel 4-RRCR parallel mechanism based on screw theory and its kinematics analysis

2012 ◽  
Vol 227 (9) ◽  
pp. 2039-2048 ◽  
Author(s):  
Sheng Guo ◽  
Congzhe Wang ◽  
Haibo Qu ◽  
Yuefa Fang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
Kinematics Analysis ◽  
Elimination Method ◽  
Direct Kinematics

In this article, a novel 4-RRCR parallel mechanism is introduced based on screw theory, and its kinematics and singularity are studied systematically. First, the degree of freedom analysis is performed using the screw theory. The formulas for solving the inverse and direct kinematics are derived. Second, a recursive elimination method is proposed to solve the Jacobian matrix based on the algebra operation of reciprocal product. Then, three kinds of singularity, i.e. limb, platform, and actuation singularities are analyzed. Finally, the analysis proves that the proposed mechanism possesses two advantages of simple forward kinematics and no platform singularity.

scholarly journals Kinematic analysis of a novel 3-CRU translational parallel mechanism

2015 ◽  
Vol 6 (1) ◽  
pp. 57-64 ◽  
Author(s):  
B. Li ◽  
Y. M. Li ◽  
X. H. Zhao ◽  
W. M. Ge
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Structural Characteristics ◽  
Parallel Mechanisms ◽  
Reachable Workspace ◽  
Potential Applications ◽  
Moving Platform ◽  
And Performance

Abstract. In this paper, a modified 3-DOF (degrees of freedom) translational parallel mechanism (TPM) three-CRU (C, R, and U represent the cylindrical, revolute, and universal joints, respectively) structure is proposed. The architecture of the TPM is comprised of a moving platform attached to a base through three CRU jointed serial linkages. The prismatic motions of the cylindrical joints are considered to be actively actuated. Kinematics and performance of the TPM are studied systematically. Firstly, the structural characteristics of the mechanism are described, and then some comparisons are made with the existing 3-CRU parallel mechanisms. Although these two 3-CRU parallel mechanisms are both composed of the same CRU limbs, the types of freedoms are completely different due to the different arrangements of limbs. The DOFs of this TPM are analyzed by means of screw theory. Secondly, both the inverse and forward displacements are derived in closed form, and then these two problems are calculated directly in explicit form. Thereafter, the Jacobian matrix of the mechanism is derived, the performances of the mechanism are evaluated based on the conditioning index, and the performance of a 3-CRU TPM changing with the actuator layout angle is investigated. Thirdly, the workspace of the mechanism is obtained based on the forward position analysis, and the reachable workspace volume is derived when the actuator layout angle is changed. Finally, some conclusions are given and the potential applications of the mechanism are pointed out.

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