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.

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.

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.

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 Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots

2005 ◽  
Vol 128 (1) ◽  
pp. 199-206 ◽  
Author(s):  
J. P. Merlet
Keyword(s):  
Optimal Design ◽  
Condition Number ◽  
Jacobian Matrix ◽  
Parallel Robots ◽  
Condition Numbers ◽  
Accuracy Index ◽  
Positioning Errors ◽  
Local Accuracy ◽  
Early Beginning ◽  
Accuracy Indices

Although the concepts of Jacobian matrix, manipulability, and condition number have existed since the very early beginning of robotics their real significance is not always well understood. In this paper we revisit these concepts for parallel robots as accuracy indices in view of optimal design. We first show that the usual Jacobian matrix derived from the input-output velocities equations may not be sufficient to analyze the positioning errors of the platform. We then examine the concept of manipulability and show that its classical interpretation is erroneous. We then consider various common local dexterity indices, most of which are based on the condition number of the Jacobian matrix. It is emphasized that even for a given robot in a particular pose there are a variety of condition numbers and that their values are not coherent between themselves but also with what we may expect from an accuracy index. Global conditioning indices are then examined. Apart from the problem of being based on the local accuracy indices that are questionable, there is a computational problem in their calculation that is neglected most of the time. Finally, we examine what other indices may be used for optimal design and show that their calculation is most challenging.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism for Rehabilitation

2007 ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai
Keyword(s):  
Control System ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Control System Design ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Moving Platform

This paper presents the geometry and the kinematic analysis of a parallel manipulator developed for ankle rehabilitation, as the beginning of a control system design process. First the geometry of the parallel mechanism is described, secondly the equations for the inverse and the forward kinematics are obtained, then the forward kinematics is analyzed in order to define all the possible configurations of the moving platform. Finally the Jacobian matrix of the rig is obtained by differentiating the position equations and the singularities are investigated, comparing the non-redundant and redundant type of mechanism.

scholarly journals A novel multiple working modes parallel mechanism with variable workspace

2018 ◽  
Vol 234 (1) ◽  
pp. 211-224
Author(s):  
Dian Li ◽  
Sheng Guo ◽  
Haibo Qu
Keyword(s):  
Trajectory Planning ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Forward Kinematics ◽  
3D Printer ◽  
Determination Method ◽  
Jacobian Matrices ◽  
Three Degrees Of Freedom

In this paper, a novel three-degrees-of-freedom multiple working modes parallel mechanism with variable workspace is proposed. Several studies including kinematic and prescribed trajectory planning are performed. First, the degrees of freedom of mechanism's two working modes are calculated based on screw theory. A prototype made by 3D printer also has been developed. Then, the inverse/forward kinematics and Jacobian matrices are obtained. The workspace and singularity are also analyzed, which show that the proposed parallel mechanism possesses singularity-free internal workspace. Finally, a working mode determination method is presented, which can be used to obtain suitable workspace in order to fully contain a prescribed trajectory. An example trajectory is used to verify the reasonability of the proposed method.

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.

On the kinematics of a new parallel mechanism with Schoenflies motion

Robotica ◽  
2015 ◽  
Vol 34 (9) ◽  
pp. 2056-2070 ◽  
Author(s):  
Po-Chih Lee ◽  
Jyh-Jone Lee
Keyword(s):  
Closed Form ◽  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Matrix Algebra ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Pick And Place

SUMMARYThis paper investigates the kinematics of one new isoconstrained parallel manipulator with Schoenflies motion. This new manipulator has four degrees of freedom and two identical limbs, each having the topology of Cylindrical–Revolute–Prismatic–Helical (C–R–P–H). The kinematic equations are derived in closed-form using matrix algebra. The Jacobian matrix is then established and the singularities of the robot are investigated. The reachable workspaces and condition number of the manipulator are further studied. From the kinematic analysis, it can be shown that the manipulator is simple not only for its construction but also for its control. It is hoped that the results of the evaluation of the two-limb parallel mechanism can be useful for possible applications in industry where a pick-and-place motion is required.

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