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.

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.

Design and kinematics analysis of a new 3CCC parallel mechanism

Robotica ◽  
2010 ◽  
Vol 28 (7) ◽  
pp. 1065-1072 ◽  
Author(s):  
Dongming Gan ◽  
Qizheng Liao ◽  
Jian S. Dai ◽  
Shimin Wei
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Polynomial Equation ◽  
Forward Kinematics ◽  
Kinematics Analysis ◽  
Eighth Order ◽  
Order Polynomial ◽  
Geometrical Constraints ◽  
Geometry Analysis ◽  
Theoretical Results

SUMMARYA CCC limb and a new 3CCC parallel mechanism have been designed in this paper based on geometry analysis. Their mobility and geometrical constraints are discussed by using screw theory and geometrical equations separately. Following that both the inverse and forward kinematics of the 3CCC parallel mechanism are proposed, in which Dixon's resultant is used to get the forward solutions for the orientation and a eighth-order polynomial equation in one unknown is obtained, leading to the results for the position analysis, numerical examples confirm these theoretical results. A short comparison with the traditional Stewart platforms is presented in terms of kinematics, workspace and trajectory planning.

Kinematic Analysis of A Novel 2-UPU/2-URU Parallel Mechanism

2011 ◽  
Vol 317-319 ◽  
pp. 469-474
Author(s):  
Shi Hua Li ◽  
Zhi Song Wang ◽  
Chang Cheng Yu ◽  
Wen Gong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Influence Coefficient ◽  
Performance Curve ◽  
Kinematics Analysis

Abstract. In this paper, a novel type of 2-UPU/2-URU asymmetric parallel mechanism is put forward, the degree of freedom and kinematics characteristics of the mechanism is analyzed. Firstly, based on screw theory, the degree of freedom of the mechanism is analyzed by using modified Grübler-Kutzbach formula of Degree of Freedom, the method is ingenious and simple. Then the kinematics analysis is done. Finally, the velocity and acceleration of the mechanism is analyzed by combining kinematic influence coefficient theory with imaginary mechanism method, and draw the velocity and acceleration performance curve of the mechanism with the MATLAB. This paper lays the foundation for further research of the parallel mechanism.

Kinematics Simulation of Parallel Mechanism Based on ADAMS

2012 ◽  
Vol 538-541 ◽  
pp. 479-482
Author(s):  
Xin Yu Du ◽  
Hong Wei Liu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Virtual Prototype ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Kinematics Simulation ◽  
Spatial Parallel Mechanism ◽  
Moving Platform ◽  
Simulation Results ◽  
Position And Orientation

In this paper,a kind of 3-UPU spatial parallel mechanism is introduced. Through deep analysis of the degree-of-freedom (DoF) for the platform using screw theory， the position and orientation of the moving platform is discussed. At last, the 3D virtual prototype modeling of this 3-UPU parallel mechanism based on software ADAMS is developed; the kinematics simulation and analysis are also carried out accordingly. From the simulation results, we can see that the proposed calculation of the DoFs and kinematics analysis is correct.

Forward kinematics analysis of parallel mechanisms with restricted workspace

2014 ◽  
Vol 229 (14) ◽  
pp. 2561-2572 ◽  
Author(s):  
Mingchao Geng ◽  
Tieshi Zhao ◽  
Chang Wang ◽  
Yuhang Chen ◽  
Erwei Li
Keyword(s):  
Jacobian Matrix ◽  
Search Method ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Iterative Search ◽  
Newton Raphson ◽  
Equivalent Method ◽  
Quasi Newton

The iterative search method (Newton-Raphson or Quasi-Newton) is an important numerical method for solving the forward kinematics problem of parallel mechanisms. But there may be a failure when the iterative search method solves the forward kinematics problems of a class of mechanisms, whose workspace is restricted. The extreme displacement singularity in the limbs is one reason for the workspace restriction. An equivalent method is proposed to remove the extremely displacement singularity in the limbs, and the forward kinematics solutions of two representative 6 degree of freedom mechanisms are given to illustrate the mechanism equivalence. For the coupled fewer degree of freedom mechanisms, the coupled motion is another reason for the workspace restriction. The virtual mechanism method and modified Jacobian matrix method are applied to solve the forward kinematics problems of this class of mechanisms. Numerical examples are given to validate the theories proposed above.

Kinematics Analysis of a 3-RRR Spherical Parallel Mechanism with Coaxial Input Shafts

2013 ◽  
Vol 404 ◽  
pp. 237-243
Author(s):  
Yu Lei Hou ◽  
Xin Zhe Hu ◽  
Da Xing Zeng
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Inverse Solution ◽  
Kinematics Analysis ◽  
Motion Feature ◽  
Displacement Problem ◽  
Spherical Parallel Mechanism ◽  
Three Degrees Of Freedom

As an important mechanism with special and extensive application, the three degrees of freedom spherical parallel mechanism is always a research hot in the mechanical fields. In this paper, the feature of the 3-RRR spherical parallel mechanism with coaxial input shafts is introduced, and its motion feature is analyzed based on the screw theory. The mobility of the spherical parallel mechanism is calculated by using the Modified Kutzbach-Grübler criterion, and the inverse displacement problem of the mechanism is solved. Then the expression of the Jacobian matrix is deduced based on the kinematics equation and its inverse solution. The contents of this paper should be useful for the further application of the spherical parallel mechanism.

Kinematics and Singularity Analysis of a Four-Degree-of-Freedom Serial-Parallel Hybrid Manipulator

2017 ◽  
Vol 29 (3) ◽  
pp. 520-527 ◽  
Author(s):  
Guangying Ma ◽  
◽  
Yuan Chen ◽  
Yunlong Yao ◽  
Jun Gao
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Independent Variables ◽  
Working Environments ◽  
Hybrid Manipulator ◽  
Parallel Hybrid ◽  
Kinematic Singularities

[abstFig src='/00290003/07.jpg' width='300' text='4DOF serial-parallel hybrid manipulator' ] For adapting to the complex working environments of amphibious manipulators, we proposed a serial-parallel hybrid quadruped walking manipulator. We simplified the leg mechanism of the serial-parallel hybrid manipulator as a 2UPU-UPR parallel mechanism, and then analyzed the degree of freedom (DOF) of the parallel mechanism by using the screw theory. The results show that the position of the<span class=”bold”>Y</span>direction and the pose of the<span class=”bold”>Z</span>direction are two independent variables which influence the mechanism movement. We deduced the kinematics inverse solution and the velocity Jacobian matrix of the 2UPU-UPR parallel mechanism. Based on the analysis of the Jacobian matrix, three kinds of kinematic singularities of the 2UPU-UPR parallel mechanism are identified. The results show that the 2UPU-UPR parallel mechanism doesn’t have the kinematic inverse singularity, but it has three kinds of kinematic forward singularities and two kinds of combined singularities. Finally, the variation of motorial parameters of this 2UPU-UPR parallel mechanism was discussed by a calculation example.

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.

Design and Kinematics Analysis of a Bionic Mechanical Goat Hoof

2013 ◽  
Vol 461 ◽  
pp. 191-200 ◽  
Author(s):  
Qun Zhang ◽  
Xi Lun Ding ◽  
Kun Xu ◽  
Hao Chen
Keyword(s):  
Mechanism Design ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
Motion Simulation ◽  
Kinematics Analysis

Different ground environments call for corresponding foot mechanism design. As for unstructured terrain, through the analysis of goat hooves structure, a robot foot mechanism simulating the goat hooves is designed in our research. According to screw theory and generalized Kutzbach-Grübler mobility criterion, degree of freedom of the bionic goat hoof mechanism is calculated. Then forward kinematics is built based on mechanism geometry. Motion simulation is carried out to verify the algorithms of forward kinematics.

scholarly journals Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism with kinematic redundancy

2021 ◽  
Author(s):  
chaoyu shen ◽  
Haibo Qu ◽  
Sheng Guo ◽  
Xiao Li
Keyword(s):  
Theoretical Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Fault Tolerant ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Kinematic Redundancy ◽  
Inverse Solutions ◽  
Three Degree Of Freedom ◽  
Actuated Joints

Abstract The kinematic redundancy is considered as a way to improve the performance of parallel mechanism. In this paper, the kinematics performance of a three degree-of-freedom parallel mechanism with kinematic redundancy (3-DOF PM-KR) and the influence of redundant part on the PM-KR are analyzed. Firstly, the kinematics model of the PM-KR is established. The inverse solutions, the Jacobian matrix and the workspace of the PM-KR are solved. Secondly, the influence of the redundant redundancy on the PM-KR has been analyzed. Since there exists kinematic redundancy, the PM-KR possesses the fault-tolerant performance. By locking one actuated joint or two actuated joints simultaneously, the fault-tolerant workspace are obtained. When the position of the redundant part is changed, the workspace and singularity will be changed. The results show that the kinematic redundancy can be used to avoid the singularity. Finally, the simulations are performed to prove the theoretical analysis.

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