scholarly journals Kinematics Comparative Study of Two Overconstrained Parallel Manipulators

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Qiang Yan ◽  
Bin Li ◽  
Yangmin Li ◽  
Xinhua Zhao
Keyword(s):  
Comparative Study ◽  
Screw Theory ◽  
Structural Characteristics ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Comparison Study ◽  
Jacobian Matrices ◽  
Numerical Examples ◽  
Translational Degree

A comparison study of kinematics characteristics of two overconstrained 2-RPU&SPR parallel manipulators (PMs) is introduced in this paper. The two 2-RPU&SPR PMs have the same kinematics properties in terms of one translational degree of freedom (DOF) and two rotational DOFs kinematics outputs. But there are some differences between the two PMs as far as joints distribution is concerned, leading to the differences in respect of workspace and dexterity of the two PMs. Firstly, based on screw theory, the structural characteristics and DOFs of the two PMs are analyzed. Secondly, the inverse and forward displacements problems for the two PMs are formulated by analytic formulae. Some numerical examples are simulated by software. Thirdly, based on algorithm for the direct displacement solution, the workspace characteristics of the two PMs are analyzed and compared. Then, the Jacobian matrices of the mechanisms are formulated. Based on the Jacobian matrices, the dexterities of the two PMs are established and compared. Finally, according to the comparisons of the properties between the two PMs, some useful conclusions are provided.

Kinematics of a partially decoupled 3R2T symmetrical parallel manipulator 3-RCRR

2008 ◽  
Vol 222 (2) ◽  
pp. 277-285 ◽  
Author(s):  
S-J Zhu ◽  
Z Huang ◽  
M Y Zhao
Keyword(s):  
Control System ◽  
Cervical Spine ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Short History ◽  
Translational Degree ◽  
And Performance

The 3R2T (three rotational and two independent translational degree of freedom (DoF)) symmetrical parallel manipulator may be adopted in bionics, for example, simulating the motion of a cervical spine based on their mobility property and performance close to isotropic limit. However, up to now, characteristics of this class of manipulators have not been well studied because of its short history. Hence, to study the feasibility of this class of manipulator for bionics, kinematics for 3-RCRR is analysed including position, singularity, velocity, and acceleration. Different from other 3R2T 5-DoF symmetrical parallel manipulators, the mobility of 3-RCRR is partially decoupled, which makes the realization of control system easier than in others.

scholarly journals Kinematic Analysis Of Tricept Parallel Manipulator

2012 ◽  
Vol 12 (5) ◽  
Author(s):  
Mir Amin Hosseini ◽  
Hamid-Reza Mohammadi Daniali
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Forward Kinematics ◽  
Jacobian Matrices ◽  
Moving Platforms ◽  
Workspace Optimization

Parallel manipulators consist of fixed and moving platforms connected to each other with some actuated links. They have some significant advantages over their serial counterparts. While, they suffer from relatively small workspaces, complex kinematics relations and highly singular points within their workspaces. In this paper, forward kinematics of Tricept parallel manipulator is solved analytically and its workspace optimization is performed. This parallel manipulator has a complex degree of freedom, therefore leads to dimensional in-homogeneous Jacobian matrices. Thus, we divide some entries of the Jacobian by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. Moreover, its workspace is parameterized using some design parameters. Then, using GA method, the workspace is optimized subjects to some geometric constraints. Finally, dexterity of the design is evaluated. Keywords- Kinematic, Workspace, Singularity, TriceptABSTRAK - Manipulator selari terdiri daripada platform tetap dan bergerak yang bersambung antara satu sama lain dengan beberapa pautan bergerak. Manipulator selari mempunyai beberapa kebaikan tertentu dibandingkan dengan yang bersamaan dengannya. Walaupun ia mempunyai ruang kerja yang sempit, hubungan kinematik kompleks dan titik tunggal tinggi dalam linkungan ruang kerjanya. Dalam kajian ini, kinematik ke hadapan manipulator selari Tricept diselesaikan secara analisa dan pengoptimuman ruang kerja dijalankan. Manipulator selari ini mempunyai darjah kebebasan yang kompleks, yang menyebabkan ia mendorong kepada kehomogenan dimensi matriks Jacobian. Catatan Jacobian dibahagikan kepada unit panjang, dimana ia menghasilkan Jacobian baru yang homogen dimensinya. Tambahan, ruang kerjanya diparameterkan dengan menggunakan beberapa parameter reka bentuk. Kemudian, dengan kaedah GA, ruang kerja mengoptimakan subjek kepada beberapa kekangan geometrik. Akhirnya, kecakatan reka bentuk dinilaikan.Keywords- Kinematic, Workspace, Singularity, Tricept

Dynamic Analysis of Spatial Four-Degree-of-Freedom Parallel Manipulators

1997 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin
Keyword(s):  
Dynamic Analysis ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Principle Of Virtual Work ◽  
Numerical Examples ◽  
Euler Approach

Abstract The dynamic analysis of spatial four-degree-of-freedom parallel manipulators is presented in this article. First, expressions for the position, velocity and acceleration of each link constituting the manipulators are obtained. Then, the principle of virtual work is used to derive the generalized input forces of the manipulators. The corresponding algorithm is implemented and numerical examples are given in order to illustrate the results. The results obtained are verified using the classical Newton-Euler approach.

scholarly journals Type Synthesis of Two DOF Hybrid Translational Parallel Manipulators

2016 ◽  
Vol 836 ◽  
pp. 48-53 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Screw Theory ◽  
Synthesis Method ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Type Synthesis ◽  
In Series ◽  
Actuation Scheme ◽  
Two Degree Of Freedom

This paper introduces a methodology for the type synthesis of two degree-of-freedom hybrid translational manipulators with identical legs. The type synthesis method is based upon the screw theory. Three types of two degree-of-freedom hybrid translational manipulators with identical legs are identified based upon their wrench decomposition. Each leg of the manipulators is composed of a proximal module and a distal module mounted in series. The assembly conditions and the validity of the actuation scheme are also defined. Eventually, some novel two degree-of-freedom hybrid translational manipulators are synthesized with the proposed procedure.

Solving active wrench of limited-degree of freedom parallel manipulators based on translational/rotational Jacobian matrices

2009 ◽  
Vol 223 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Y Lu ◽  
B Hu ◽  
J Yu
Keyword(s):  
Virtual Work ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Principle Of Virtual Work ◽  
Jacobian Matrices ◽  
Limited Degree

A methodology is proposed for unified solving active wrench of the limited-degree of freedom (DOF) parallel manipulators (PMs). First, the geometric constraints and the inverse displacement kinematics are analysed. Second, the formulae for unified solving the inverse/forward velocity and the translational/rotational Jacobian matrices and inverse/forward Jacobian matrices are derived. Third, the analytic formulae for unified solving the active wrench of limited-DOF PMs are derived based on the principle of virtual work. Finally, a 3-DOF PM with linear/rotational active legs is presented to illustrate the use of the methodology.

Determination of singularities of some 4-DOF parallel manipulators by translational/rotational Jacobian matrices

Robotica ◽  
2009 ◽  
Vol 28 (6) ◽  
pp. 811-819 ◽  
Author(s):  
Yi Lu ◽  
Yan Shi ◽  
Jianping Yu
Keyword(s):  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Analytic Approach ◽  
Simple Process ◽  
Jacobian Matrices ◽  
Complicated Process

SUMMARYA novel analytic approach is proposed for determining the singularities of some four degree of freedom (DOF) parallel manipulators (PMs). First, the constraint and displacement of a general 4-DOF PM are analyzed. Second, a common 3 × 4 translational Jacobian matrix Jν and a common 3 × 4 rotational Jacobian matrix Jω are derived, and a 4 × 4 general Jacobian matrix J of the 4-DOF PMs is derived from Jν and Jω. Since a complicated process to determine singularities from the 4 × 6 Jacobian matrix is transformed into a simple process to determine singularity from J, the singularities of the some 4-DOF PMs with 3 translations and 1 rotation, or with 3 rotations and 1 translation, or with combined translation–rotations are analyzed and determined easily by this approach.

Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms

2004 ◽  
Vol 126 (1) ◽  
pp. 109-118 ◽  
Author(s):  
Jing Wang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Main Idea ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Redundant Manipulators ◽  
Parallel Mechanisms ◽  
Jacobian Matrices ◽  
Kinematic Chains ◽  
Analysis And Design

This paper addresses the singularity analysis and the design of three new types of kinematically redundant parallel mechanisms, i.e., the four-degree-of-freedom planar and spherical parallel mechanisms and the seven-degree-of-freedom spatial Stewart platform. The main idea in the design of these parallel manipulators is the addition of one redundant degree of freedom in one of the kinematic chains of the nonredundant manipulator. Such manipulators can be used to avoid the singularities inside the workspace of nonredundant manipulators. After describing the geometry of the manipulators, the velocity equations are derived and the expressions for the Jacobian matrices are obtained. Then, the singularity conditions are discussed. Finally, the expressions of the singularity loci of the kinematically redundant mechanisms are obtained and the singularity loci of the nonredundant and redundant manipulators are compared. It is shown here that the conditions for the singularity of the redundant manipulators are reduced drastically relative to the nonredundant ones. As a result, the proposed kinematically redundant parallel manipulators may be of great interest in several applications.

Instantaneous Kinematics and Singularity Analysis of a Novel Three-Legged Mobile Robot With Active S-R-R-R Legs

2008 ◽  
Author(s):  
Ping Ren ◽  
Dennis Hong
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
The Body ◽  
Jacobian Matrices ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Grassmann Line Geometry ◽  
Actuation Scheme ◽  
Complete Investigation

STriDER (Self-excited Tripedal Dynamic Experimental Robot) is a unique three-legged walking robot that utilizes its innovative tripedal gait to walk. Previous work on the kinematic analysis of STriDER mainly focused on solving the forward and inverse displacement problems. As a continuation, this paper addresses the instantaneous kinematics and singularity analysis. The kinematic configuration of STriDER is modeled as a three-legged in-parallel manipulator when all three feet of the robot are in contact with the ground without slipping. The results obtained from this study can be implemented to the velocity control and the resistance of disturbance forces, thus improving the motion accuracy and stability of the robot. By using screw theory, the screw-based Jacobian matrices of the manipulator can be derived since the forward displacement problems have already been solved. Based on these Jacobian matrices, the transformation equations from the active joint rates to the velocities of the body and vice versa are derived. Then, a complete investigation on the identification and elimination of singularities is presented. Unlike serial manipulators, in-parallel manipulators have two types of singularities, i.e., forward and inverse singularities. The inverse singularities are identified by checking the singular configurations of individual legs and the determinant of the inverse Jacobian matrix. By using Grassmann line geometry, the analytical conditions under which the forward singularities occur are obtained. A study on each case of these singular configurations shows that the redundant-actuation scheme of the active joints can effectively eliminate forward singularities.

Kinematic Analysis and Singularity Loci of Spatial Four-Degree-of-Freedom Parallel Manipulators Using a Vector Formulation

1998 ◽  
Vol 120 (4) ◽  
pp. 555-558 ◽  
Author(s):  
J. Wang ◽  
C. M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
New Method ◽  
Numerical Determination ◽  
Jacobian Matrices ◽  
Flight Simulators ◽  
Important Design ◽  
Robotic Applications

The kinematic analysis and the determination of the singularity loci of spatial four-degree-of-freedom parallel manipulators with prismatic or revolute actuators are discussed in this article. A new method for the derivation of the velocity equations and the corresponding Jacobian matrices is presented. The numerical determination of the workspace boundaries is then briefly discussed. Finally, the determination of the singularity loci is performed using the velocity equations and examples are given to illustrate the results obtained. Spatial four-degree-of-freedom parallel manipulators can be used in several robotic applications as well as in flight simulators. The determination of their singularity loci is a very important design issue.

scholarly journals Acceleration Analysis of 3-DOF Planar Parallel Manipulators by Means of Screw Theory

2016 ◽  
Vol 45 (2) ◽  
pp. 89-95
Author(s):  
Soheil Zarkandi
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Second Order ◽  
Degree Of Freedom ◽  
Planar Parallel Manipulator ◽  
Acceleration Analysis ◽  
Three Degree Of Freedom ◽  
Planar Parallel Manipulators

This paper deals with the second order kinematics of three degree-of-freedom (DOF) planar parallel manipulators. The simple and compact expressions are derived for both the inverse and forward acceleration analyses using screw theory. Moreover, as an example, a 3-DOF planar parallel manipulator is introduced and its kinematics is analyzed using the proposed method.

Sign in / Sign up

Export Citation Format

Share Document