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.

Determination of the Workspace of 6-DOF Parallel Manipulators

1989 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.

Motion Performance Analysis of Double-Cylinder Parallel Manipulators

2009 ◽  
Author(s):  
Hong Zhou ◽  
Shehu T. Alimi ◽  
Aravind Ravindranath ◽  
Hareesh Vepuri
Keyword(s):  
Performance Analysis ◽  
Parallel Manipulator ◽  
Critical Role ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Operation Speed ◽  
Transmission Angle ◽  
Motion Performance ◽  
Two Degree Of Freedom

Double-cylinder parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-cylinder parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a critical role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to apply this type of parallel manipulator.

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

scholarly journals Analysis of Finite Self Motion and Finite Dwell in Closed-Loop Mechanisms and Parallel Manipulators

2001 ◽  
Author(s):  
Sandipan Bandyopadhyay ◽  
Ashitava Ghosal
Keyword(s):  
Parallel Manipulator ◽  
Closed Loop ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Kinematic Constraints ◽  
Constraint Equations ◽  
First Order ◽  
Necessary And Sufficient Criteria ◽  
Necessary And Sufficient ◽  
Self Motion

Abstract In this paper, we present the necessary and sufficient criteria for finite self motion and finite dwell of the passive links of a parallel manipulator or a closed-loop mechanism. We study the first order properties of the constraint equations associated with the kinematic constraints inherent in a closed-loop mechanism or a parallel manipulator, and arrive at the criteria for the mechanism to gain a degree-of-freedom at a singular point of its workspace. By analyzing the second order properties of the constraint equations, we show that the gain of degree-of-freedom may lead to finite self motion of the passive links if certain configurational and architectural criteria are met. Special configurations and architecture may also lead to finite dwell of the passive links, and the criteria for the same has been derived. The results are illustrated with the help of several closed-loop mechanisms.

Motion Performance Analysis of Double-Slider Two-DOF Parallel Manipulators

2010 ◽  
Author(s):  
Hong Zhou ◽  
Mukesh Nagapuri ◽  
Sheetal Reddy Mamidi ◽  
Raj Kumar Gandham
Keyword(s):  
Performance Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Operation Speed ◽  
Transmission Angle ◽  
Motion Performance ◽  
The Common ◽  
Two Degree Of Freedom

Double-slider parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-slider parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a crucial role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to design this type of parallel manipulator.

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.

A novel relative degree-of-freedom criterion for a class of parallel manipulators with kinematic redundancy and its applications

2016 ◽  
Vol 231 (22) ◽  
pp. 4227-4240 ◽  
Author(s):  
Haibo Qu ◽  
Sheng Guo ◽  
Ying Zhang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Open Loop ◽  
Degree Of Freedom ◽  
Relative Degree ◽  
Kinematic Redundancy ◽  
Mechanism Synthesis ◽  
Key Points ◽  
Moving Platform ◽  
The Difference

The mobility of a whole parallel manipulator and the relative degree-of-freedom are the key points in mechanism synthesis and analysis, which often can be used to verify the existence of mechanisms. In this paper, the difference between the mobility of a parallel manipulator and the relative degree-of-freedom is discussed. First, a novel relative degree-of-freedom criterion is proposed based on the principle of determining the moving platform by N point positions, which is suitable for a kind of parallel manipulator with spherical joints attached to the moving platform. Next, the relative degree-of-freedom criterion is used to calculate the independent motions of the moving platform compared with the modified Kutzbach–Grübler criterion. The proposed relative degree-of-freedom criterion is different from the modified Kutzbach–Grübler criterion in result value and physical meaning. Finally, the type synthesis of such parallel manipulator with open-loop limbs or closed-loop limbs is performed based on the proposed relative degree-of-freedom criterion.

On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators with a Coplanar Platform

1994 ◽  
Vol 116 (2) ◽  
pp. 587-593 ◽  
Author(s):  
C. M. Gosselin ◽  
J. Sefrioui ◽  
M. J. Richard
Keyword(s):  
Parallel Manipulator ◽  
Minimal Polynomial ◽  
Polynomial Solution ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Real Solutions ◽  
Revolute Joints ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator ◽  
Direct Kinematics

This paper presents a polynomial solution to the direct kinematic problem of a class of spherical three-degree-of-freedom parallel manipulators. This class is defined as the set of manipulators for which the axes of the three revolute joints attached to the gripper link are coplanar and symmetrically arranged. It is shown that, for these manipulators, the direct kinematic problem admits a maximum of 8 real solutions. A polynomial of degree 8 is obtained here to support this result and cases for which all the roots of the polynomial lead to real configurations are presented. Finally, the spherical parallel manipulator with collinear actuators, which received some attention in the literature, is also treated and is shown to lead to a minimal polynomial of the same degree. Examples of the application of the method to manipulators of each category are given and solved.

Analysis of Two Spherical Parallel Manipulators With Hidden Revolute Joints

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Ju Li ◽  
J. Michael McCarthy
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Internal Constraints ◽  
Quadric Surfaces ◽  
Revolute Joints ◽  
Serial Chain ◽  
Point Of Intersection ◽  
Spherical Parallel Manipulator

In this paper, we examine two spherical parallel manipulators (SPMs) constructed with legs that include planar and spherical subchains that combine to impose constraints equivalent to hidden revolute joints. The first has supporting serial chain legs constructed from three revolute joints with parallel axes, denoted R∥R∥R, followed by two revolute joints that have intersecting axes, denoted RR̂. The leg has five degrees-of-freedom and is denoted R∥R∥R-RR̂. Three of these legs can be assembled so the spherical chains all share the same point of intersection to obtain a spherical parallel manipulator denoted as 3-R∥R∥R-RR̂. The second spherical parallel manipulator has legs constructed from three revolute joints that share one point of intersection, denoted RRR̂, and a second pair of revolute joints with axes that intersect in a different point. This five-degree-of-freedom leg is denoted RRR̂-RR̂. The spherical parallel manipulator constructed from these legs is 3-RRR̂-RR̂. We show that the internal constraints of these two types of legs combine to create hidden revolute joints that can be used to analyze the kinematics and singularities of these spherical parallel manipulators. A quaternion formulation provides equations for the quartic singularity varieties some of which decompose into pairs of quadric surfaces which we use to classify these spherical parallel manipulators.

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