Forward Acceleration of Kinematic Limbs for Redundant Serial–Parallel Manipulators

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Yi Lu ◽  
Zefeng Chang ◽  
Nijia Ye
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
The Novel ◽  
Jacobian Matrices ◽  
Acceleration Model ◽  
Forward Kinematic ◽  
General Velocity

Abstract A forward acceleration of the kinematic limbs for the redundant serial–parallel manipulators is studied. The relationships between the input velocity/acceleration and the output general velocity/acceleration of the kinematic limbs are discovered. The forward kinematic Jacobian matrices and the forward kinematic Hessian matrices are derived. A unified forward acceleration of the kinematic limbs is established for solving the output general acceleration of the kinematic limbs by only giving the input general velocity/acceleration of every parallel manipulator. A novel 2(RPS + SPR + UPS + SPU) type serial–parallel manipulator is constructed, several formulas are derived for solving the full forward general acceleration of the kinematic limbs in the redundant serial–parallel manipulator based on the unified forward acceleration model. The theoretical solutions are proved to be correct by the simulation solution of the novel serial–parallel manipulator.

A Novel Parallel Mechanism With 3-RRUR Legs

2007 ◽  
Author(s):  
Yanwen Li ◽  
Yueyue Zhang ◽  
Lumin Wang ◽  
Zhen Huang
Keyword(s):  
Machine Tools ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Symmetrical Structure ◽  
Forward Kinematic ◽  
Accumulated Error

This paper investigates a novel 4-DOF 3-RRUR parallel manipulator, the number and the characteristics of its degrees of freedom are determined firstly, the rational input plan and the invert and forward kinematic solutions are carried out then. The corresponding numeral example of the forward kinematics is given. This type of parallel manipulators has a symmetrical structure, less accumulated error, and can be used to construct virtual-axis machine tools. The analysis in this paper will play an important role in promoting the application of such manipulators.

Kinematic analyses of novel translational parallel manipulators

2013 ◽  
Vol 228 (2) ◽  
pp. 330-341 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Horacio Orozco-Mendoza ◽  
Alvaro Sánchez-Rodríguez ◽  
Gursel Alici
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Output Displacement ◽  
Kinematic Analyses ◽  
Linear Actuators ◽  
The One ◽  
Forward Kinematic ◽  
Primary Contribution

This study reports on the kinematic analyses of four translational parallel manipulators (3RPC, SPS + 2RPC, RPPR + 2RPC and RPPR + 2PPP) articulated with linear actuators. They are based on serially connected chains which are connected with cylindrical (C), prismatic (P), revolute (R), spherical (S) and universal (U) joints. Of these manipulators, the one which is a fully decoupled, fully isotropic and singularity-free translational parallel manipulator (RPPR+2PPP) offers a one-to-one correspondence between its input and output displacement. This makes its forward and inverse position analyses simpler with a set of linear equations to be solved. Although the other manipulators have coupled kinematics, they still have simpler forward kinematic equations over other well-known translational parallel manipulators reported in the literature. We also employ screw theory to undertake the velocity and acceleration analyses. The primary contribution of this manuscript is to show how the 3-RPC translational parallel manipulator can be gradually modified in order to obtain a fully isotropic, fully decoupled and singularity-free translational 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

Kinematics and Singularity Analysis of the Hexaglide Parallel Robot

2008 ◽  
Author(s):  
Mansour Abtahi ◽  
Hodjat Pendar ◽  
Aria Alasty ◽  
Gholamreza Vossoughi
Keyword(s):  
Machine Tools ◽  
Parallel Manipulator ◽  
High Speed ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
The Past ◽  
Different Types ◽  
Forward Kinematic

In the past few years, parallel manipulators have become increasingly popular in industry, especially, in the field of machine tools. Hexaglide is a 6 DOF parallel manipulator that can be used as a high speed milling machine. In this paper, the kinematics and singularity of Hexaglide parallel manipulator are studied systematically. At first, this robot has been modeled and its inverse and forward kinematic problems have been solved. Then, formulas for solving inverse velocity are derived and Jacobian matrix is obtained. After that, three different types of singularity for this type of robot have been investigated. Finally a numerical example is presented.

Comparative Kinematic Analysis and Design Optimization of Redundant and Nonredundant Planar Parallel Manipulators Intended for Haptic Use

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1463-1477 ◽  
Author(s):  
Houssem Saafi ◽  
Houssein Lamine
Keyword(s):  
Design Optimization ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Analysis And Design ◽  
Planar Parallel Manipulator ◽  
Forward Kinematic ◽  
Planar Parallel Manipulators

SUMMARYThis paper investigates a comparative kinematic analysis between nonredundant and redundant 2-Degree Of Freedom parallel manipulators. The nonredundant manipulator is based on the Five-Bar mechanism, and the redundant one is a 3-RRR planar parallel manipulator. This study is aimed to select the best structure for a haptic application. This latter requires a mechanism with a desired workspace of 10 cm × 10 cm and an admissible force of 5 N in all directions. The analysis criteria are the accuracy of the forward kinematic model and the required actuator torques. Thereby, the geometric parameters of the two structures are optimized in order to satisfy the required workspace such that parallel singularities are overcome. The analysis showed that the nonredundant optimally designed manipulator is more suitable for the haptic application.

On Singularities of Planar Parallel Manipulators

1993 ◽  
Author(s):  
H. R. Mohammadi Daniali ◽  
P. J. Zsombor-Murray ◽  
Jorge Angeles
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Classification Scheme ◽  
Parallel Manipulators ◽  
The Other ◽  
Jacobian Matrices ◽  
General Classification ◽  
Three Degrees Of Freedom ◽  
Planar Parallel Manipulators

Abstract The singularities of the Jacobian matrices of two manipulator with three degrees of freedom are analyzed. One is a planar 3-legged manipulator; the other, a planar double-triangular manipulator. A general classification of parallel-manipulator singularities into three groups is described. The classification scheme relies on the properties of the Jacobian matrices of the manipulator. Finally, the three types of singularity are identified for the two manipulators.

Design and Singularity Analysis of a 3-Translational-DOF In-Parallel Manipulator*

2002 ◽  
Vol 124 (3) ◽  
pp. 419-426 ◽  
Author(s):  
L. Romdhane ◽  
Z. Affi ◽  
M. Fayet
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Orientation Error ◽  
Kinematic Chains ◽  
Prismatic Joints ◽  
Forward Kinematic ◽  
3D Solid ◽  
Novel Design

In this work, we shall present a novel design of a 3-translational-DOF in-parallel manipulator having 3 linear actuators. Three variable length legs constitute the actuators of this manipulator, whereas two other kinematic chains with passive joints are used to eliminate the three rotations of the platform with respect to the base. This design presents several advantages compared to other designs of similar 3-translational-dof parallel manipulators. First, the proposed design uses only revolute or spherical joints as passive joints and hence, it avoids problems that are inherent to the nature of prismatic joints when loaded in arbitrary way. Second, the actuators are chosen to be linear and to be located in the three legs since this design presents higher rigidity than other. In the second part of this paper, we addressed the problem of kinematic analysis of the proposed in-parallel manipulator. A mixed geometric and vector formulation is used to show that two solutions exist for the forward kinematic analysis. The problem of singularities is also investigated using the same method. In this work, we investigated the singularities of the active legs and the two types of singularity were identified: architectural singularities and configurational singularities. The singularity of the passive chains, used to restrict the motion of the platform to only three translations, is also investigated. In the last part of this paper, we built a 3D solid model of the platform and the amplitude of rotation due to the deformation of the different links under some realistic load was determined. This allowed us to estimate the “orientation error” of the platform due to external moments. Moreover, this analysis allowed us to compare the proposed design (over constrained) with a modified one (not over constrained). This comparison confirmed the conclusion that the over constraint design has a better rigidity.

The Design of Parallel Manipulators of Star Topology Under Isotropic Constraint

2001 ◽  
Author(s):  
Luc Baron ◽  
Ghislain Bernier
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Geometrical Parameters ◽  
Home Position ◽  
Star Topology ◽  
Jacobian Matrices ◽  
Constraint Manifold ◽  
Necessary And Sufficient

Abstract This paper proposes a necessary and sufficient number of 18 geometrical parameters allowing to describe the design manifold of the Star topological class, i.e., all geometries of manipulators having the same topology and mobility as the Y-Star parallel manipulator. The isotropic constraints are then applied on this manifold in order to define the constraint manifold of isotropic designs, i.e., those having isotropic Jacobian matrices at their home position. This constraint manifold is of dimension 11 and greatly facilitates the design of isotropic manipulators in this topological class.

Novel XY Compliant Parallel Manipulators for Large Displacement Translation With Enhanced Stiffness

2010 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong
Keyword(s):  
Range Of Motion ◽  
Building Block ◽  
Parallel Manipulator ◽  
Large Range ◽  
Parallel Manipulators ◽  
Large Displacement ◽  
Analytical Models ◽  
The Novel ◽  
Out Of Plane ◽  
Error Motion

A novel XY compliant parallel manipulator (CPM) and a spatial double three-beam module both with distributed compliance are first proposed for large range of translation. Then, an improved XY CPM is proposed by combining the above XY CPM and a spatial double three-beam module in parallel. The normalized analytical models are further presented for the novel XY CPM, double three-beam module and improved XY CPM. It is shown that the improved XY CPM has the following merits: (1) large range of motion, constrained parasitic error motion, output-decoupling, maximal actuation isolation and minimal lost motion; and (2) large out-of-plane stiffness and no friction with base. The improved XY CPM may also be used as a building block to construct new spatial CPMs.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

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