A Parallelogram-Based Parallel Manipulator for Schönflies Motion

2006 ◽  
Vol 129 (12) ◽  
pp. 1243-1250 ◽  
Author(s):  
Oscar Salgado ◽  
Oscar Altuzarra ◽  
Enrique Amezua ◽  
Alfonso Hernández
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Singularity Analysis ◽  
End Effector ◽  
Fixed Direction ◽  
Axis Parallel ◽  
Schönflies Motion ◽  
4 Degrees Of Freedom

A parallelogram-based 4 degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Schönflies motion that allows the end effector to translate in all directions and rotate around an axis parallel to a fixed direction. The theory of group of displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and an improved stiffness to the manipulator. This paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity, and the singularity analysis. Finally, a prototype of the manipulator, adding some considerations about its singularity-free design, and some technical applications in which the manipulator can be used are presented.

A Parallelogram-Based Parallel Manipulator For Scho¨nflies Motion

2006 ◽  
Author(s):  
Oscar Salgado ◽  
Oscar Altuzarra ◽  
Enrique Amezua ◽  
Alfonso Herna´ndez
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Singularity Analysis ◽  
End Effector ◽  
Fixed Direction ◽  
Axis Parallel

A parallelogram-based four degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Scho¨nflies motion, that allows the end-effector to translate in all directions and rotate around an axis parallel to a fixed direction. The Theory of Group of Displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and a improved stiffness to the manipulator. The paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity and the singularity analysis. Finally, a prototype of the manipulator and some technical applications in which the manipulator can be used are presented.

A symmetric parallel Schönflies-motion manipulator for pick-and-place operations

Robotica ◽  
2011 ◽  
Vol 29 (6) ◽  
pp. 853-862 ◽  
Author(s):  
O. Altuzarra ◽  
B. Şandru ◽  
Ch. Pinto ◽  
V. Petuya
Keyword(s):  
Group Theory ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Mechanical Device ◽  
End Effector ◽  
Pick And Place ◽  
Schönflies Motion ◽  
Motion Generator ◽  
Two Alternatives

SUMMARYThis paper presents a new symmetric parallel Schönflies-motion generator. The design is an evolution of a previous robot with linear inputs. The complete kinematic analysis of the 4-degree-of-freedom (dof) parallel manipulator is presented. The degrees of freedom are obtained from the Group Theory, the direct and inverse position problems are solved obtaining the manipulator's workspace, and the Jacobian analysis is presented. Then the isotropic configurations of the manipulator are discussed and the local dexterity map within the workspace is produced. Finally, two alternatives of a rotational mechanical device, which will increase the angular end-effector range, are proposed.

Kinematics of a Particular 3T1R Parallel Manipulator of Type 2PRPU

2017 ◽  
Author(s):  
Henrique Simas ◽  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
End Effector ◽  
Serial Robots ◽  
Fixed Direction ◽  
Pick And Place ◽  
Displacement Group ◽  
4 Degrees Of Freedom

Schoenflies-motion generators (SMGs) are 4-degrees-of-freedom (dof) manipulators whose end effector can perform translations along three independent directions, and rotations around one fixed direction (Schoenflies motions). Such motions constitute the 4-dimensional (4-D) Schoenflies subgroup of the 6-D displacement group. The most known SMGs are the serial robots named SCARA. Pick-and-place tasks are typical industrial applications that SMGs can accomplish. In the literature, 3T1R parallel manipulators (PMs) have been also proposed as SMGs. Here, a somehow novel 3T1R PM is presented and studied. Its finite and instantaneous kinematics are analyzed in depth, and analytic and geometric tools that are useful for its design are presented. The proposed SMG has a single-loop not-overconstrained architecture with actuators on or near the base and can make the end effector perform a complete rotation.

Synthesis and Design of a Novel 3T1R Fully-Parallel Manipulator

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Oscar Salgado ◽  
Oscar Altuzarra ◽  
Víctor Petuya ◽  
Alfonso Hernández
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Complete Type ◽  
Pick And Place ◽  
Schönflies Motion

In this paper a new topology of four degrees-of-freedom 3T1R fully-parallel manipulator is presented, which is defined only using lower kinematic pairs. The paper starts with a complete type synthesis of different topologies of fully-parallel manipulators that can perform the so-called Schönflies motion, based on the Theory of Groups of Displacements. After imposing some practical requirements, the different possibilities of manipulators are reduced to only one topology of fully-parallel and fully-symmetrical parallel manipulator. Then, the kinematic analysis of the manipulator is shown, including the closed-form resolution of both forward and inverse position problems, the velocity and the singularity analysis. Finally, a prototype of the manipulator is presented, which is intended to be used in pick and place applications.

Simplified Kinematics for a Parallel Manipulator Generator of the Schönflies Motion

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mohammad H. Abedinnasab ◽  
Daniel Lichtblau
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Kinematic Chain ◽  
Singularity Analysis ◽  
Input Output ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Novel Method ◽  
Schönflies Motion

This work is devoted to simplify the inverse–forward kinematics of a parallel manipulator generator of the 3T1R motion. The closure equations of the displacement analysis are formulated based on the coordinates of two points embedded in the moving platform. Afterward, five quadratic equations are solved by means of a novel method based on Gröbner bases endowed with first-order perturbation and local stability of parameters. Meanwhile, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that concern, the inclusion of pseudokinematic pairs connecting the limbs to the fixed platform and a passive kinematic chain to the robot manipulator allows to avoid the handling of rank-deficient Jacobian matrices. The workspace of the robot is determined by using a discretized method associated to its inverse–forward displacement analysis, whereas the singularity analysis is approached based on the input–output equation of velocity. Numerical examples are provided with the purpose to show the application of the method.

The QuadroG Robot, a Parallel Robot With a Configurable Platform for Haptic Applications

2015 ◽  
Author(s):  
Salua Hamaza ◽  
Patrice Lambert ◽  
Marco Carricato ◽  
Just Herder
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Parallel Robot ◽  
Parallel Robots ◽  
End Effector ◽  
Contact Points ◽  
Loop Chain ◽  
End Effectors ◽  
4 Degrees Of Freedom

This paper explores the fundamentals of parallel robots with configurable platforms (PRCP), as well as the design and the kinematic analysis of those. The concept behind PRCP is that the rigid (non-configurable) end-effector is replaced by a closed-loop chain, the configurable platform. The use of a closed-loop chain allows the robot to interact with the environment from multiple contact points on the platform, which reflects the presence of multiple end-effectors. This results in a robot that successfully combines motion and grasping capabilities into a structure that provides an inherent high stiffness. This paper aims to introduce the QuadroG robot, a 4 degrees of freedom PRCP which finely merges planar motion together with grasping capabilities.

Singularity Analysis of 2-DOF Parallel Manipulator

2012 ◽  
Vol 569 ◽  
pp. 589-592
Author(s):  
Jong Gyu Lee ◽  
Sang Ryong Lee ◽  
Choon Young Lee ◽  
Seung Han Yang
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Strong Influence ◽  
Orientation Angle ◽  
Singularity Analysis ◽  
End Effector ◽  
Jacobian Matrices ◽  
Singular Configurations ◽  
Workspace Boundary

The end-effector of 2-DOF parallel manipulator has an orientation. Jacobian matrices are obtained by kinematic analysis. The singular configurations of the manipulator are found using these matrices and the certain characteristic of these configurations is investigated. With the result from simulation, we found that these configurations happened to workspace-interior as well as workspace-boundary and the orientation angle of the end-effector exerted a strong influence on the singularity of the manipulator.

scholarly journals SINGULARITY ANALYSIS OF THE 4 RUU PARALLEL MANIPULATOR USING GRASSMANN-CAYLEY ALGEBRA

2011 ◽  
Vol 35 (4) ◽  
pp. 515-528 ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Clément Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Fixed Direction ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of four degrees of freedom parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity among its six Plücker vectors. Some points at infinity are thus introduced to formulate the superbracket of Grassmann-Cayley algebra, which corresponds to the determinant of the Jacobian matrix. By exploring this superbracket, all the singularity conditions of such manipulators can be enumerated. The study is illustrated through the singularity analysis of the 4-RUU parallel manipulator.

Delta robot: Inverse, direct, and intermediate Jacobians

2006 ◽  
Vol 220 (1) ◽  
pp. 103-109 ◽  
Author(s):  
M López ◽  
E Castillo ◽  
G García ◽  
A Bashir
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Kinematic Chain ◽  
End Effector ◽  
Jacobian Matrices ◽  
Singular Configurations ◽  
Delta Robot ◽  
Intermediate Jacobian

In the context of a parallel manipulator, inverse and direct Jacobian matrices are known to contain information which helps us identify some of the singular configurations. In this article, we employ kinematic analysis for the Delta robot to derive the velocity of the end-effector in terms of the angular joint velocities, thus yielding the Jacobian matrices. Setting their determinants to zero, several undesirable postures of the manipulator have been extracted. The analysis of the inverse Jacobian matrix reveals that singularities are encountered when the limbs belonging to the same kinematic chain lie in a plane. Two of the possible configurations which correspond to this condition are when the robot is completely extended or contracted, indicating the boundaries of the workspace. Singularities associated with the direct Jacobian matrix, which correspond to relatively more complicated configurations of the manipulator, have also been derived and commented on. Moreover, the idea of intermediate Jacobian matrices have been introduced that are simpler to evaluate but still contain the information of the singularities mentioned earlier in addition to architectural singularities not contemplated in conventional Jacobians.

Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Vol 6 (2) ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Surgical Instruments ◽  
End Effector ◽  
Minimally Invasive Surgical ◽  
Inverse Kinematics Problem

A crucial design challenge in minimally invasive surgical (MIS) robots is the provision of a fully decoupled four degrees-of-freedom (4-DOF) remote center-of-motion (RCM) for surgical instruments. In this paper, we present a new parallel manipulator that can generate a 4-DOF RCM over its end-effector and these four DOFs are fully decoupled, i.e., each of them can be independently controlled by one corresponding actuated joint. First, we revisit the remote center-of-motion for MIS robots and introduce a projective displacement representation for coping with this special kinematics. Next, we present the proposed new parallel manipulator structure and study its geometry and motion decouplebility. Accordingly, we solve the inverse kinematics problem by taking the advantage of motion decouplebility. Then, via the screw system approach, we carry out the Jacobian analysis for the manipulator, by which the singular configurations are identified. Finally, we analyze the reachable and collision-free workspaces of the proposed manipulator and conclude the feasibility of this manipulator for the application in minimally invasive surgery.

Sign in / Sign up

Export Citation Format

Share Document