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.

Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator

2010 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment Gosselin ◽  
James M. Ritchie
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Alternative Formulation ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Actuated Joints ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators — leg actuation singularity — is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator.

Forward Displacement Analysis of a Quadratic Spherical Parallel Manipulator: The Agile Eye

2009 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment Gosselin
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Singularity Analysis ◽  
Alternative Solution ◽  
Alternative Formulation ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Input Space ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic spherical parallel manipulator: the Agile Eye. An alternative formulation of the kinematic equations of the Agile Eye is proposed. The singularity analysis of the Agile Eye is then dealt with. After an alternative solution to the FDA has been presented, a formula is revealed for producing a unique current solution to the FDA for a given set of inputs. A regular cube in the input space, which is singularity free, is also proposed for the Agile Eye. This work will facilitate the control of the Agile Eye.

Forward Displacement Analysis and Singularity Analysis of a Special 2-DOF 5R Spherical Parallel Manipulator

2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type I ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Self Motion ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

This paper deals with the forward displacement analysis and singularity analysis of a special 2-DOF 5R spherical parallel manipulator, in which the angle between the axes of any two adjacent revolute joints is a right angle. An alternative formulation of the kinematic equations of the 5R spherical parallel manipulator is proposed. A formula is then derived to produce directly the unique current solution to the forward displacement analysis of the 5R spherical parallel manipulator. It will also be addressed to keep the spherical parallel manipulator in the same working mode and assembly mode by simply restraining the range of an input angle. Unlike other parallel manipulators, the 5R spherical parallel manipulator always undergoes self-motion in a type-II singular configuration, and the 3R leg of the 5R spherical parallel manipulator also always undergoes self-motion in a type-I singular configuration.

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 Formula That Produces a Unique Solution to the Forward Displacement Analysis of a Quadratic Spherical Parallel Manipulator: The Agile Eye

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Unique Solution ◽  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Singularity Analysis ◽  
Alternative Solution ◽  
Alternative Formulation ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic spherical parallel manipulator: the Agile Eye. An alternative formulation of the kinematic equations of the Agile Eye is proposed. The singularity analysis of the Agile Eye is then dealt with. After an alternative solution to the FDA has been presented, a formula is revealed that produces a unique current solution to the FDA for a given set of inputs. A regular cube in the input-space, which is singularity free, is also proposed for the Agile Eye. This work will facilitate the control of the Agile Eye.

A Simple Method to Solve the Instantaneous Kinematics of the 5-RUR Parallel Manipulator

Robotica ◽  
2019 ◽  
Vol 37 (6) ◽  
pp. 1143-1157 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mohammad H. Abedinnasab ◽  
Md. Nazrul Islam
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Input Output ◽  
Linear Combinations ◽  
Kinematic Constraint ◽  
Simple Method ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Constraint Equations ◽  
Moving Platform

SummaryIn this work a simple method to solve the kinematics of the 5-R$\underbar{P}$UR parallel manipulator is introduced. Dealing with the displacement analysis, the kinematic constraint equations required to address the forward–inverse displacement analysis are established according to linear combinations of two vectors attached to the moving platform. Then, besides the solution of the inverse displacement analysis two strategies are proposed in order to solve the forward position analysis. Finally, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. Numerical examples are provided with the purpose to illustrate the proposed method. Furthermore, the numerical results obtained by means of screw theory are confirmed with the aid of commercially available software.

A parallel manipulator inspired by the original Stewart platform

2012 ◽  
Vol 227 (4) ◽  
pp. 831-844 ◽  
Author(s):  
J Gallardo-Alvarado ◽  
MA García-Murillo
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Flight Simulator ◽  
Input Output ◽  
Forward Displacement ◽  
Numerical Examples ◽  
Forward Displacement Analysis

This study addresses the kinematics of a new parallel manipulator inspired by the eight-bar linkage proposed as a flight simulator by Stewart almost five decades ago. Due to its partially decoupled topology, the forward displacement analysis of the robot is obtained in a nearly closed-form solution. The input–output equations of velocity and acceleration of the manipulator are systematically derived by resorting to reciprocal-screw theory. Numerical examples are included in the contribution in order to show the application of the method of kinematic analysis. As far as the authors are aware, the topology proposed in this contribution has not been reported in previous works.

Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator

2011 ◽  
Vol 3 (1) ◽  
Author(s):  
Xianwen Kong ◽  
Clément Gosselin ◽  
James M. Ritchie
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Alternative Formulation ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Actuated Joints ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators—leg actuation singularity—is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator.

Forward Displacement Analysis and Singularity Analysis of a 2-DOF 5R Spherical Parallel Manipulator

2009 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Alternative Formulation ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Self Motion ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

This paper deals with the forward displacement analysis and singularity analysis of a 2-DOF 5R spherical parallel manipulator. An alternative formulation of the kinematic equations of the 2-DOF spherical parallel manipulator is proposed. A formula is then derived to produce directly the unique current solution to the FDA of the 2-DOF spherical parallel manipulator. It is proved that the formula is associated with the same assembly mode and working mode as the reference configuration of the spherical parallel manipulator. Unlike other parallel manipulators, the 2-DOF 5R spherical parallel manipulator always undergoes self-motion in a Type 2 singular configuration, and the 3R leg of the 2-DOF spherical parallel manipulator also always undergoes self-motion in a Type 1 singular configuration.

Forward Displacement Analysis of Three New Classes of Analytic Spherical Parallel Manipulators

1998 ◽  
Author(s):  
Xian-Wen Kong
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Dual Solutions ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
The Third ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

Abstract The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

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