Generation and forward displacement analysis of two new classes of analytic 6-SPS parallel manipulators

2001 ◽  
Vol 18 (6) ◽  
pp. 295-304 ◽  
Author(s):  
Xianwen Kong ◽  
Cl�ment M. Gosselin
Keyword(s):  
Parallel Manipulators ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Forward Displacement Analysis

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.

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 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.

Generation and Forward Displacement Analysis of RP_R-PR-RP_R Analytic Planar Parallel Manipulators

2002 ◽  
Vol 124 (2) ◽  
pp. 294-300 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Real Solutions ◽  
Planar Parallel Manipulator ◽  
Forward Displacement Analysis ◽  
Planar Parallel Manipulators

Analytic manipulators are manipulators for which a characteristic polynomial of fourth degree or lower can be obtained symbolically. Six types of RP_R-PR-RP_R analytic planar parallel manipulators (APPMs) are first generated using the component approach and the method based on the structure of the univariate equation. Of the six types, four are composed of Assur II kinematic chains while the other two are composed of Assur III kinematic chains. The forward displacement analysis (FDA) of two types of RP_R-PR-RP_R APPMs composed of Assur III kinematic chains is then performed. The FDA of each of the two types of APPMs composed of Assur III kinematic chains is reduced to the solution of a univariate cubic equation and a quadratic equation in sequence. It is also proven that the maximum number of real solutions to the FDA is 4 for the RP_R-PR-RP_R planar parallel manipulator with one aligned platform and one orthogonal platform. Examples with 4 real solutions for the RP_R-PR-RP_R planar parallel manipulator with one aligned platform and one orthogonal platform or 6 real solutions for the RP_R-PR-RP_R planar parallel manipulator with two aligned platforms are given at the end of this paper.

Forward Displacement Analysis of 5SPS-1CCS Parallel Manipulator Based on Hyper-Chaotic Newton Method

2012 ◽  
Vol 507 ◽  
pp. 196-201
Author(s):  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Mapping ◽  
Homotopy Continuation Method ◽  
Newton Iterative Method ◽  
Forward Displacement Analysis

Forward displacement analysis of parallel manipulators lead finally to solve the complex nonlinear equations, and its process is extremely difficult. The Newton iterative method is an important iterative technique for high-dimension nonlinear equations, but it is comparatively sensitive to initial value. To take chaos sequences as initial points of Newton iterative method, it can rapidly find all solutions of nonlinear equations. The novel approach of Newton iterative method based on parameter coupled hyper-chaotic mapping for solving nonlinear equations is presented. The mathematic model of the generalized 5SPS-1CCS parallel manipulator is created based on quaternion. A numerical example is given out, and its result is compared with the result of homotopy continuation method. The analysis results show that the new algorithm is simple, high efficiency, universal and can be used to forward displacement analysis of other coupled parallel manipulators.

scholarly journals A novel three degrees of freedom partially decoupled robot with linear actuators

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 467-475 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Gürsel Alici ◽  
Ramón Rodríguez-Castro
Keyword(s):  
Degrees Of Freedom ◽  
Control Point ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution ◽  
End Effector ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Common Control ◽  
Forward Displacement Analysis

SUMMARYIn this work, a new translational robot formed with two different parallel manipulators with a common control point is introduced. An asymmetric parallel manipulator provides three translational degrees of freedom to the proposed robot while the orientation of the end-effector platform is kept constant by means of a Delta-like manipulator. An exact solution is easily derived to solve the forward displacement analysis while a semi-closed form solution is available for solving the inverse displacement analysis. The infinitesimal kinematics of the robot is approached by applying the theory of screws. Finally, a numerical example that consists of solving the inverse/forward displacement analysis as well as the forward acceleration analysis of the end-effector platform is presented. The example also includes the computation of the workspace and the direct/inverse singularities of the example.

Determination of the Uniqueness Domains of 3-RPR Planar Parallel Manipulators With Similar Platforms

2000 ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Planar Parallel Manipulator ◽  
Free Region ◽  
Expression Form ◽  
Forward Displacement Analysis ◽  
Planar Parallel Manipulators

Abstract A uniqueness domain is a part of the Cartesian workspace corresponding to the same assembly mode of the 3-RPR (planar parallel) manipulator. This paper presents an efficient method to determine the uniqueness domains of the 3-RPR manipulators with similar platforms. The method is based on the singularity and forward displacement analysis (FDA) of the 3-RPR manipulator with similar platforms. The singularity analysis and the FDA of the 3-RPR manipulator with similar platforms is first performed. It is then proved that each of the solutions distributes into different singularity-free regions of the manipulator. Each singularity-free region corresponds to one uniqueness domain of the 3-RPR manipulator with similar platforms which can thus be determined in a direct way. At last, it is proved that the four solutions in analytic expression form to the forward displacement analysis correspond to different uniqueness domains for the 3-RPR manipulator with similar aligned platforms. This simplifies further the FDA in this case as the unique solution to the FDA can be found without the need to compute all the four solutions as long as the singularity-free region in which the manipulator works is given.

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