Forward Displacement Analysis of a Quadratic Planar Parallel Manipulator: 3-RPR Parallel Manipulator With Similar Triangular Platforms

2008 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Unique Solution ◽  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Planar Parallel Manipulator ◽  
Free Region ◽  
One To One ◽  
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 parallel manipulator: 3-RPR planar parallel manipulator with similar triangular platforms. Although it has been revealed numerically elsewhere that for this parallel manipulator, the four solutions to the FDA fall, respectively, into its four singularity-free regions (in its workspace), it is unclear if there exists a one-to-one correspondence between the four formulas, each producing one solution to the FDA, and the four singularity-free regions. This paper will prove that such a one-to-one correspondence exists. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-free region in which it works is specified.

Forward Displacement Analysis of a Quadratic Planar Parallel Manipulator: 3-RP̱R Parallel Manipulator With Similar Triangular Platforms 1

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Unique Solution ◽  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Algebraic Approach ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Planar Parallel Manipulator ◽  
Free Region ◽  
One To One ◽  
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 parallel manipulator: 3-RP̱R planar parallel manipulator with similar triangular platforms. Although it has been revealed numerically elsewhere that for this parallel manipulator, the four solutions to the FDA fall, respectively, into its four singularity-free regions (in its workspace), it is unclear if there exists a one-to-one correspondence between the four formulas, each producing one solution to the FDA, and the four singularity-free regions. Using an algebraic approach, this paper will prove that such a one-to-one correspondence exists. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-free region in which it works is specified.

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.

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 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.

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.

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.

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.

Mobility and Position Analysis of a Novel 3-DOF Translational Parallel Mechanism

2006 ◽  
Author(s):  
Daxing Zeng ◽  
Zhen Huang ◽  
Linlin Zhang
Keyword(s):  
Closed Form ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Continuation Method ◽  
Mobility Analysis ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Displacement Problem ◽  
Numerical Example ◽  
Forward Displacement Analysis

This paper presents the mobility analysis, the inverse and forward displacement analysis, and workspace of a novel 3-DOF 3-RPUR parallel manipulator. Closed-form inverse displacement solutions are obtained by the Denavit-Hartenberg method. The forward displacement problem is analyzed by using the continuation method and proved applying the result of the inverse displacement analysis. The workspace of the mechanism is also obtained. A numerical example is given in the paper.

Sign in / Sign up

Export Citation Format

Share Document