A Novel Approach for Obtaining Assembly Modes of a 3UPS-S Fully Spherical Parallel Manipulator

2016 ◽  
Vol 32 (5) ◽  
pp. 555-563
Author(s):  
J. Enferadi
Keyword(s):  
Parallel Manipulator ◽  
Dynamics Simulation ◽  
Mathematical Tool ◽  
Forward Displacement ◽  
Rodrigues Formula ◽  
Coupled Equations ◽  
Novel Approach ◽  
Trigonometric Equations ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

AbstractThe 3(UPS)-S fully spherical parallel manipulator is the most famous fully spherical parallel manipulator (FSPM). In this paper, we propose a novel approach to model the forward displacement analysis of the manipulator to obtain its assembly modes. Rodrigues’ formula is used as a mathematical tool to perform the proposed modeling. Utilizing geometry of the manipulator, two coupled trigonometric equations are obtained. Using Bezout's elimination method, the two coupled equations are transformed to one polynomial of degree eight. Finally, an example is given with eight real solutions. Therefore, the degree of the polynomial is minimal and the introduced modeling method is optimal. This is very important to control modelling and dynamics simulation. Also, the proposed method can be extended to the other FSPMs (e.g., 3(RPSP)-S, 3(RPSP)-S and 3(RSS)-S).

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 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 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 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.

Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator

2006 ◽  
Vol 129 (6) ◽  
pp. 611-616 ◽  
Author(s):  
Pierre-Luc Richard ◽  
Clément M. Gosselin ◽  
Xianwen Kong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Quadratic Equation ◽  
Design Stage ◽  
Forward Displacement ◽  
Singular Configurations ◽  
The Family ◽  
Moving Platform ◽  
Forward Displacement Analysis

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Schönflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations, and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.

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.

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