Analytic Form of the Six-Dimensional Singularity Locus of the General Gough-Stewart Platform

2004 ◽  
Author(s):  
Haidong Li ◽  
Cle´ment M. Gosselin ◽  
Marc J. Richard ◽  
Boris Mayer-St-Onge
Keyword(s):  
Analytic Form ◽  
Stewart Platform ◽  
Jacobian Matrices ◽  
Analytical Expression ◽  
Flight Simulators ◽  
Velocity Equation ◽  
Singularity Locus ◽  
Important Design ◽  
Robotic Applications

The determination of the 6-D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables (x, y, z, φ, θ, ψ), using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.

Analytic Form of the Six-Dimensional Singularity Locus of the General Gough-Stewart Platform

2005 ◽  
Vol 128 (1) ◽  
pp. 279-287 ◽  
Author(s):  
Haidong Li ◽  
Clément M. Gosselin ◽  
Marc J. Richard ◽  
Boris Mayer St-Onge
Keyword(s):  
Analytic Form ◽  
Stewart Platform ◽  
Jacobian Matrices ◽  
Analytical Expression ◽  
Flight Simulators ◽  
Velocity Equation ◽  
Singularity Locus ◽  
Important Design ◽  
Robotic Applications

The determination of the 6D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables (x,y,z,ϕ,θ,ψ), using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.

Kinematic Analysis and Singularity Loci of Spatial Four-Degree-of-Freedom Parallel Manipulators Using a Vector Formulation

1998 ◽  
Vol 120 (4) ◽  
pp. 555-558 ◽  
Author(s):  
J. Wang ◽  
C. M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
New Method ◽  
Numerical Determination ◽  
Jacobian Matrices ◽  
Flight Simulators ◽  
Important Design ◽  
Robotic Applications

The kinematic analysis and the determination of the singularity loci of spatial four-degree-of-freedom parallel manipulators with prismatic or revolute actuators are discussed in this article. A new method for the derivation of the velocity equations and the corresponding Jacobian matrices is presented. The numerical determination of the workspace boundaries is then briefly discussed. Finally, the determination of the singularity loci is performed using the velocity equations and examples are given to illustrate the results obtained. Spatial four-degree-of-freedom parallel manipulators can be used in several robotic applications as well as in flight simulators. The determination of their singularity loci is a very important design issue.

Kinematic Analysis and Singularity Loci of Spatial Four-Degree-of-Freedom Parallel Manipulators

1996 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulators ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Numerical Determination ◽  
Inverse Kinematic Problem ◽  
Flight Simulators ◽  
Important Design ◽  
Robotic Applications

Abstract The kinematic analysis and the determination of the singularity loci of spatial four-degree-of-freeedom parallel manipulators with prismatic or revolute actuators are discussed in this article. After introducing the architecture of the spatial parallel four-degree-of-freedom manipulators, algorithms for the solution of the inverse kinematic problem are provided for the two kinds of manipulators considered. Two different methods are presented for the derivation of the velocity equations and the corresponding Jacobian matrices are derived. The numerical determination of the workspace boundaries is then briefly discussed. Finally, the determination of the singularity loci is performed using the velocity equations and examples are given to illustrate the results obtained. Spatial four-degree-of-freedom parallel manipulators can be used in several robotic applications as well as in flight simulators. The determination of their singularity loci is a very important design issue.

The Stewart Platform of General Geometry Has 40 Configurations

1993 ◽  
Vol 115 (2) ◽  
pp. 277-282 ◽  
Author(s):  
M. Raghavan
Keyword(s):  
Numerical Technique ◽  
Stewart Platform ◽  
Multivariate Polynomial ◽  
Prismatic Joint ◽  
Flight Simulators ◽  
Arbitrary Complex ◽  
Set Up ◽  
General Geometry ◽  
Six Degree Of Freedom ◽  
Robotic Applications

The Stewart platform is a six-degree-of-freedom, in-parallel linkage. It is used in automotive and flight simulators, positioning tables for assembly and robotic applications, and various other applications requiring linkages with high structural stiffness. It consists of a base link, a coupler link, and six adjustable-length legs supporting the coupler link. Each leg consists of a prismatic joint with ball-joint connections to the base and coupler, respectively. The forward kinematics problem for the Stewart platform may be stated as follows: given the values of the six prismatic joint displacement inputs to the linkage, compute the position and orientation of the coupler link. This problem may be set up as a system of nonlinear multivariate polynomial equations. We solve this problem using a numerical technique known as polynomial continuation. We show that for Stewart platforms of general geometry (i.e., platforms in which the linkage parameters are arbitrary complex numbers) this problem has 40 distinct solutions.

The Stewart Platform of General Geometry Has 40 Configurations

1991 ◽  
Author(s):  
Madhusudan Raghavan
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Technique ◽  
Stewart Platform ◽  
Multivariate Polynomial ◽  
Six Degrees Of Freedom ◽  
Prismatic Joint ◽  
Flight Simulators ◽  
Set Up ◽  
General Geometry ◽  
Robotic Applications

Abstract The Stewart platform is a six-degrees-of-freedom, in-parallel linkage. It is used in automotive and flight simulators, positioning tables for assembly and robotic applications, and various other applications requiring linkages with high structural stiffness. It consists of a base link, a coupler link, and six adjustable-length legs supporting the coupler link. Each leg consists of a prismatic joint with ball-joint connections to the base and coupler respectively. The forward kinematics problem for the Stewart platform may be stated as follows: given the values of the six prismatic joint displacement inputs to the linkage, compute the position and orientation of the coupler link. This problem may be set up as a system of nonlinear multivariate polynomial equations. We solve this problem using a numerical technique known as polynomial continuation. We show that for Stewart platforms of general geometry (i.e., platforms in which the linkage parameters are arbitrary complex numbers) this problem has 40 distinct solutions.

Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Theoretical Orientation ◽  
Robotic Manipulators ◽  
Stewart Platform ◽  
Closed Region ◽  
Leg Length ◽  
Fixed Frame ◽  
Cartesian Space ◽  
Orientation Workspace

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the theoretical orientation workspace of the Gough–Stewart platform with given leg length ranges [ρimin,ρimax]. By use of the roll-pitch-yaw angles (ϕ,θ,ψ), the theoretical orientation workspace at a prescribed position P0 can be defined by up to 12 workspace surfaces. The defined orientation workspace is a closed region in the 3D orientation Cartesian space Oϕθψ. As all rotations R(x,ϕ), R(y,θ), and R(z,ψ) take place with respect to the fixed frame, any point of the defined orientation workspace provides a clear measure for the platform to, respectively, rotate in order around the (x,y,z) axes of the fixed frame. An algorithm is presented to compute the size (volume) of the theoretical orientation workspace and intersectional curves of the workspace surfaces. The defined theoretical orientation workspace can be applied to determine a singularity-free orientation workspace.

Kinematic and Workspace Modelling of a 6-PUS Parallel Mechanism

2018 ◽  
Author(s):  
Jérôme Landuré ◽  
Clément Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Accurate Description ◽  
Transmission Ratio ◽  
Inverse Kinematic Problem ◽  
Jacobian Matrices ◽  
Six Degree Of Freedom

This article presents the kinematic analysis of a six-degree-of-freedom six-legged parallel mechanism of the 6-PUS architecture. The inverse kinematic problem is recalled and the Jacobian matrices are derived. Then, an algorithm for the geometric determination of the workspace is presented, which yields a very fast and accurate description of the workspace of the mechanism. Singular boundaries and a transmission ratio index are then introduced and studied for a set of architectural parameters. The proposed analysis yields conceptual architectures whose properties can be adjusted to fit given applications.

scholarly journals DSJM: A Software Toolkit for Direct Determination of Sparse Jacobian Matrices

2016 ◽  
pp. 275-283 ◽  
Author(s):  
Mahmudul Hasan ◽  
Shahadat Hossain ◽  
Ahamad Imtiaz Khan ◽  
Nasrin Hakim Mithila ◽  
Ashraful Huq Suny
Keyword(s):  
Direct Determination ◽  
Jacobian Matrices ◽  
Software Toolkit

scholarly journals SUBSTANTIATION OF THE FORM AND DETERMINATION OF THE CONSTRUCTIVE PARAMETERS OF THE ROTATION ROLLER OF SOIL

2018 ◽  
Vol 13 (3) ◽  
pp. 72-76
Author(s):  
Гумар Булгариев ◽  
Gumar Bulgariev ◽  
Геннадий Пикмуллин ◽  
Gennadiy Pikmullin ◽  
Ильгиз Галиев ◽  
...  
Keyword(s):  
Analytical Study ◽  
Point Of View ◽  
Design Parameters ◽  
Industrial Complex ◽  
Stage Of Development ◽  
Pass Through ◽  
Spiral Plate ◽  
Working Device ◽  
Important Design

At the present stage of development of the country’s agro-industrial complex, the technological process of surface tillage by combined soil-cultivating machines, simultaneously combining a number of operations in one pass through the field, causes the presence in their designs of the necessary set of various promising working organs. In view of the foregoing, a rotary soil ripper with a spiral-plate working member equipped with radially directed teeth and connected by means of rods with end flanges has been developed. Also, the researched ripper has the limits of penetration of the working element in the form of flat discs equipped with flanges and the radial stop have the ability to rotate around their axes independently of the ripper shaft. An analytical study of the working units of this ripper was carried out from the point of view of the influence of their size and teeth on the process of interaction with the soil, on the basis of which some of their parameters were determined. In conclusion, it was concluded that the analytical equations obtained allow us to justify the choice of the most important design parameters of the proposed new design and design a toothed rotary working device that reduces to constructive implementation after calculating their basic dimensions.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

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