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.

Evaluation and Representation of the Orientation Workspace of the Gough-Stewart Platform

2008 ◽  
Author(s):  
Qimi Jiang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Numerical Algorithm ◽  
Robotic Manipulators ◽  
Stewart Platform ◽  
Leg Length ◽  
Fixed Frame ◽  
Orientation 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 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 orientation workspace at a prescribed position can be defined by 12 workspace surfaces. The obtained orientation workspace is a region in the 3D Cartesian orientation space O φ θ ψ. 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 orientation workspace provides a clear measure for the platform to respectively rotate in order around the (x, y, z) axes of the fixed frame. Also, as the shape of the 3D orientation workspace is very complex, a numerical algorithm is presented to compute its volume.

scholarly journals A Unified Method for Computing Position and Orientation Workspaces of General Stewart Platforms

2011 ◽  
Author(s):  
Oriol Bohigas ◽  
Llui´s Ros ◽  
Montserrat Manubens
Keyword(s):  
Complex Shape ◽  
Three Dimensional ◽  
Stewart Platform ◽  
Large Dimension ◽  
Connected Components ◽  
Cartesian Space ◽  
Position And Orientation ◽  
Stewart Platforms ◽  
Orientation Workspace ◽  
Unified Method

The workspace of a Stewart platform is a complex six-dimensional volume embedded in the Cartesian space defined by six pose parameters. Because of its large dimension and complex shape, such workspace is difficult to compute and represent, so that comprehension on its structure is being gained by studying its three-dimensional slices. While successful methods have been given to determine the constant-orientation slice, the computation and appropriate visualization of the constant-position slice (also known as the orientation workspace) has proved to be a challenging task. This paper presents a unified method for computing both of such slices, and any other ones defined by fixing three pose parameters, on general Stewart platforms involving mechanical limits on the active and passive joints. Additional advantages over previous methods include the ability to determine all connected components of the workspace, and any motion barriers present in its interior.

Determination of Constant Orientation Workspace of a Stewart Platform by Geometrical Method

2015 ◽  
Vol 813-814 ◽  
pp. 997-1001 ◽  
Author(s):  
S. Gokul Narasimhan ◽  
R. Shrivatsan ◽  
K. Venkatasubramanian ◽  
Anjan Kumar Dash
Keyword(s):  
Algebraic Method ◽  
Parallel Manipulators ◽  
Stewart Platform ◽  
Closed Form Expression ◽  
Robot Design ◽  
Form Expression ◽  
Novel Method ◽  
Workspace Optimization ◽  
Orientation Workspace

Determination of workspace is one of the main considerations in the design of any robot since the workspace geometry is considered a fundamental issue for robot design. This also plays a crucial role in trajectory planning. Among parallel manipulators, 6-DOF Stewart platforms is the most researched and widely used robot. However, till date there is no closed form expression of workspace volume for Stewart platform. In this paper, a novel method is proposed to find out the workspace volume of Stewart platform. In this paper, individual workspace of each leg of the manipulator (P-U-S) is determined and then translated by a common distance towards their geometrical center thus generating constant orientation workspace. To determine the workspace volume, geometric intersection of the six spheres is computed. This results in workspace of definite shape and size, whose volume is calculated using simple formulae. It is observed that the geometric way of determination of workspace area is computationally less tedious than the algebraic method. This also helps a lot for workspace optimization of such manipulators.

scholarly journals A Linear Relaxation Method for Computing Workspace Slices of the Stewart Platform

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Oriol Bohigas ◽  
Montserrat Manubens ◽  
Lluís Ros
Keyword(s):  
Complex Shape ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Stewart Platform ◽  
Large Dimension ◽  
Linear Relaxation ◽  
Connected Components ◽  
Cartesian Space ◽  
Orientation Workspace ◽  
Unified Method

The workspace of a Stewart platform is a complex six-dimensional volume embedded in the Cartesian space defined by six pose parameters. Because of its large dimension and complex shape, this volume is difficult to compute and represent, and comprehension on its structure is being gained by studying its three-dimensional slices. While successful methods have been given to determine the constant-orientation slice, the computation and appropriate visualization of the constant-position slice (also known as the orientation workspace) has proved to be a challenging task. This paper presents a unified method for computing both of such slices, and any other ones defined by fixing three pose parameters, on general Stewart platforms possibly involving mechanical limits on the active and passive joints. Advantages over existing methods include, in addition to the previous, the ability to determine all connected components of the workspace, and any motion barriers present in its interior.

Determination of the Actual Configuration of the General Stewart Platform Using Only One Additional Sensor

1999 ◽  
Vol 121 (1) ◽  
pp. 21-25 ◽  
Author(s):  
V. Parenti-Castelli ◽  
R. Di Gregorio
Keyword(s):  
Stewart Platform ◽  
Rigid Bodies ◽  
Displacement Sensor ◽  
Leg Length ◽  
Displacement Sensors ◽  
On Line ◽  
Actual Configuration ◽  
General Geometry

This paper presents a procedure for the determination of the actual configuration of the general geometry Stewart platform (GSP), a fully-parallel manipulator that features two rigid bodies connected to each other via spherical pairs by six controlled-length legs. The six leg length measurements, provided by the displacement sensors incorporated in the leg hardware equipment, do not make it possible to uniquely find the GSP configuration because several configurations are possible for a given set of leg lengths. Several extra sensors in addition to those incorporated in the leg equipment have been proposed in the literature in order to obtain a one-to-one correspondence between the measurements and the actual GSP configuration. The proposed procedure makes use of only one additional displacement sensor and relies upon the analytical results available in the literature for a particular type of Stewart platform. The procedure, which uniquely defines the actual configuration of the GSP, is not intended for on-line implementation. Three different algorithms are proposed for computation and their efficiency compared. A case study is reported that confirms the effectiveness of the procedure.

Determination of the Workspace of 6-DOF Parallel Manipulators

1989 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.

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.

Experimental Investigations on the Contour Generation of a Reconfigurable Stewart Platform

2013 ◽  
pp. 291-301
Author(s):  
G. Satheesh Kumar ◽  
T. Nagarajan
Keyword(s):  
Error Analysis ◽  
Natural Frequency ◽  
Vibration Isolation ◽  
Stewart Platform ◽  
Design Tool ◽  
Experimental Investigations ◽  
Variable Geometry ◽  
Optimum Geometry ◽  
Complete Set

Reconfiguration of Stewart platform for varying tasks accentuates the importance for determination of optimum geometry catering to the specified task. The authors in their earlier work (Satheesh et al., 2008) have indicated the non availability of an efficient holistic methodology for determining the optimum geometry. Further, they have proposed a solution using the variable geometry approach through the formulation of dimensionless parameters in combination with generic parameters like configuration and joint vector. The methodology proposed provides an approach to develop a complete set of design tool for any new reconfigurable Stewart platform for two identified applications viz., contour generation and vibration isolation. This paper details the experimental investigations carried out to validate the analytical results obtained on a developed Stewart platform test rig and error analysis is performed for contour generation. The experimental natural frequency of the developed Stewart platform has also been obtained.

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