Determination of the maximal singularity-free orientation workspace for the Gough–Stewart platform

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.813-814.997 ◽

2015 ◽

Vol 813-814 ◽

pp. 997-1001 ◽

Cited By ~ 1

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.

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Determination of the maximal singularity-free zones in the six-dimensional workspace of the general Gough–Stewart platform

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2006.04.006 ◽

2007 ◽

Vol 42 (4) ◽

pp. 497-511 ◽

Cited By ~ 77

Author(s):

Haidong Li ◽

Clément M. Gosselin ◽

Marc J. Richard

Keyword(s):

Stewart Platform ◽

Maximal Singularity

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

Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2008-49089 ◽

2008 ◽

Cited By ~ 1

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.

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Maximal Singularity-Free Total Orientation Workspace of the Gough–Stewart Platform

Journal of Mechanisms and Robotics ◽

10.1115/1.3147200 ◽

2009 ◽

Vol 1 (3) ◽

Cited By ~ 9

Author(s):

Qimi Jiang ◽

Clément M. Gosselin

Keyword(s):

Parallel Robot ◽

Stewart Platform ◽

Parallel Robots ◽

Maximal Singularity ◽

Orientation Workspace

The maximal singularity-free total orientation workspace is highly desirable in a context of design of parallel robots. In practice, this type of workspace is interesting because a parallel robot often works in a given range of orientations. In this work, an algorithm is presented to compute the maximal singularity-free total orientation workspace of the Gough–Stewart platform. In order to demonstrate the presented algorithm, an example is provided.

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Maximal singularity-free orientation workspace over a position region of Gough–Stewart platform

Advanced Robotics ◽

10.1080/01691864.2015.1067644 ◽

2015 ◽

Vol 29 (22) ◽

pp. 1427-1436 ◽

Cited By ~ 6

Author(s):

Qimi Jiang ◽

Clément M. Gosselin ◽

Yujun Wang ◽

Can Fang

Keyword(s):

Stewart Platform ◽

Maximal Singularity ◽

Orientation Workspace

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Experimental Investigations on the Contour Generation of a Reconfigurable Stewart Platform

Advanced Engineering and Computational Methodologies for Intelligent Mechatronics and Robotics ◽

10.4018/978-1-4666-3634-7.ch019 ◽

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

Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2011-47836 ◽

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.

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