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.

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.

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.

Parameterization of Three-Dimensional Rigid Body Guidance Incorporating Planar Gear Connections in a Spatial Closed-Loop Mechanism With Parallel Consecutive Axes

2008 ◽  
Author(s):  
Javier Rolda´n Mckinley ◽  
Carl Crane ◽  
David B. Dooner
Keyword(s):  
Computer Animation ◽  
Closed Loop ◽  
Three Dimensional ◽  
Motion Generation ◽  
Repetitive Motion ◽  
End Effector ◽  
Spatial Mechanism ◽  
Joint Axis ◽  
Position And Orientation ◽  
Six Degree Of Freedom

This paper introduces a reconfigurable closed-loop spatial mechanism that can be applied to repetitive motion tasks. The concept is to incorporate five pairs of non-circular gears into a six degree-of–freedom closed-loop spatial chain. The gear pairs are designed based on given mechanism parameters and a user defined motion specification of a coupler link of the mechanism. It is shown in the paper that planar gear pairs can be used if the spatial closed-loop chain is comprised of six pairs of parallel joint axes, i.e. the first joint axis is parallel to the second, the third is parallel to the fourth, ..., and the eleventh is parallel to the twelfth. This paper presents the synthesis of the gear pairs that satisfy a specified three-dimensional position and orientation need. Numerical approximations were used in the synthesis the non-circular gear pairs by introducing an auxiliary monotonic parameter associated to each end-effector position to parameterize the motion needs. The findings are supported by a computer animation. No previous known literature incorporates planar non-circular gears to fulfill spatial motion generation needs.

An Algorithm for Generation of Coordinated Robot Trajectories in Cartesian Space

2013 ◽  
Vol 196 ◽  
pp. 169-180 ◽  
Author(s):  
Adam Słota
Keyword(s):  
Virtual Environment ◽  
Relative Position ◽  
Accuracy Analysis ◽  
Simulation Environment ◽  
Coordinated Motion ◽  
Generation Algorithm ◽  
Cartesian Space ◽  
Position And Orientation ◽  
End Effectors ◽  
Trajectory Generation Algorithm

In the paper a trajectory generation algorithm for two robots’ coordinated motion is presented. Two instances of the algorithm, each for one robot, run in the same time and calculate trajectories’ position and orientation coordinates. Initial and end robots’ end-effectors poses are defined and values of linear and angular speeds are programmed. To minimize relative position and orientation errors an idea of corrective motion is introduced. Trajectory coordinates are calculated as the sum of programmed and corrective motion. The algorithm was implemented in a simulation environment and results of simulation are presented. Static accuracy analysis for general case and stability verification for fixed values of robots’ parameters are described. Finally, an outline of proposed procedure of building a virtual environment for reachability verification and collision checking is presented.

Dynamics Decomposition for Stewart Platforms

1994 ◽  
Vol 116 (1) ◽  
pp. 67-69 ◽  
Author(s):  
Zhiming Ji
Keyword(s):  
Dynamic Analysis ◽  
Driving Forces ◽  
Stewart Platform ◽  
Inertia Effect ◽  
Moving Plate ◽  
Stewart Platforms

This paper shows that special features of the Stewart platform can lead to the decomposition of the moving plate and the legs in the dynamic analysis. Formulas for evaluating, separately, the driving forces needed for the movement of the legs are developed for studying the combined inertia effect of all the leg rotations in a Stewart platform. The proposed formulation is easy to implement for Stewart platforms with nonnegligible leg inertia.

The Optimum Cage Position and Orientation on the ALIF with Facet Screw Fixation: A Finite Element Analysis and the Taguchi Method

2011 ◽  
Vol 27 (3) ◽  
pp. 309-320 ◽  
Author(s):  
C.-Y. Fan ◽  
C.-K. Chao ◽  
C.-C. Hsu ◽  
K.-H. Chao
Keyword(s):  
Finite Element ◽  
Taguchi Method ◽  
Screw Fixation ◽  
Three Dimensional ◽  
Element Model ◽  
Lateral Position ◽  
Element Analysis ◽  
Control Factors ◽  
Position And Orientation ◽  
Noise Factors

ABSTRACTAnterior Lumbar Interbody Fusion (ALIF) has been widely used to treat internal disc degeneration. However, different cage positions and their orientations may affect the initial stability leading to different fusion results. The purpose of the present study is to investigate the optimum cage position and orientation for aiding an ALIF having a transfacet pedicle screw fixation (TFPS). A three-dimensional finite element model (ALIF with TFPS) has been developed to simulate the stability of the L4/L5 fusion segment under five different loading conditions. The Taguchi method was used to evaluate the optimized placement of the cages. Three control factors and two noise factors were included in the parameter design. The control factors included the anterior-posterior position, the medio-lateral position, and the convergent-divergent angle between the two cages. The compressive preload and the strengths of the cancellous bone were set as noise factors. From the results of the FEA and the Taguchi method, we suggest that the optimal cage positioning has a wide anterior placement, and a diverging angle between the two cages. The results show that the optimum cage position simultaneously contributes to a stronger support of the anterior column and lowers the risk of TFPS loosening.

scholarly journals Regions of Feasible Point-to-Point Trajectories in the Cartesian Workspace of Fully-Parallel Manipulators

1999 ◽  
Author(s):  
Damien Chablat ◽  
Philippe Wenger
Keyword(s):  
Parallel Manipulator ◽  
Cartesian Product ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Inverse Kinematic ◽  
Connected Components ◽  
Feasible Point ◽  
Cartesian Space ◽  
Point Trajectories ◽  
Point To Point

Abstract The goal of this paper is to define the n-connected regions in the Cartesian workspace of fully-parallel manipulators, i.e. the maximal regions where it is possible to execute point-to-point motions. The manipulators considered in this study may have multiple direct and inverse kinematic solutions. The N-connected regions are characterized by projection, onto the Cartesian workspace, of the connected components of the reachable configuration space defined in the Cartesian product of the Cartesian space by the joint space. Generalized octree models are used for the construction of all spaces. This study is illustrated with a simple planar fully-parallel manipulator.

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.

Workspace Evaluation of Stewart Platforms

1992 ◽  
Author(s):  
Oren Masory ◽  
Jian Wang
Keyword(s):  
Stewart Platform ◽  
Design Tool ◽  
Kinematic Constraints ◽  
Stewart Platforms ◽  
Selection Of

Abstract The workspace and the dexterity of a Stewart Platform are effected by the choice of its major dimensions, actuators’ stroke and the kinematic constraints of its joints. An investigation of the effects of these parameters on workspace volume of the platform is presented. The obtained results were normalized so that these can be used as a design tool for the selection of dimensions, joints and actuators.

Placing Three-Dimensional Models in an Uncalibrated Single Image of an Architectural Scene

2004 ◽  
Vol 13 (6) ◽  
pp. 692-707 ◽  
Author(s):  
Sara Keren ◽  
Ilan Shimshoni ◽  
Ayellet Tal
Keyword(s):  
Augmented Reality ◽  
Three Dimensional ◽  
3D Models ◽  
Automatic Extraction ◽  
Single Image ◽  
Vanishing Points ◽  
Correct Position ◽  
3D Objects ◽  
Position And Orientation ◽  
Three Dimensional Models

This paper discusses the problem of inserting 3D models into a single image. The main focus of the paper is on the accurate recovery of the camera's parameters, so that 3D models can be inserted in the “correct” position and orientation. The paper addresses two issues. The first is an automatic extraction of the principal vanishing points from an image. The second is a theoretical and an experimental analysis of the errors. To test the concept, a system that “plants” virtual 3D objects in the image was implemented. It was tested on many indoor augmented-reality scenes. Our analysis and experiments have shown that errors in the placement of the objects are unnoticeable.

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