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.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

1996 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Rigid Body ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Body Location ◽  
Position And Orientation ◽  
General Geometry ◽  
Two Bodies

Abstract The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

1998 ◽  
Vol 120 (2) ◽  
pp. 293-298 ◽  
Author(s):  
C. Innocenti
Keyword(s):  
Rigid Body ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Body Location ◽  
Position And Orientation ◽  
General Geometry ◽  
Two Bodies

The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

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.

Real-Time Forward Kinematics of the General 6-6 Stewart Platform Using One Extra Sensor

2000 ◽  
Author(s):  
Tae-Young Lee ◽  
Jae-Kyung Shim
Keyword(s):  
Real Time ◽  
Stewart Platform ◽  
Forward Kinematics ◽  
Double Precision ◽  
Leg Length ◽  
Precision Data ◽  
Constrained System ◽  
C Language ◽  
Estimates Of Solutions ◽  
Actual Configuration

Abstract The forward kinematics of the Stewart platform is to find the postures of the moving platform for a given set of leg lengths. In case of the general Stewart platform, the number of solutions of the problem is up to forty in the complex domain. Theoretically, it is not possible to uniquely determine the actual configuration with six leg length measurements only. An approach to get a single actual configuration is to make over-constrained system by adding extra sensors. This paper presents an algebraic elimination-based method for the real-time forward kinematics of the general Stewart platform with one extra sensor. The proposed algorithm does not require initial estimates of solutions unlike the numerical iterative methods, and can be implemented in C language using conventional double precision data with 15 significant digits. A numerical example is given to confirm the effectiveness and correctness of the developed algorithm for real-time computation.

A New Algorithm Based on Two Extra-Sensors for Real-Time Computation of the Actual Configuration of the Generalized Stewart-Gough Manipulator

1998 ◽  
Author(s):  
V. Parenti-Castelli ◽  
R. Di Gregorio
Keyword(s):  
Real Time ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Computational Burden ◽  
The Real ◽  
Position Analysis ◽  
Extra Information ◽  
Actual Configuration ◽  
General Geometry

Abstract It is well known that the direct position analysis of fully-parallel manipulators provides more than one solution, i.e., more than one configuration of the mechanism is possible for a given set of the actuated variables of motion. Extra information is, thus, necessary to find the actual configuration of the manipulator. This paper presents a new algorithm for the real-time computation of the actual configuration of the generalized Stewart-Gough manipulator, also known as 6-6 fully-parallel manipulator with general geometry. The proposed algorithm makes use of two extra rotary sensors in addition to the six normally implemented in the servosystems of the manipulator. A one-to-one correspondence between the sensor measurements and the manipulator configuration is provided. With respect to other algorithms recently presented in the literature, the proposed method greatly reduces the computational burden. Finally a case study shows the effectiveness of the proposed procedure.

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.

Real-Time Computation of the Actual Posture of the General Geometry 6-6 Fully-Parallel Mechanism Using Two Extra Rotary Sensors

1996 ◽  
Author(s):  
V. Parenti-Castelli ◽  
R. Di-Gregorio
Keyword(s):  
Real Time ◽  
Parallel Mechanism ◽  
Computation Time ◽  
Good Compromise ◽  
One To One ◽  
Actual Configuration ◽  
General Geometry

Abstract The paper presents three algorithms for the determination of the actual configuration of the general geometry 6-6 fully-parallel mechanism by using two extra rotary sensors in addition to the six ones that are normally implemented in the servosystems of the six actuated legs. The three proposed algorithms provide a one-to-one correspondence between the sensor measurements and the configuration of the mechanism. Comparison of the three algorithms, that are all for real-time computation, is presented and one of them is shown to be a good compromise between precision and computation time.

Real-Time Computation of the Actual Posture of the General Geometry 6-6 Fully-Parallel Mechanism Using Two Extra Rotary Sensors

1998 ◽  
Vol 120 (4) ◽  
pp. 549-554 ◽  
Author(s):  
V. Parenti-Castelli ◽  
R. Di Gregorio
Keyword(s):  
Real Time ◽  
Parallel Mechanism ◽  
Computation Time ◽  
Good Compromise ◽  
One To One ◽  
Actual Configuration ◽  
General Geometry

The paper presents three algorithms for the determination of the actual configuration of the general geometry 6-6 fully-parallel mechanism by using two extra rotary sensors in addition to the six ones that are normally implemented in the servosystems of the six actuated legs. The three proposed algorithms provide a one-to-one correspondence between the sensor measurements and the configuration of the mechanism. Comparison of the three algorithms, that are all for real-time computation, is presented and one of them is shown to be a good compromise between precision and computation time.

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