An Algebraic Method for Direct Position Analysis of the General Stewart Platform Manipulator Robot

2009 ◽  
Vol 626-627 ◽  
pp. 405-410
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Q.Z. Liao
Keyword(s):  
Parallel Manipulator ◽  
Algebraic Method ◽  
Stewart Platform ◽  
Mobile Platform ◽  
Analysis Problem ◽  
Position Analysis ◽  
General Geometry ◽  
Six Degree Of Freedom ◽  
Manipulator Robot ◽  
Base Platform

Stewart platform manipulator robot is a six degree of freedom, parallel manipulator, which consists of a base platform, a mobile platform and six limbs connected at six distinct points on the base platform and the mobile platform respectively. The direct position analysis problem of Stewart platform relates to the determination of the mobile platform pose for a given set of the lengths of the limbs. In this paper, we present a concise algebraic method for solving the direct position analysis problem for the fully parallel manipulator with general geometry, often referred to as General Stewart platform manipulator. Based on the presented algebraic method, we derive a 40th degree univariate polynomial from a determinant of 20×20 Sylvester’s matrix, which is relatively small in size. We also obtain a complete set of 40 solutions to the most general Stewart platform. The proposed method is comparatively concise and reduces the computational burden. Finally the method is demonstrated by a numerical example.

A Real Parameter Continuation Method for Complete Solution of Forward Position Analysis of the General Stewart

2002 ◽  
Vol 124 (2) ◽  
pp. 236-244 ◽  
Author(s):  
Zongliang Mu ◽  
Kazem Kazerounian
Keyword(s):  
Numerical Method ◽  
Complete Solution ◽  
Continuation Method ◽  
Stewart Platform ◽  
Target System ◽  
Analysis Problem ◽  
Position Analysis ◽  
Six Degree Of Freedom ◽  
Target Platform ◽  
Base Platform

Stewart Platform is a six degree of freedom, parallel manipulator, which consists of a base platform, a coupler platform and six limbs connected at six distinct points on the base platform and the coupler platform. The forward position analysis problem of Stewart Platform amounts to finding all its possible configurations based on the knowledge of the lengths of its limbs. In this paper, we present a numerical method for solving the forward position analysis problem for the most general Stewart Platform. This is a numerical method based on the polynomial continuation as established in recent works in the literature. However, one main difference is that the start system and the homotopy used here are based on physical design rather than pure mathematical equations. First, the target Stewart Platform is geometrically simplified into a platform, which, as the start platform, can be solved analytically. Then, a homotopy is constructed between the kinematics equations of the start platform and those of the target platform. By changing the parameters of the start platform incrementally into the parameters of the target system while tracking solutions of the start platform, a complete set of 40 solutions to the target platform can be found. Through this process, all of the extraneous paths have been eliminated before the solution tracking procedure starts and only isolated solutions of the start platform are tracked. The process for solutions to switch between real and complex is examined.

Six Degree of Freedom Active Isolation in Flexible Supporting Structures: Numerical Simulation and Experiment

2003 ◽  
Author(s):  
Yuan Cheng ◽  
Qian Zhou ◽  
Ge-Xue Ren ◽  
Hui Zhang
Keyword(s):  
Stewart Platform ◽  
Degree Of Freedom ◽  
Active Isolation ◽  
Dynamics And Control ◽  
Six Degree Of Freedom ◽  
Multi Body ◽  
And Control ◽  
Flexible Cables ◽  
Base Platform ◽  
Supporting Structures

This paper studies the six degree-of-freedom active isolation of flexible supporting structures using Gough-Stewart platform. The problem arises from a large radio telescope in which the astronomical equipment is mounted on a platform to be stabilized, while the base platform of the mechanism itself is carried by a cable car moving along flexible cables. In this paper, the stabilization problem is equivalent to a dynamics and control problem of multi-body system. A control law of the prediction of the base platform and PD feedback is proposed for the six actuators of the Gough-Stewart platform. Based on numerical results, a model experimental setup has been built up. The control effects are measured with LTD 500 Laser Tracker.

Design and kinematic analysis of a rotary positioner

Robotica ◽  
2006 ◽  
Vol 25 (1) ◽  
pp. 75-85 ◽  
Author(s):  
Borys Shchokin ◽  
Farrokh Janabi-Sharifi
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Stewart Platform ◽  
Optimal Combination ◽  
Variable Length ◽  
Mobile Platform ◽  
Constant Length ◽  
Forward And Inverse Kinematics ◽  
Circular Base

A rotary positioner (RP) is a type of parallel manipulator that is similar to a Stewart Platform. Instead of having variable-length bars, however, an RP has constant-length limbs located between a mobile platform as well as six circular motors distributed on a circular base. This paper offers a detailed investigation of an RP, focusing on its mechanism and analyzing its forward and inverse kinematics. It also computes an RP's constant orientation and orientation workspaces, taking into account the constraints imposed by passive joints and links interference. The optimal combination of the main parameters for an RP's maximum possible translation and orientation is also provided.

Displacement Analysis of a Six-DOF Parallel Manipulator With 3R3P and 4R2P Chains

1998 ◽  
Author(s):  
R. Kamra ◽  
D. Kohli ◽  
A. K. Dhingra
Keyword(s):  
Parallel Manipulator ◽  
Solution Procedure ◽  
Analysis Problem ◽  
Forward Displacement ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Tangent Method ◽  
Six Dof ◽  
Six Degree Of Freedom ◽  
Forward Displacement Analysis

Abstract This paper addresses the forward displacement analysis of a six degree of freedom platform manipulator which is actuated by three different configurations involving six chains with six joints in each chain. The displacement analysis problem involves finding all possible positions and orientations of the platform along with all the joint variables in response to the inputs supplied. The forward displacement analysis problem is solved using the “Suppressed Tangent method.” The proposed solution procedure is illustrated through three numerical examples. The first example deals with forward displacement analysis of a platform manipulator actuated by six 3R3P chains whereas the second and third examples deal with a manipulator actuated by five 3R3P and one 4R2P, and four 3R3P and two 4R2P chains respectively.

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.

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.

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

1999 ◽  
Vol 122 (3) ◽  
pp. 294-298 ◽  
Author(s):  
Vincenzo Parenti-Castelli ◽  
Raffaele Di Gregorio
Keyword(s):  
Real Time ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Computational Burden ◽  
The Real ◽  
Position Analysis ◽  
Extra Information ◽  
Actual Configuration ◽  
General Geometry

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 five out of the six sensors 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. [S1050-0472(00)01703-7]

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.

Sign in / Sign up

Export Citation Format

Share Document