Direct Position Kinematics of the 3-1-1-1 Stewart Platforms

1994 ◽  
Vol 116 (4) ◽  
pp. 1102-1107 ◽  
Author(s):  
M. Husain ◽  
K. J. Waldron
Keyword(s):  
Special Class ◽  
General Feature ◽  
Stewart Platform ◽  
Numerical Example ◽  
Geometric Argument ◽  
Stewart Platforms ◽  
Base Platform

In this work, a closed from solution for the direct position kinematics problem of a special class of Stewart Platform is presented. This class of mechanisms has a general feature that the top platform is connected to the six limbs at four locations. Three limbs connect at one location and the remaining limbs connect to the top platform singly at three separate locations. The base platform is connected at six different locations as is the case in the general platform. This particular class of mechanism is termed as 3-1-1-1 mechanism in this paper. It has been shown that there are a maximum of sixteen real assembly configurations for the direct position kinematics problem. This has been verified using a geometric argument also. The numerical example solved in this paper demonstrates that it is possible to obtain a set of solutions which are all real.

Direct Position Kinematics of the 3-1-1-1 Stewart Platforms

1992 ◽  
Author(s):  
Muqtada Husain ◽  
Kenneth J. Waldron
Keyword(s):  
Closed Form ◽  
Special Class ◽  
General Feature ◽  
Closed Form Solution ◽  
Stewart Platform ◽  
Form Solution ◽  
Numerical Example ◽  
Geometric Argument ◽  
Stewart Platforms ◽  
Base Platform

Abstract In this work, a closed form solution for the direct position kinematics problem of a special class of Stewart Platform is presented. This class of mechanisms has a general feature that the top platform is connected to the six limbs at four locations. Three limbs connect at one location and the remaining limbs connect to the top platform singly at three separate locations. The base platform is connected at six different locations as is the case in the general platform. This particular class of mechanism is termed as 3-1-1-1 mechanism in this paper. It has been shown that there are a maximum of sixteen real assembly configurations for the direct position kinematics problem. This has been verified using a geometric argument also. The numerical example solved in this paper demonstrates that it is possible to obtain a set of solutions which are all real.

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.

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.

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.

Kinematic Analyses of 5-DOF 3-RCRR Parallel Mechanism

2005 ◽  
Author(s):  
Zhen Huang ◽  
Si J. Zhu
Keyword(s):  
Reference Point ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Mobility Analysis ◽  
End Effector ◽  
Numerical Example ◽  
Rotation Center ◽  
Kinematic Analyses ◽  
Base Platform ◽  
Virtual Pairs

This paper presents the kinematic analyses of a 5-DOF 3-RCRR parallel mechanism. The end-effector of this mechanism can rotate round rotation center and one reference point on it can translate in a plane parallels to the base platform. Since the traditional Kutzbach-Gru¨bler formula is not valid for this mechanism, the modified Kutzbach-Gru¨bler formula and screw theory are used in the mobility analysis. The Duffy’s spherical analytic theory is used in forward/reverse position analyses. In forward/reverse velocity/acceleration analyses, virtual mechanism principle is used to build a virtual parallel mechanism (3-PvRCRR), which is equivalent to the initial mechanism (3-RCRR) on kinematics if all rates of virtual pairs (Pv) are set to be zero. At the end, some kinematics curves are presented with a numerical example.

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.

Research on Inverse Kinematic Design of a Certain Hydraulic Stewart Platform

2011 ◽  
Vol 58-60 ◽  
pp. 2442-2445
Author(s):  
Zhi Yong Qu ◽  
Zheng Mao Ye
Keyword(s):  
Machine Tools ◽  
Stewart Platform ◽  
Inverse Kinematic ◽  
Design And Optimization ◽  
Kinematic Design ◽  
Structural Rigidity ◽  
The Future ◽  
Stewart Platforms ◽  
Kinematic Loop ◽  
Motion Dynamics

Stewart platforms have recently attracted attention as simulator and machine tools because of their conceptual potentials in high motion dynamics and accuracy combined with high structural rigidity due to their closed kinematic loop. This paper, composed of inverse kinematic design and optimization, attempts to ground the foundation on dynamics design and choice in the future.

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.

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.

Jerk distribution of a 6–3 Gough-Stewart platform

2003 ◽  
Vol 217 (1) ◽  
pp. 77-84 ◽  
Author(s):  
J Gallardo-Alvarado
Keyword(s):  
Lie Algebra ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Stewart Platform ◽  
Symmetric Form ◽  
Generalized Coordinates ◽  
Numerical Example ◽  
Moving Platform ◽  
Klein Form ◽  
Bilinear Symmetric Form

This paper is devoted to forward and inverse jerk analyses, by means of screw theory, of a Gough-Stewart platform with special topology, namely type 6–3. Given a set of generalized coordinates, and their time derivatives, the reduced jerk state or, for brevity, the jerkor of the moving platform, with respect to the fixed platform, is easily obtained by taking advantage of the properties of the Klein form, a bilinear symmetric form of the Lie algebra, e(3). Finally, the joint rate jerks of the parallel manipulator are found, expressing in screw form the jerkor of the moving platform with respect to the fixed platform. A numerical example is provided.

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