Geometric Optimization of the MSSM Gough–Stewart Platform

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Isosceles Triangle ◽  
Stewart Platform ◽  
Geometric Optimization ◽  
Geometric Parameters ◽  
Size Ratio ◽  
Base Plane ◽  
Reference Orientation ◽  
Equilateral Triangles ◽  
Global Optimal ◽  
Similar Triangles

This work focuses on analyzing the effects of the geometric parameters on the singularity-free workspace in order to determine the optimal architecture for the minimal simplified symmetric manipulator Gough–Stewart platform. To this end, the reference orientation is taken as the considered orientation because it is an impartial orientation. In this orientation, the singularity surface becomes a plane coinciding with the base plane. Accordingly, an analytic algorithm is developed to determine the singularity-free workspace. The analysis shows that: (1) for similar isosceles triangle base and platform, the optimal architecture is one for which both the base and the platform are equilateral triangles, and the size ratio between the platform and the base is 12; and (2) if the base and the platform are not similar triangles, the global optimal architecture is difficult to determine. Only an approximate optimal architecture is available.

Effects of Orientation Angles on the Singularity-Free Workspace and Orientation Optimization of the Gough–Stewart Platform

2009 ◽  
Vol 2 (1) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Stewart Platform ◽  
Robot Design ◽  
Parallel Mechanisms ◽  
Base Plane ◽  
Optimal Orientation ◽  
Reference Orientation ◽  
Global Optimal ◽  
Orientation Optimization

The singularity-free workspace of parallel mechanisms is highly desirable in a context of robot design. This work focuses on analyzing the effects of the orientation angles on the singularity-free workspace of the Gough–Stewart platform in order to determine the optimal orientation. In any orientation with ϕ=θ=0 deg and ψ≠±90 deg, the singularity surface becomes a plane coinciding with the base plane. Hence, an analytic algorithm is presented in this work to determine the singularity-free workspace. The results show that the singularity-free workspace in some orientations can be larger than that in the reference orientation with ϕ=θ=ψ=0 deg. However, the global optimal orientation is difficult to determine. Only an approximate optimal orientation is available. The results obtained can be applied to the design or parameter setup of the Gough–Stewart platform.

scholarly journals Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles - II

10.37236/815 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
A. M. d'Azevedo Breda ◽  
Patrícia S. Ribeiro ◽  
Altino F. Santos
Keyword(s):  
Equilateral Triangle ◽  
Isosceles Triangle ◽  
Subsequent Paper ◽  
Euclidean Sphere ◽  
Regular Polygons ◽  
Combinatorial Description ◽  
Equilateral Triangles

The study of dihedral f-tilings of the Euclidean sphere $S^2$ by triangles and $r$-sided regular polygons was initiated in 2004 where the case $r=4$ was considered [5]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and $r$-sided regular polygons, for any $r\ge 5$, was described. Later on, in [3], the classification of all f-tilings of $S^2$ whose prototiles are an equilateral triangle and an isosceles triangle is obtained. The algebraic and combinatorial description of spherical f-tilings by equilateral triangles and scalene triangles of angles $\beta$, $\gamma$ and $\delta$ $(\beta>\gamma>\delta)$ whose edge adjacency is performed by the side opposite to $\beta$ was done in [4]. In this paper we extend these results considering the edge adjacency performed by the side opposite to $\delta$.

Optimized Analysis of the Hollow Floor Based on the Niche Genetic Algorithms

2013 ◽  
Vol 421 ◽  
pp. 751-755
Author(s):  
Chuan Teng Huang ◽  
Zhi Jun Wang
Keyword(s):  
Genetic Algorithms ◽  
Optimal Solution ◽  
Threshold Value ◽  
Geometric Parameters ◽  
Optimization Analysis ◽  
Global Optimal Solution ◽  
Excellent Mechanical Property ◽  
Section Design ◽  
Global Optimal ◽  
Niche Genetic Algorithms

Nowadays, the hollow floor is widely used due to its excellent mechanical property and economic benefit.However, its related specification is absence of evaluation in geometric parameters. The optimized analysis aimed at the hollow floor under vertical load, the total cost of the hollow floor is considered as a objective function, the maximum deflection and the threshold value of the geometric parameters are considered as constrain conditions. The program, which introduces the section design and compiled by the python script, based on the niche genetic algorithms is used to analyze the optimization of a hollow floor. Comparing to the global optimal solution, the program achieves good results. It indicates that the niche genetic algorithms is efficient and suited for the optimization analysis of hollow floor. The above mentioned conclusions will be conducive to engineering design and further research in this field.

Singularity Equations of Gough-Stewart Platforms Using a Minimal Set of Geometric Parameters

2007 ◽  
Author(s):  
Qimi Jiang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Singularity Analysis ◽  
Geometric Optimization ◽  
Geometric Parameters ◽  
Minimal Set ◽  
New Approach ◽  
Practical Point ◽  
Fixed Frame ◽  
Solid Foundation ◽  
Stewart Platforms ◽  
Mobile Frame

So far, in the derivation of the singularity equations of Gough-Stewart platforms, all research works defined the mobile frame by making its origin coincide with the considered point on the platform. One problem can be that the obtained singularity equation contains too many geometric parameters and is not convenient for singularity analysis, especially not convenient for geometric optimization. Another problem can be that the obtained singularity equation cannot be used directly in practice. To solve these problems, this work presents a new approach to derive the singularity equation of the Gough-Stewart platform. The main point is that the origin of the mobile frame is separated from the considered point and chosen to coincide with a special point of the platform in order to minimize the geometric parameters defining the platform. Similarly, by defining a proper fixed frame, the geometric parameters defining the base can also be minimized. In this way, no matter which practical point of the platform is chosen as the considered point, the obtained singularity equation contains only a minimal set of geometric parameters and becomes a solid foundation for the geometric optimization based on singularity analysis.

Singularity Equations of Gough–Stewart Platforms Using a Minimal Set of Geometric Parameters

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Singularity Analysis ◽  
Geometric Optimization ◽  
Geometric Parameters ◽  
Minimal Set ◽  
New Approach ◽  
Practical Point ◽  
Fixed Frame ◽  
Solid Foundation ◽  
Stewart Platforms ◽  
Mobile Frame

So far, in the derivation of the singularity equations of Gough–Stewart platforms, all researchers defined the mobile frame by making its origin coincide with the considered point on the platform. One problem can be that the obtained singularity equation contains too many geometric parameters and is not convenient for singularity analysis, especially not convenient for geometric optimization. Another problem can be that the obtained singularity equation cannot be used directly in practice. To solve these problems, this work presents a new approach to derive the singularity equation of the Gough–Stewart platform. The main point is that the origin of the mobile frame is separated from the considered point and chosen to coincide with a special point on the platform in order to minimize the geometric parameters defining the platform. Similarly, by defining a proper fixed frame, the geometric parameters defining the base can also be minimized. In this way, no matter which practical point of the platform is chosen as the considered point, the obtained singularity equation contains only a minimal set of geometric parameters and becomes a solid foundation for the geometric optimization based on singularity analysis.

GEOMETRIC OPTIMIZATION OF PLANAR 3-RPR PARALLEL MECHANISMS

2007 ◽  
Vol 31 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Equilateral Triangle ◽  
Unit Area ◽  
Geometric Optimization ◽  
Parallel Mechanisms ◽  
Leg Length ◽  
Simple Singularity ◽  
Maximal Singularity ◽  
Important Concern ◽  
Singularity Locus ◽  
Similar Triangles

To pursue the maximal singularity-free workspace of parallel mechanisms is a very important concern for robot designers. This paper focuses on the case of planar 3-RPR parallel mechanisms. First, a relatively simple singularity equation of any point on the platform is derived. The obtained singularity equation shows that the singularity locus of any point on the platform is a circle of the same size, as long as the base and the platform are similar triangles. Furthermore, the three centres of the workspace circles lie exactly on the singularity circle. With these useful observations, the singularity-free workspace as well as the maximal leg length ranges can be determined. For a base of unit area, it is found that robots with equilateral triangle base and platform can obtain the maximal singularity-free workspace. Three case studies demonstrate this observation. Finally, a procedure for this kind of robot geometric design is provided.

Solution of the Direct Position Kinematics Problem of the General Stewart Platform Using Advanced Polynomial Continuation

1992 ◽  
Author(s):  
S. V. Sreenivasan ◽  
Prabjot Nanua
Keyword(s):  
Closed Form ◽  
Numerical Algorithm ◽  
Polynomial System ◽  
Stewart Platform ◽  
Geometric Parameters ◽  
Polynomial Equations ◽  
Number Of Solutions ◽  
Closed Form Solutions ◽  
General Geometry ◽  
First Time

Abstract In this paper the direct position kinematics problem of the most general geometry of the Stewart platform has been solved numerically. It is found that this problem has exactly 40 distinct, finite solutions. No closed form solutions are available for this problem. This problem was addressed for the first time by Raghavan recently, and the results obtained here are in agreement with the ones obtained by Raghavan. The formulation and the variable set used in this work lead to a simpler polynomial system of lower overall degree. Further, the geometric parameters of the general Stewart platform have been used to generate a ‘near-general’ Stewart platform. Even though the near-general Stewart platform also has exactly 40 finite, distinct, configurations, it is represented by much simpler polynomial equations. The polynomial system obtained from this near-general Stewart platform is used as the start system in an advanced polynomial continuation scheme to solve the general Stewart problem. This process eliminates a large number of solutions at infinity that have no geometric significance. This leads to an efficient numerical algorithm that is about twenty times faster than traditional continuation schemes.

Advanced Optimal Control-Based Design of a Gough-Stewart Platform

2021 ◽  
Author(s):  
Minglei Zhu ◽  
Shijie Song ◽  
Dawei Gong
Keyword(s):  
Optimal Control ◽  
Optimal Design ◽  
Design Methodology ◽  
Visual Servoing ◽  
Optimization Problems ◽  
Stewart Platform ◽  
Geometric Parameters ◽  
Design Parameters ◽  
Observation Error ◽  
Positioning Accuracy

Abstract Designing a robot with the best accuracy is always the attractive research direction in robot community. In order to create a Gough-Stewart platform with guaranteed accuracy performance for a dedicated controller, this paper describes a novel advanced optimal design methodology: control-based design methodology. This advanced optimal design method considers the controller positioning accuracy in the design process for getting the optimal geometric parameters of the robot. In this paper, three types of visual servoing controllers are applied to control the motions of the Gough-Stewart platform: leg-direction-based visual servoing, line-based visual servoing and image moment visual servoing. Depend on these controllers, the positioning error models considering the camera observation error together with the controller singularities are analyzed. In the next step, the optimization problems are formulated in order to get the optimal geometric parameters of the robot and the placement of the camera for the Gough-Stewart platform for each type of controller. Then, we perform the co-simulations on the three optimized Gough-Stewart platforms in order to test the positioning accuracy and the robustness with respect to the manufacturing errors. It turns out that the optimal control-based design methodology helps getting both the optimum design parameters of the robot and the performance of the controller {robot + dedicated controller}.

scholarly journals NUMERICAL STUDY OF THE INFLUENCE OF GEOMETRIC PARAMETERS ON THE AVALIABLE POWER IN A SOLAR CHIMNEY

2015 ◽  
Vol 14 (1) ◽  
pp. 103 ◽  
Author(s):  
R. S. Vieira ◽  
C. Garcia ◽  
I. C. A. Junior ◽  
J. A. Souza ◽  
L. A. O. Rocha ◽  
...  
Keyword(s):  
Turbulence Modeling ◽  
Numerical Study ◽  
Great Influence ◽  
Physical Principle ◽  
Geometric Optimization ◽  
Geometric Parameters ◽  
Solar Chimney ◽  
Future Studies ◽  
Solar Chimney Power Plant ◽  
The One

In the presented work, it is made a numerical study about the main physical principle of a solar chimney (SCPP – Solar Chimney Power Plant) and the influence of some geometric parameters on the available power in the SCPP. The main objectives are to test the applicability of the studied numerical model in future studies of SCPP geometric optimization and to test the action of the collector inlet height (H1) and the chimney outlet diameter (D2) on the available power of the device. For that it is considered an incompressible, turbulent, steady flow with mixed convective heat transfer in a two-dimensional and axisymmetric domain, similar to the one found in a solar chimney. The conservation equations of mass, momentum and energy are numerically solved using the finite volume method, more specifically with the FLUENT software. The classical turbulence modeling (RANS) was used for the turbulence approach with standard model k – ε. The other geometric parameters: collector radius (R) and the inlet and outlet of the turbine section, R1 and R2, are also constant. The verification results indicated a good agreement with those presented in the literature, even using a simplified domain. It was also observed that the H1 parameter is almost insensitive in the solar chimney performance, whereas the D2 variable presented great influence in the available power. The best performance was attained for an intermediate value of D2, D2 = 0.44 m. For this value, the available power was almost 72% and 19% higher from those obtained in the inferior and superior extremes of the studied D2 variable, D2 = 0.22 m and 0.88 m, respectively. It was also observed that there is a very good possibility of optimization of the chimney geometry in future studies.

Direct Position Analysis of the 4–6 Stewart Platforms

1994 ◽  
Vol 116 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Ning-Xin Chen ◽  
Shin-Min Song
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Stewart Platform ◽  
Form Solution ◽  
Parallel Robots ◽  
Geometric Parameters ◽  
Degree Polynomial ◽  
Position Analysis ◽  
Half Angle ◽  
Stewart Platforms

Although Stewart platforms have been applied in the design of aircraft and vehicle simulators and parallel robots for many years, the closed-form solution of direct (forward) position analysis of Stewart platforms has not been completely solved. Up to the present time, only the relatively simple Stewart platforms have been analyzed. Examples are the octahedral, the 3–6 and the 4–4 Stewart platforms, of which the forward position solutions were derived as an eighth or a twelfth degree polynomials with one variable in the form of square of a tan-half-angle. This paper further extends the direct position analysis to a more general case of the Stewart platform, the 4–6 Stewart platforms, in which two pairs of the upper joint centers of adjacent limbs are coincident. The result is a sixteenth degree polynomial in the square of a tan-half-angle, which indicates that a maximum of 32 configurations may be obtained. It is also shown that the previously derived solutions of the 3–6 and 4–4 Stewart platforms can be easily deduced from the sixteenth degree polynomial by setting some geometric parameters be equal to 1 or 0.

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