scholarly journals Closed-Form Solution to the Position Analysis of Watt–Baranov Trusses Using the Bilateration Method

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Nicolás Rojas ◽  
Federico Thomas
Keyword(s):  
Closed Form ◽  
Characteristic Polynomial ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations ◽  
Characteristic Polynomials ◽  
Position Analysis ◽  
Exact Position ◽  
Kinematic Loops ◽  
First Time

The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial almost invariably involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. The use of kinematic loops to this end has seldom been questioned despite deriving the characteristic polynomial from them requires complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, the bilateration method has recently been used to obtain the characteristic polynomials of the three-loop Baranov trusses without relying on variable eliminations nor trigonometric substitutions and using no other tools than elementary algebra. This paper shows how this technique can be applied to members of a family of Baranov trusses resulting from the circular concatenation of the Watt mechanism irrespective of the resulting number of kinematic loops. To our knowledge, this is the first time that the characteristic polynomial of a Baranov truss with more that five loops has been obtained, and hence, its position analysis solved in closed form.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A closed-form solution for the position analysis of a novel fully spherical parallel manipulator – ERRATUM

Robotica ◽  
2015 ◽  
Vol 35 (5) ◽  
pp. 1137-1137
Author(s):  
Javad Enferadi ◽  
Amir Shahi
Keyword(s):  
Closed Form ◽  
Parallel Manipulator ◽  
Mechanical Engineering ◽  
Closed Form Solution ◽  
Form Solution ◽  
Position Analysis ◽  
Spherical Parallel Manipulator

There was an error in the spelling of the author's affiliation. Where the affiliation read “Department of mechanical engineering, Mashad Branch, Islamic Azad University, Mashad, Iran” it should instead have read “Department of mechanical engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran”.The publisher regrets this error.

Development and Kinematic Position Analysis of a Novel Class 2 Tensegrity Robot

2018 ◽  
Author(s):  
Carlos G. Manríquez-Padilla ◽  
Karla A. Camarillo-Gómez ◽  
Gerardo I. Pérez-Soto ◽  
Juvenal Rodríguez-Reséndiz ◽  
Carl D. Crane
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Novel ◽  
Universal Joint ◽  
Position Analysis ◽  
Experimental Prototype ◽  
Inverse Position Analysis ◽  
Kinematic Position

This paper presents a novel class 2 tensegrity robot which has contact between its rigid elements with a universal joint. Also, an strategy to obtain the forward and inverse position kinematic analysis using the parameters Denavit–Hartenberg in the distal convention is presented, obtaining the closed–form solution for the inverse position analysis and it was validated through simulation where a point of the robot followed the desired trajectory. Finally, the results were implemented in the experimental prototype of the novel class 2 tensegrity robot.

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.

Direct Position Analysis of the 4-6 Stewart Platforms

1992 ◽  
Author(s):  
Ning-Xin Chen ◽  
Shin-Min Song
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parallel Robots ◽  
Geometric Parameters ◽  
Degree Polynomial ◽  
Unknown Variable ◽  
Position Analysis ◽  
Half Angle ◽  
Stewart Platforms

Abstract Although Stewart platforms have been applied in the designs of aricraft and vehicle simulators and parallel robots in many years, their closed-form solution of direct (forward) position analysis has not been completely solved. Up to the present time, only the relatively simple Stewart platforms have been analyzed. Examples are the octahedral Stewart and the 4-4 Stewart platforms, in which two pairs of both upper and lower joint centers are coincident. The former results in in an eighth degree polynomial and the latter results in an eighth and a twelfth degree polynomials for different cases. The single unknown variable is in the form of square of a tan-half-angle. This paper further extends the direct position analysis to a more genearl case of the Stewart platform, the 4-6 Stewart platforms, in which two pairs of 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 4-4 and and 3-6 Stewart platforms can be easily deduced from the sixteenth degree polynomial by setting some geometric parameters be equal to 1 or 0.

scholarly journals Closed-Form Solution of a Peripherally Fixed Circular Membrane under Uniformly Distributed Transverse Loads and Deflection Restrictions

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Teng-fei Wang ◽  
Xiao-ting He ◽  
Yang-hui Li
Keyword(s):  
Approximate Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Axisymmetric Deformation ◽  
Form Solution ◽  
Circular Membrane ◽  
Rigid Plate ◽  
Membrane Stress ◽  
Transverse Loads ◽  
First Time

The problem of axisymmetric deformation of a peripherally fixed and uniformly loaded circular membrane under deflection restrictions (by a frictionless horizontal rigid plate) was analytically solved, where the assumption of constant membrane stress adopted in the existing work was given up, and a closed-form solution of this problem was presented for the first time. The numerical analysis shows that the closed-form solution presented here has higher calculation accuracy than the existing approximate solution.

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