Closed-form solution of the direct kinematics of the 6–3 type Stewart Platform using one extra sensor

Meccanica ◽  
1996 ◽  
Vol 31 (6) ◽  
pp. 705-714 ◽  
Author(s):  
Vincenzo Parenti-Castelli ◽  
Raffaele Di Gregorio
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Stewart Platform ◽  
Form Solution ◽  
Direct Kinematics

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 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.

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
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