Geodesic
Modeling and evaluation of the Stewart platforms
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 3, pp. 279-286.

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This paper presents an efficient algorithm for solving the forward kinematics problem and an application for the motion modeling of the Stewart platforms. The developed application is able: (i) to solve the forward kinematics problem with a given accuracy; (ii) to calculate the trajectory of a tool positioned on the mobile platform; (iii) to calculate a possible deviation of the tool from a nominal position or a trajectory if lengths of the legs are varying within given tolerances; (iv) to detect the crossing of the legs during motions of a mobile platform. A projected movement of the Stewart platform can be specified by explicit parametric expressions for platform coordinates or by the spline-interpolation of trajectory nodes. The computational core of the application is based on the new efficient algorithm, which provides the minimum number of unknowns and the quadratic convergence rate even if two subsequently calculated positions are far apart. 
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A. V. Korobeinikov; V. E. Turlapov. Modeling and evaluation of the Stewart platforms. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 3, pp. 279-286. http://geodesic.mathdoc.fr/item/SJVM_2006_9_3_a6/

[1] Stewart D. A., “Platform with six degrees of freedom”, Proc. Inst. Mech. Engr., 180(5) (1965), 371–386 | DOI

[2] MacNeal-Schwendler Corporation (MSC) – MSC. Dynamic Designer, http://www.dynamicdesignermotion.com.

[3] Dasgupta B., Mruthyunjaya T. S., “The Stewart platform manipulator: a review”, Mechanism and Machine Theory, 35:1 (2000), 15–40 | DOI | MR | Zbl

[4] Glazunov V. A., Koliskor A. Sh., Chernov V. F. et al., “On solution of direct problem of Lcoordinate mechanisms locations”, Problemy mashinostroenija i nadezhnosti mashin, 1991, no. 2, 100–105 (In Russian) | MR

[5] Glazunov V. A., Koliskor A. Sh., Krainev A. F., Spatial Parallel Structure Mechanisms, Nauka, Moscow, 1991 (In Russian)

[6] Turlapov V. E., “Solution of kinematic problems for the Stewart platform by zero order method”, Elektron. zh. “Prikladnaya geometriya”, MAI, 4:5 (2002), 23–40 (In Russian); http://www.mai.ru/~apg/ | Zbl

[7] Innocenti C., Parenti-Castelli V., “Forward kinematics of the general 6-6 fully parallel mechanism – an exhaustive numerical approach via a mono-dimensional-search algorithm”, J. of Mechanical Design, 115:4 (1993), 932–937 | DOI

[8] Turlapov V. E., “Explicit solutions of the problem of spatial lever mechanisms locations on the class of single-loop groups”, Problemy mashinostroenija i nadezhnosti mashin, 1997, no. 3, 87–96 (In Russian)