Modeling and evaluation of the Stewart platforms

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.