Title: DIRECT KINEMATICS OF THE GENERAL STEWART PLATFORM
Keywords: Stewart platform, direct kinematics, dual Euler- Rodrigues parameters
Abstract: A Stewart platform is a rigid body wich is connected to a supporting flame by six legs of variable lengths spherical joints at both ends of the legs. Neither the six joints fixed on the frame are coplanar ot otherwise regularly arranged. The problem of direct kinematics is to determine all position of the platform satisfyng the condition that the six legs have prescribed lengths. Husty  was the first who succeeded in formulating a set of aquations for dual Euler- Rodrigues parameters determining all position. Since these equations are written in terms of cartesian vector coordinates they can only be handled by an automatic formula manipulation program. Continued elimination resulted in an equation of 40th order for a single variable. The upper bound of 40 solutions was reconfirmed by Wampler . His proof is based on dual Euler- Rodrigues parameters in vector formulation. Wampler suggested that the same vector formulation might also simplify the formulation of Husty's equations.
Вид: публикация в национален форум