Direct kinematic solution of a Stewart platform

The Stewart platform is a fully parallel, six-degree-of-freedom manipulator mechanism. Although its inverse kinematics have been extensively studied, no solutions to the direct position kinematics problem have been previously presented in the literature. A solution of the direct kinematics problem of the case in which the six limbs form three concurrent pairs at either the base or the hand member is presented. Even though it is not the most general possible configuration, this case does include many arrangements that have been used in practical robot mechanisms