Forward kinematics of a class of parallel (Stewart) platforms with closed-form solutions

The condition under which closed-form solutions of forward kinematics of parallel platforms are obtainable is explored. It is found that forward position analysis has closed-form solutions if one rotational degree of freedom (DOF) of a parallel platform is decoupled from the other five DOFs. Geometrically, this condition is satisfied when five end points at the platform or at the base are on the same line. A general case in which these five points do not coincide with each other is studied first and is shown to have 16 possible closed-form solutions. The computation of these solutions is very efficient compared to that of Stewart platforms. The different geometries of parallel platforms with closed-form solutions are discussed