AbstractThis article studies the geometrical condition for closed‐form solutions of forward kinematics of parallel platforms. It is shown that closed‐form solutions are available if 1 rotational degree of freedom (dof) of the moving platform is decoupled from the other 5 dof. Geometrically, this condition is satisfied when five end‐points at the moving platform (or at the base) are colinear. A general case that these five points do not coincide with each other is studied first and is shown to have 16 possible closed‐form solutions. The variations of parallel platforms that satisfy the above‐mentioned geometrical condition are then discussed. Some of them have the additional feature that the three rotational dof are fully decoupled from the 3 translational dof and their closed‐form solutions are further simplified. One particular case has extremely simple forward kinematics and could be used as an alternative to the Stewa