FORWARD KINEMATICS OF A CLASS OF PARALLEL (STEWART) PLATFORMS WITH CLOSED-FORM SOLUTIONS

This 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 Stewart platform.