A closed-form solution of the forward displacement analysis of a class of in-parallel mechanisms

A class of in-parallel platforms of special geometry with algebraically solvable, closed-form, forward-displacement solutions is presented. It is shown that all variables of the forward-displacement analysis problem from linear or quadratic equations for those mechanisms where the S joints in the base and movable platform are each in one plane and the base and movable platform have the same form but are different sizes. For the more special case in which the six S joints are located in the vertices of a regular hexagon both on the base and on the movable platform, the platform becomes unconstrained