Closed-form forward position kinematics for a (3-1-1-1)/sup 2/ fully parallel manipulator

This paper derives closed-form equations to solve the forward position kinematics of fully parallel manipulators with a 3-1-1-1 architecture on both the (planar) base and top platforms; the tetrahedrons emerging from the base and top platforms must have one leg in common. The closed-form solutions allow real-time execution on standard computer hardware: since only a few linear and quadratic equations have to be solved, all eight configurations can be found within milliseconds.