Kinematics of A Three-Dof Platform with Three Extensible Limbs

A three degree-of-freedom manipulator that has a fairly large translational workspace is presented. The mechanism consists of a fixed base, a moving platform, and three extensible limbs. Each limb consists of a prismatic joint and two universal joints connecting the moving platform to the fixed base. Both the direct and inverse kinematics are investigated. The inverse kinematics problem yields two equal and opposite limb lengths for each limb while the direct kinematics problem is reduced to a second-degree polynomial in one unknown. Further, the workspace and singular conditions of the manipulator are discussed.