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The 321-HEXA: a fully-parallel manipulator with closed-form position and velocity kinematics

This paper presents analytical solutions for the forward displacement and velocity kinematics of the "321-HEXA", a fully-parallel manipulator design with R-RR-RRR legs as in the "HEXA" design and with a "3-2-1" top platform. The forward position and velocity kinematics rely on simple geometric algorithms that find the position and velocity of the top of a tetrahedron from the knowledge of the tetrahedron's side lengths as well as the position and velocity of the base triangle points. The forward position kinematics give eight solutions, requiring linear and quadratic equations only. The inverse kinematics requires the solution of one quartic equation for each leg.