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Direct kinematics of manipulators with hyper degrees of freedom and Frenet-Serret formula

The kinematic structure of a manipulator with hyper degrees of freedom is discussed from a theoretical viewpoint. Conditions for the kinematic structure are derived from a geometrically natural requirement that its direct kinematics tends to Frenet-Serret formula as its number of degrees of freedom increases. It is shown that the manipulator has to have two-degree-of-freedom joints, each of which consists of a twist and a one-directional bend.