The total kinetic energy of a flexible-link manipulator system is due to the motions of joints and links and the kinetic energy resulting from the payload. The kinetic energy for a revolute joint j is represented here, where I and W are the joint matrix and the angular velocity vector of joint j, respectively. In the case of prismatic joint j, at any instant of time, a part of the translating beam is outside the joint hub and is free to vibrate, while the remaining part of the beam is inside the joint hub and is restrained from vibrating. The kinetic energy owing to part of the beam inside the joint hube is given here.

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