The dynamic equations of motion are obtained using Lagrange's formulation of dynamics. It may be noted that the generalised force corresponding to joint variable qr, is the joint point Gj (torque tj for a revolute joint, or force Fj for a prismatic joint). For the flexible deformation variables (qf), the corresponding generalised force will be zero, if the corresponding elastic deflections or rotations have no displacement at those locations where external forces are applied; note that this corresponds to the case when a clamped condition is used for the controlled end of the link. The general form of Lagrange's equations (for the clamped condition), then, for joint variable qr, are the following, where T is the total kinetic energy of the flexible manipulator system, and V is the total potential energy owing to elastic deformations and gravity.

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