Kinematics and dynamics of under-actuated manipulators

The kinematics and dynamics of underactuated manipulators are discussed. It is shown that, due to the presence of passive hinges, the dynamics of the underactuated manipulators are considerably more complex than those of fully actuated manipulators. Spatial operator algebra techniques are used to develop expressions for the dynamical equations of motion, the mass matrix, the generalized Jacobian, and the Jacobian that describes the coupling between the motions of the active and passive hinges. An efficient and recursive inverse dynamics algorithm, the complexity of which depends only linearly on the number of degrees of freedom, is also described. The structure of this algorithm is a hybrid combination of well-known inverse and forward dynamics algorithms for fully actuated manipulators