A kinematic singularity occurs when the Jacobian matrix associated with the forward kinematic map loses rank. At a singular configuration, the end-effector velocities are restricted to a subspace of the task space velocities. Also, rate control schemes that require the inversion of the Jacobian matrix fail at such singularities. However, even at a singular configuration, if the kinematic map is generic the end-effector can achieve a desired end-effector acceleration. The second order kinematic equations are derived for a serial chain manipulator using screw theory to demonstrate this. These equations are then used to develop a scheme to determine the joint rates from the desired end-effector velocity and acceleration at singularities. The theory and the algorithm are illustrated using simple examples and computer simulations.

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