The structure is addressed of time-optimal control of robotic manipulators along a specified geometric path subject to constraints on control torques. Both regular and singular (where one or more effective inertia components is/are zero on any finite time interval) cases are studied by using the extended Pontryagin's minimum principle and a parametrization method. It is shown that the structure of the time-optimal control law requires either(a) one and only onecontrol torque to be always in saturation in every finite time interval along its optimal trajectory, while the rest of them adjust their values so that the motion of the robot is guaranteed along the constrained path, or (b)at least oneof the actuators to take on its extremal values. The first form of the control law dominates the robot motion along the optimal trajectory although the second form may exist. The theoretical results are verified by various existing numerical examples.