This paper investigates a difficult problem of tracking control for robotic manipulations with guaranteed high accuracy. Uncertain kinematics, unknown torques including unknown gravitational torque, unknown friction torque, and uncertain dynamics induced by uncertain moment of inertia and disturbance, are addressed. The approach is developed in the framework of observer-based control design. Two sliding-mode observers are proposed to handle uncertain kinematics and to estimate unknown torques, respectively. Using the estimated information, a control law is then synthesized to guarantee that the desired trajectory can be followed after finite-time with zero tracking error. Experimental results are presented to show the performance of the proposed control approach.