Figure Q3 shows a robotic manipulator with the end effector at point C. Joints O, A and B are of the revolute type, and can be assumed to be frictionless. The lengths of the links are given as l1, l2, and l3. q1, q2, and q3 are measured as positive in the counter-clockwise direction. The links are assumed rigid and weightless. The rectangular coordinate frame XOY is defined as in the figure.