An astronaut is operating a shuttle manipulator with an inspection end effecter attached to the tip of the arm. For the sake of simplicity we consider only the three revolute joints, ?1, ?2, ?3 , and the three links, as shown in the figure below. A Cartesian coordinate system, O-xy, is attached to the object to be inspected. The distance of the coordinate origin O is L from the location of the first joint. Answer the following questions using the notation shown in the figure.

Inspection End Effecter x Bo Joint 3 y L Object Figure 3 Shuttle manipulator inspecting an object surface. All the angles are measured in the right hand sense. 02 in the figure is therefore negative.