Inspection End Effecter 02 Joint 3 y Bo L Object Figure 1. Shuttle manipulator inspecting an object surface
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, θ1, θ2 and θ3 , and the three links, as shown in the figure. 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.
a) Obtain the forward kinematic equations relating the end effecter position and orientation, xe , ye and φe to the three joint angles, θ1 , θ2 and θ3 . Note that the end effecter position and orientation are viewed from the Cartesian coordinate system attached to the object, O-xy.
b) Obtain the Jacobian matrix associated with the kinematic equations of Part a).
Note: All the angles are measured in the right hand sense. θ2 in the figure is therefore negative.
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