Robotics 2009/10 Exercise

InstitutfrZuverlssigkeitstechnik

Dipl.Ing.M.Gomse

Lagrangian formulation of manipulator kinematics Use the Lagrangian approach to derive the torque equations of the manipulator

shown in Figure 1.

For simplicity, we assume that the mass distribution is extremely simple: All mass

exists as a point mass at the distal end of each link. These masses are and .

Given: ,, , , Hint: sin sin cos cos cos

a) Derive the position of and in Cartesian form

b) Derive the velocity of and in Cartesian form

c) Derive the torque equations of the manipulator with Lagrangian approach.

g

Figure 1

x

y