Question

I . ( 30%) Consider a three-link RRR manipulator its Jacobian matrix with respect to the base frame given in the following 3023 Based on the above Jacobian matrix, draw schematically the robot with the correct frame to each link, where 12 and /3 are the link length for link 2 and 3, respectively. Give the reason why it is so. a) b) Obtain the 'J for the given J based on the frame assignment in a); o) Using either of the above Jacobians (J or °J ), determine the set of angle which the manipulator is at a workspace-interior singularity and draw schematically the configuration of the singularity If you allow to add one link parameter (not a joint variable) in the manipulator in order to eliminate singularities inside the workspace, which link parameter you would like to use? Why? Draw a diagram to show it. d)

Answer 1

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3-DOF RRR articulated from J = [-s_1(l_2c_2 + l_3c_23) C_1 (l_2c_2 + l_3C_23) 0 - c_1 (l_2 s_2 + l_3 s_23) -s_1(l_2s_2 +l_3s_23) l_2c_2 +l_3c_23 -l_3c_1 s_23 -l_3s_1s_23 l_3c_23] = > The above specified Jacobean is for 3-DOF spherical articulated arm