PROBLEM SET 6 1. What is the Jacobian for translational velocities of point “P” for the following robot? X0 Y0 Y1 X1, Y2 X2 X3 Y3 P 1 What is the velocity of point “P” after 1 second if all the joints are rotating at

(2=-90° at home position) (3=-90° at home position) Problem 1 Link i Twist i Link length ai Link offset di Joint angle i i=0 … i=1 A1=1 1 (1=90° at home position) i=2 A2=1 2 (2=-90° at home position) i=3 3 (3=-90° at home position)

Problem 1

Problem 1 The transformation matrix for is

Problem 1 The transformation matrix of point “P” w.r.t. frame {3} is

Problem 1

Problem 1 Note: A1=1, A2=1: At t=1,

Problem 1 X0 Y0 Y1 X1, Y2 X2 X3 Y3 P 1 We should get the same answer if we used the transformation matrices.