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How to Compute the Jacobian of a Robot Manipulator: A Numerical Example | Robotic Systems
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In this video I explain, through an example, how to compute the Jacobian matrix of a robot. If you want to contribute to the development of this type of video tutorials:
Matlab code used to compute the results of the example:
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trans = @ (t) [eye (3) t; zeros (1,3) 1];
rotx = @ (ang) [1 0 0 0, 0 cos (ang) -sin (ang) 0, 0 sin (ang) cos (ang) 0, 0 0 0 1];
rotz = @ (ang) [cos (ang) -sin (ang) 0 0; sin (ang) cos (ang) 0 0, 0 0 1 0, 0 0 0 1];
DHR = @ (q, p) rotz (q (1) + p (1)) * trans ([0; 0; p (2)]) * trans ([p (3); 0; 0]) * rotx (p (4));
A01 = DHR (pi / 2, [0; 352; 70; -pi / 2]);
A12 = DHR (0, [- pi / 2; 0; 360; 0]);
A23 = DHR (-pi / 2, [0; 0; 0; -pi / 2]);
A34 = DHR (0, [0; 380; 0; pi / 2]);
A45 = DHR (0, [0; 0; 0; -pi / 2]);
A56 = DHR (0, [0; 65; 0; 0]);
A02 = A01 * A12;
A03 = A02 * A23;
A04 = A03 * A34;
A05 = A04 * A45;
A06 = A05 * A56;
z0 = [0; 0; 1];
z1 = A01 (1: 3.3);
t1 = A01 (1: 3.4);
z2 = A02 (1: 3.3);
t2 = A02 (1: 3.4);
z3 = A03 (1: 3.3);
t3 = A03 (1: 3.4);
z4 = A04 (1: 3.3);
t4 = A04 (1: 3.4);
z5 = A05 (1: 3.3);
t5 = A05 (1: 3.4);
t6 = A06 (1: 3.4);
J = [cross (z0, t6) cross (z1, t6-t1) cross (z2, t6-t2) cross (z3, t6-t3) cross (z4, t6-t4) cross (z5, t6-t5); z0 z1 z2 z3 z4 z5]
rank (J)
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This video is part of a set of video tutorials used in robotics subjects at the Universitat Politècnica de València.
Matlab code used to compute the results of the example:
%%%%%%%%%%%
trans = @ (t) [eye (3) t; zeros (1,3) 1];
rotx = @ (ang) [1 0 0 0, 0 cos (ang) -sin (ang) 0, 0 sin (ang) cos (ang) 0, 0 0 0 1];
rotz = @ (ang) [cos (ang) -sin (ang) 0 0; sin (ang) cos (ang) 0 0, 0 0 1 0, 0 0 0 1];
DHR = @ (q, p) rotz (q (1) + p (1)) * trans ([0; 0; p (2)]) * trans ([p (3); 0; 0]) * rotx (p (4));
A01 = DHR (pi / 2, [0; 352; 70; -pi / 2]);
A12 = DHR (0, [- pi / 2; 0; 360; 0]);
A23 = DHR (-pi / 2, [0; 0; 0; -pi / 2]);
A34 = DHR (0, [0; 380; 0; pi / 2]);
A45 = DHR (0, [0; 0; 0; -pi / 2]);
A56 = DHR (0, [0; 65; 0; 0]);
A02 = A01 * A12;
A03 = A02 * A23;
A04 = A03 * A34;
A05 = A04 * A45;
A06 = A05 * A56;
z0 = [0; 0; 1];
z1 = A01 (1: 3.3);
t1 = A01 (1: 3.4);
z2 = A02 (1: 3.3);
t2 = A02 (1: 3.4);
z3 = A03 (1: 3.3);
t3 = A03 (1: 3.4);
z4 = A04 (1: 3.3);
t4 = A04 (1: 3.4);
z5 = A05 (1: 3.3);
t5 = A05 (1: 3.4);
t6 = A06 (1: 3.4);
J = [cross (z0, t6) cross (z1, t6-t1) cross (z2, t6-t2) cross (z3, t6-t3) cross (z4, t6-t4) cross (z5, t6-t5); z0 z1 z2 z3 z4 z5]
rank (J)
%%%%%%
This video is part of a set of video tutorials used in robotics subjects at the Universitat Politècnica de València.
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