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Course: MAE 417, Fall 2009
School: Cornell
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Word Count: 382

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r01 3 r2c r1c 1 r12 2 r3c % % % % Equations of motion for a planar 3-link robot MAE 417/517 March 25, 2008 Daniel Brown % y is the vector of [theta1, theta2, theta3, Dtheta1, Dtheta2, Dtheta3] % p contains the parameter [I1, I2, I3, m1, m2, m3, r1c, r2c, r3c, r01, r12] % the inertia is taken about the center of mass, and r1c is the measure % from the origin (first joint) of link 1 to its center of mass. r12...

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r01 3 r2c r1c 1 r12 2 r3c % % % % Equations of motion for a planar 3-link robot MAE 417/517 March 25, 2008 Daniel Brown % y is the vector of [theta1, theta2, theta3, Dtheta1, Dtheta2, Dtheta3] % p contains the parameter [I1, I2, I3, m1, m2, m3, r1c, r2c, r3c, r01, r12] % the inertia is taken about the center of mass, and r1c is the measure % from the origin (first joint) of link 1 to its center of mass. r12 is the measure from % the origin of link 1 to the origin of link 2 function dy = planar3link(t,y,p) % Unpack the parameters I1=p(1); I2=p(2); I3=p(3); m1=p(4); m2=p(5); m3=p(6); r1c=p(7); r2c=p(8); r3c=p(9); r01=p(10); r12=p(11); % sines and cosines used in the equations c2 = cos(y(2)); c23 = cos(y(2)+y(3)); c3 = cos(y(3)); s2 = sin(y(2)); s23 = sin(y(2)+y(3)); s3 = sin(y(3)); % Mass matrix--It is symmetric m11 = I1+I2+I3 + r1c^2*m1 + m2*(r01^2+r2c^2+2*r01*r2c*c2) ... + m3*(r01^2+r12^2+r3c^2+2*r01*r12*c2+2*r01*r3c*c23+2*r12*r3c*c3); m12 = I2+I3 + m2*(r2c^2+r01*r2c*c2) + ... m3*(r12^2+r3c^2+r01*r12*c2+r01*r3c*c23+2*r12*r3c*c3); m13 = I3 + m3*(r3c^2+r01*r3c*c23+r12*r3c*c3); m22 = I2+I3 + m2*r2c^2 + m3*(r12^2+r3c^2+2*r12*r3c*c3); m23 = I3 + m3*(r3c^2+r12*r3c*c3); m33 = I3 + m3*r3c^2; M = [m11 m12 m13; m12 m22 m23; m13 m23 m33]; % Coriolis and centripetal terms (cross terms) u111 u122 u133 u112 u113 u123 u222 u211 u212 u213 u223 u233 u311 u322 u333 u312 u313 u323 = = = = = = = = = = = = = = = = = = 0; -m2*r01*r2c*s2 - m3*(r01*r12*s2+r01*r3c*s23); -m3*(r01*r3c*s23+r12*r3c*s3); 2*u122; 2*u133; u113; 0; -u122; 0; -2*m3*r12*r3c*s3; u213; u2...

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