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% decision variables [gamma;f1;f2]

c = [1; zeros(4,1)];

% sum forces and torque in inertial frame

G = [0 t1(1) n1(1) t2(1) n2(1);

0 t1(2) n1(2) t2(2) n2(2);

0, t1(2)*r1(1) - t1(1)*r1(2), n1(2)*r1(1) - n1(1)*r1(2), t2(2)*r2(1) - t2(1)*r2(2), n2(2)*r2(1) - n2(1)*r2(2)];

A = G;

b = zeros(3,1);

% create C and d for friction cone

C = zeros(0,5);

C = [C;-1 0 -1 0 0]; %f_1z + gamma >= 0

C = [C;-1 1 -mu 0 0]; %mu f_1z + gamma >= f_1x

C = [C;-1 -1 -mu 0 0]; %f_1x + gamma >= -mu f_1z

% same for f2

C = [C;-1 0 0 0 -1]; %f_2z + gamma >= 0

C = [C;-1 0 0 1 -mu]; %mu f_1z + gamma >= f_1x

C = [C;-1 0 0 -1 -mu]; %f_1x + gamma >= -mu f_1z

% bound gamma

C = [C;-1 0 0 0 0]; % gamma >= -1

d = [zeros(6,1);1];

% PROBLEM SETUP, DO NOT EDIT

% Construct vectors r1 and r2

r1=sym('r1',[2 1]);

sym(r1,'real');

r2=sym('r2',[2 1]);

sym(r2,'real');

n1=sym('n1',[2 1]);

sym(n1,'real');

t1=sym('t1',[2 1]);

sym(t1,'real');

n2=sym('n2',[2 1]);

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Force Closure | Problem Set 8 | 6.832x Courseware | edX https://courses.edx.org/courses/MITx/6.832x/3T2014/courseware/wee...

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Force Closure | Problem Set 8 | 6.832x Courseware | edX https://courses.edx.org/courses/MITx/6.832x/3T2014/courseware/wee...

3 of 3 10/01/2015 14:58

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