Clear[t1, t2, t3];
l1 = 1.0;
l2 = 1.0;
l3 = 1.0;
tfinal = 10;
J[t1_,t2_,t3_] := {{-l1 Sin[t1] - l2 Sin[t1 + t2] - 
        l3 Sin[t1 + t2 + t3], -l2 Sin[t1 + t2] - 
        l3 Sin[t1 + t2 + t3], -l3 
        Sin[t1 + t2 + t3]}, {
      l1 Cos[t1] + l2 Cos[t1 + t2] + l3 Cos[t1 + t2 + t3], 
      l2 Cos[t1 + t2] + l3 Cos[t1 + t2 + t3], 
      l3 Cos[t1 + t2 + t3]}};

g = {};
count = 1;
dt = 0.01;
{t1,t2,t3} = {0.0,Pi/2,2 Pi/3};
Do[
ns = Flatten[NullSpace[J[t1,t2,t3]]];
If[ns[[1]] < 0, ns = -ns];
{t1,t2,t3} += ns*dt;
	orig = {0,0};
	p1 = {l1 Cos[t1], l1 Sin[t1]};
	p2 = {l1 Cos[t1] + l2 Cos[t1 + t2], l1 Sin[t1]  + l2 Sin[t1 + t2]};
	p3 = {l1 Cos[t1] + l2 Cos[t1 + t2] + l3 Cos[t1 + t2 + t3], 
      l1 Sin[t1] + l2 Sin[t1 + t2] + l3 Sin[t1 + t2 + t3]};
	If[count >= 10,
	g = Append[g, Graphics[{RGBColor[1,0,0], Line[{orig,p1,p2,p3}]}]];
		count = 0];
	Print[Flatten[NullSpace[J[t1,t2,t3]]]];
	count++,
	{t, 0, tfinal, dt}];

<<Graphics`Animation`;
ShowAnimation[g, PlotRange->{{-3,3},{-3,3}}, Axes->True];
