vars={α1,α2,z,λ1,λ2};

F[t]:=-1;

s1=Sin[α1[t]-α2[t]];
c1=Cos[α1[t]-α2[t]];
LM=(L1 L2 m2)/2;
eqns={(J1+m2 (L1^2)) α1''[t]+LM c1 α2''[t]==-LM s1 α2'[t]
-(L1 Cos[α1[t]] λ1[t]+L1 Sin[α1[t]] λ2[t]),
LM c1 α1''[t]+J2 α2''[t]==LM s1 ((α1'[t])^2)
-(L2 Cos[α2[t]] λ1[t]+L1 Sin[α2[t]] λ2[t]),
m3 z''[t]==-F[t]-λ2[t]};

constraints = (({{L1 Sin[α1[t]]+L2 Sin[α2[t]]==0}, {z[t]-L1 Cos[α1[t]]-L2 Cos[α2[t]]==0}}));

params={J1->4.5,J2->5.5,m1->1,m2->1,m3->1,L1->1,L2->2,g->9.81};

{sliderCrank}=NDSolve[{eqns,constraints,α1[0]==Pi/4,α1'[0]==-1}/.params,vars,{t,0,20},Method->{"IndexReduction"->Automatic}];

Plot[Evaluate[{λ1[t],λ2[t]}/.sliderCrank],{t,0,10},PlotStyle->{Red,Blue},
PlotLegends->Placed[LineLegend[{Red,Blue},{"Tension in Crank (λ1)","Tension in Connecting Rod (λ2)"}],Bottom],ImageSize->300]