Clear["Global`*"]; 

\[Theta]1[t] := (Sqrt[m2]*(c1*Cos[t*\[Omega]1 + \[Phi]1] -
c2*Cos[t*\[Omega]2 + \[Phi]2]))/Sqrt[m1 + 2*m2]; 

\[Theta]2[t] := (g*len*Sqrt[m2]*(m1 + m2)*(c1*Cos[t*\[Omega]1 + \[Phi]1] +
c2*Cos[t*\[Omega]2 + \[Phi]2]))/(Sqrt[m1 + 2*m2]*Sqrt[g^2*len^2*m2*(m1 +
m2)]); 

\[Omega]1 := Sqrt[(g*len*(m1 + m2) - Sqrt[g^2*len^2*m2*(m1 +
m2)])/(len^2*m1)]; 

\[Omega]2 := Sqrt[(Sqrt[g^2*len^2*m2*(m1 + m2)] + g*len*(m1 +
m2))/(len^2*m1)]; 

values = {len -> 1, g -> 1, \[Phi]1 -> 0, \[Phi]2 -> 0}; 

line[c1_, c2_, m1_, m2_] = Line[{{0, 0}, {len*Sin[\[Theta]1[t]],
(-len)*Cos[\[Theta]1[t]]}, {len*Sin[\[Theta]1[t]] + len*Sin[\[Theta]2[t]], 

       -(len*Cos[\[Theta]1[t]] + len*Cos[\[Theta]2[t]])}}] //. values; 

point1[c1_, c2_, m1_, m2_] = Disk[{len*Sin[\[Theta]1[t]],
(-len)*Cos[\[Theta]1[t]]}, 0.1] //. values; 

point2[c1_, c2_, m1_, m2_] = Disk[{len*Sin[\[Theta]1[t]] +
len*Sin[\[Theta]2[t]], -(len*Cos[\[Theta]1[t]] + len*Cos[\[Theta]2[t]])},
0.1] //. values; 

Manipulate[ListAnimate[Table[Graphics[{{Gray, Rectangle[{-1, 0}, {1, 0.1}]},
N[line[c1, c2, m1, m2]], N[point1[c1, c2, m1, m2]], N[point2[c1, c2, m1,
m2]]}, 

     PlotRange -> {{-2, 2}, {0.2, -2.5}}], {t, 0, 10*Pi, 2*(Pi/50.)}],
AnimationRepetitions -> 1, AnimationRate -> 10, ControlPlacement -> Bottom],
{c1, 0, 1}, 

  {c2, 0, 1}, {m1, 1, 3}, {m2, 1, 3}, FrameMargins -> 0, SaveDefinitions ->
True]