Needs["Graphics`Shapes`"];

R = 
        2;   
\(r = 
      1; \  (*\ 小球の半径\ *) 
φ = 2/3\ Pi;\)
\(ω = 
      1;  (*\ 角速度一定\ *) 

θ = ω\ t;\ \ 
\)
timeend = 4 Pi;

Q = 
        TranslateShape[
          RotateShape[Sphere[R], φ, φ, 
            1/2 φ], {0, 0, 0}];
tenkyu[u_] := 
        TranslateShape[
          RotateShape[Sphere[u], 0, (R/u) θ, 
            0], {0, (R + u) Cos[-θ], (R + 
                  u) Sin[-θ]}];

Do[
Show[
Graphics3D[{Q, 
            tenkyu[r]}, 
PlotRange -> {{-R - 2 r, 
                R + 2 r}, {-R - 2 r, R + 2 r}, {-R - 2 r, 
                R + 2 r}}, 
ViewPoint -> {2  R, 2  R, 
              R - r}, 
Boxed -> False, 
          Axes -> 
            False
]
]
, {t, 0, timeend, 1/20 Pi}
]