Molecular planetary gearsets

Common planetary gearsets are composed of three components: the sun gear, the planet gears (and the planet carrier to which the planet gears are fixed), and the ring gear. Each of these components can be input, output, or fixed. The gear ratio, which is the ratio of the rotation speeds of the input and output component, is determined by the setting of these components and the number of teeth of the sun and ring gear:
  1. When Input=S, Output=C, Stationary=R, gear ratio = 1 + r / s;
  2. When Input=S, Output=R, Stationary=C, gear ratio = - r / s;
  3. When Input=C, Output=R, Stationary=S, gear ratio = r / ( r + s );
where r is the number of teeth of the ring gear and s is the number of teeth of the sun gear. If the ratio is greater than 1, it is a reduction (the output component rotates more slowly than the input one). Otherwise, it is an overdrive (the output component rotates more quickly than the input one).

Are the above formulas also applicable to molecular planetary gearsets? Check it out yourself with a hypothetical molecular planetary gearset shown below. More broadly, what problems will we encounter when we apply the concepts from mechanical engineering to molecular nanotechnology?

Case 1: Van der Waals (VDW) spacefilling display mode Case 2: Ball-and-stick display mode
Case 3: Stick display mode Case 1: Wireframe display mode, VDW shading, VDW lines and kinetic energy shading
Case 3: Denaulay triangulation mode Case 2: Spacefilling and kinetic energy shading mode

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