Based on the Roberval principle, a self balanced cradle could be made with gears.
Each cradle wing is resting on a remaining horizontal arm which is fastened to the outer gear.
A spring is placed in the pedestal so the bar is able to drop with the increasing weight and size of a larger book.
- cradle.png (46.74 KiB) Viewed 9711 times
An existing
example illustrates the working.
- gear_balance.png (10.83 KiB) Viewed 9713 times
Five gears are on a rigid beam IH. The bar is free to rotate about the central axis located on the support pedestal. The gears rotate, except for the center one that is fastened to the pedestal and cannot move. Horizontal arms LI and KE remain horizontal at all times, for they are fastened to the gears at each end of the main beam IH. Therefore the equal mass round weights P and p can be placed anywhere on these arms and the system is still in balance. In fact, if the arm KE were made extremely long, both weights could be on the left side of the central axis. They could be directly above or below each other, or p could even be to the left of P. The system would still be in balance.
