The ICW engine solution.We've misled and distracted you long enough. We tried to focus your attention everywhere but toward the real flaw. The animated GIF causes you to notice the motion of the balls and carriers, making it seem as if they are the only movable mass. But the water moves, too, and that isn't shown in the animation. That's the trouble with animations of physical phenomena. They show you only what their designer thinks you should see. They can deceive you, especially because they appeal to your senses more than do words or equations on a printed page. Teachers, take note.
When a carrier capsule and ball move up the tube, water is displaced from where the capsule moves to, and an equal volume of water moves into the space where the capsule was. The capsule with its metal ball weighs less than an equal volume of water. That's why it moves up the tube when allowed to. So when it moves up, an equal volume (but heavier) amount of water moves down. The center of mass of the entire system moves down, below the axle. So when the capsule arrives at the top of the tube (Y) The tube is now bottom-heavy. The ball which has rolled into the sidearm does initiate clockwise motion, but it has to do work lifting the center of mass of the rest of the system. But when you view the animation, you are led to think only of the metal balls rising to a higher level, not realizing that as they do this, the center of mass of the entire apparatus moves down. The center of mass of this system is always below the axle at all times.
There's no possibility of a torque except in the sidearms. But if the ball does gave the apparatus a torque as it rolls down the upper sidearm, it would give the apparatus an equal and opposite torque when it rolls down that same sidearm if the sidearm actually reached the bottom. The net work done in these two hypothetical processes would be zero. This ineffectiveness of the sidearm dynamics was noted by a correspondent. However, as we showed above, the sidearm never gets to the bottom because the entire apparatus is always bottom-heavy, its center of mass being below the axle. But even if it did reach the bottom, that wouldn't aid the cause of achiving perpetual motion.
Historical footnote: The sidearm dynamics are exactly like that of one of the earliest (known) perpetual motion machine wheel, the Bhaskara wheel (c. 1159). It was a wheel with tilted hollow tubes around the rim. Each tube had mercury, or a rolling ball, inside. Since the wheel, in rotating 180° brings a tube from top to bottom, the sense of tilt of the tube is inverted. So the torque given to the wheel due to the ball rolling from one end to the other inside the tube at the top exactly equals the counter-torque when the ball rolls back to the other end of the tube when the tube is at the bottom. I have not seen this simple explanation of the futility of this kind of overbalanced wheel anywhere in print. To make matters worse, the direction of that torque at the top can be opposite to that naively assumed, depending on the tilt of the tube. It can also depend on the speed given the wheel, if the wheel is started by giving it a push.If you began with the system at rest in the position shown in the color picture, you'd have only enough stored potential energy to turn the apparatus through some angle (dependent on the length and tilt of the sidearms), then the system would come to rest. If you began with the system at rest with the carriers and balls at their lowest positions, you'd only have enough stored potential energy to turn the apparatus through 360°, with no energy left over. If you gave the wheel a good push to get it started, you could get it spinning for a number of revolutions, but dissipative forces would eventually bring it to a halt.
But that animation does seduce you into thinking otherwise, doesn't it? When I first saw this device, I considered it somewhat "inelegant". But after thinking it through, I realized it was sufficiently diabolical in construction to merit space in the museum.
By the way, "Phineas Mason" is a pseudonym, not the invetor's real name.
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