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What is the most efficient way to transfer motion? Answered

What is the most efficient way to transfer lateral movement to vertical movement via a ramp.
The following curve is equal on both sides of the apex, if that is the correct term.  Is this the best way to transfer the movement to strait vertical or should something else such as a long start to the incline and then a sudden shoot up.


I would have thought that the best profile would be a simple radius (1/4 of a circle) which would give you a smooth profile at start end exit of the curve, and maintain a constant angular acceleration through it (as long as the velocity is constant).

Depends on the materials, depends on the quality of your wheel bearings.

The starting potential energy is the same no matter what the curve looks like, and if you ignore losses the output kinetic energy would be the same. So figure out where the losses will be and what their magnitude will be, and use those to derive your answer.

Beyond those hints: The point of homework is for YOU to practice using what you've been taught. Do so. If your teacher is at all decent, you've been given the tools you need.

Well, my teacher isn't but I am working on testing this. I just wondered if there was a ramp style that would result in less energy lost to friction and other forces.

There may be, but it's going to depend on what those forces are. Do some calculations, draw some hypotheses, do some experiments (or simulations, though those depend on your accounting for the forces correctly), look at the results and see what's most promising, form new hypotheses which refine your initial guesses, repeat.

I'll point out one obvious limiting factor: with the cart design you've shown us, if the curve gets too sharp the nose of the cart will scrape on the ramp.

Or, if you really need crib notes, go research the issue yourself rather than asking us to hand it to you on a platter. But we've given you the hints you need, I think.

Ok, the wheels on the cart stick out form the sides along with the wheels so that solves that problem. I guessed I would have to test this my self, but there is always the chance that sombody has already done it and could save me important time and money.

Some obvious issues, which you will need to resolve in order to answer this question.

The wheels need to stay on the ramp at all times, which means that the minimum radius of curvature must be longer than the distance from the front wheel bottom to the forward corner of the vehicle. Otherwise, the nose will hit the ramp and the vehicle will stop.

Second, your losses will be driven by frictional forces through out the whole mechanism (ramp, vehicle, wheels, axles, etc.). They will be exacerbated by any forces which are not along the direction of motion.

For example, that near right angle at the bottom means that you're trying to suddenly change the motion from horizontal to vertical, which requires a force ~normal to the velocity. That force will consequently push the axles against the sides of the bearings, increasing friction and slowing you down.

How can you minimize that effect? Once you've answered that question, you should be able to solve the rest of the problem.

The wheels are outside the vehicle along with the rails, but yea I am trying to find out how to minimize the effects.