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In general, I want understand how the Power transmission in flexible tools works such as this flexible pick up tool in this link: https://www.youtube.com/watch?v=TLbCatz4Pnkv=q9AkmsTNLkY . Specifically, I want to find a model of the inside tool, that describe the relationship between the axial input force at the one end and the axial output force at the other end given a certain shape of the tool. I know, that the mechanical name of the flexible tool inside is called flexible multibody, but I fail to find useful resources, which describe a direct relationship between axial input force and axial output force. I tried looking for the datasheet of similar products, but I didn't find any useful information.

I would be more than thankful, if someone can provide me with a useful guidance.

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Many ways of transmitting power, mechanical with a steel cable with opposing winds or hydraulics using oil or compressed air come to mind. A datasheet for a product will explain the product but not always all the details of the parts used to make it.

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First of all, welcome to Stack Exchange Engineering!

I think what you're looking for is how the forces work through the tool, not power transmission (which is work over time; power transmission would be more like power going through a flexible Dremel attachment). But this is a great question, and recognizing that it isn't just a simple thing puts you way ahead of the pack.

I'm going to try to put this simply, but I may assume too much. I may also be too simple for you and if so, I apologize.

Any solid system can be broken down from forces on one end into forces on the other end. Every force will be transmitted from the claw end into the exact same force (same vector) on the handle plus a moment (rotating force) on the handle in 1 to 3 exes (left/right, forward/backward, up/down: typically named how you want it as x, y, & z directions). A turning force on the end of the tool will also be transmitted to the handle exactly in the same plane as on the end.

The shape of the device does not matter at all, except in how forces in the middle work. This translation of forces is what makes crazy-shaped holders grab things off the edge of tables. https://www.walmart.com/c/kp/purse-hooks-for-tables.

I don't know what your trigonometry background is, but this generally involves:

  1. Setting a reference grid (directions), in the x, y, and z axes. Think north/south, east/west, & up/down. A typical set of axes would have one of the axes going right through the handle so that the forces on the handle are easy to describe.

  2. Turn the force on one end of the tool into the component x, y, and z forces at the end of the tool using sines & cosines. Forces are generally pounds in the USA, newtons everywhere else except Myanmar & Liberia.

  3. Transfer the exact same forces to the handle and then translate the x, y, and z direction forces into a single force vector, again using sines & cosines. We would try to keep the forces as components translated into component forces relative to the handle direction (in/out, left/right, & up/down relative to the handle).

  4. Translate any turning force (moment) on the end back to the handle as well. Directions of moments are described as going right through the middle of the "wheel" in the direction of the axle. The "right-hand rule" is used to visualize this - if you make your right hand into a thumbs-up position (sorry, West Africans & Middle-Easterners, I know what this means there), your fingers will go on the direction of the turning force (the way the wheel rotates), and the thumb will be at right angles to the moment (right through the axle). So if we twist the end, that exact same twist will be passed on to the handle, in the exact same orientation. Moments are described as foot-pounds or inch-pounds in the USA, newton-meter everywhere else. One pound of force one foot away equals 1 foot-pound.

  5. Use the component forces on the end to create new moment forces on the handle. Each x, y, z force on the handle times the distance from the handle (usually the center of the grip) generates a turning moment. This is what makes it rotate in your hand, and why holding a shovel parallel to the ground by the middle of the handle is much easier than holding it by the end of the handle. It's also why putting a heavy motorcycle on a hitch carrier on your trailer hitch can rip the hitch off your vehicle even if the weight of the bike is less than the rated tongue weight.

  6. Turn the moments into a useful set of rotational forces relative to the handle. In airplanes they call these moments pitch, roll, and yaw - controlled by elevator, ailerons, and rudder respectively.

  7. Doing it right would also involve the gravity force exerted on the tool through it's center of gravity (usually the balance point.

This same process can be used at any point in the tool. For example, the friction-fit joint that lets the magnet move to any angle on a magnetic pickup tool - we can determine what the forces would be on that joint as well.

We learn this in engineering school ("I once wanted to be an en-ga-neer, now I is one.") in Statics. We start in 2 dimensions, and eventually move to three dimensions. The classic engineering case is a truss bridge and analyzing the forces through each truss member. We describe movements and forces of multiple-linkage devices in Dynamics (things like car suspension or steering parts).

The process is described much more detail and with diagrams in the following links.

https://www.youtube.com/watch?v=wtU8uHnAWk8

https://engineering.purdue.edu/~aprakas/CE297/CE297-Ch3.pdf

Trigonometry knowledge is required, which is why that class is a pre-requisite to engineering courses. It isn't hard, tho, for the part we need. Here's one web resource. https://www.mathsisfun.com/geometry/unit-circle.html

Ask more questions here and I will try to help. I love this stuff & would love to bring someone new into the field.

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