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I wish to model a fishing rod (or a rope) by joining short segments. (The segments may have equal (short) length but each segment should be assigned its own individual mass.) One segment will influence the next by the torque between the segments. For the time being the joints can be regarded as plate springs (torque proportional to bending angle (a or alfa), individual k for each joint).

When I apply torque to the first segment (the "handle"), the torque will spread to the rest of the segments.

The problem is that I do not understand how to compute the movements that will occur at segment one (with mass m1) and the following segments, when I apply torque T1 to segment one (during time dt).

https://www.dropbox.com/s/ze7g6dzrzzd6757/DSC_0113.JPG

I am a (retired) medical doctor with interest in biomechanics, so please use only basic physical terminology. (I wish to migrate the model to biomechanical use. I have written computer programs for models before, so hopefully I can manage that part if I just get the motion equations straight.)

cvr
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  • Thank you John Rennie. As you can see I am new here, so I must please ask: Should I repeat the question in the other forum or will it be moved "automatically"? – cvr Jun 05 '14 at 09:23
  • If you're in a hurry for an answer I would delete this question and ask a new question in CompSciSE. I would guess a moderator will be along in a while to move the question, but I'm not sure how long it will take. –  Jun 05 '14 at 09:38
  • I leave it here for a while first, to see if any one replies. Thanks for your suggestion. – cvr Jun 05 '14 at 09:42
  • Are you sure you want torque (springs) rather than a simpler "chain-link" model? A fishing rod has a lot of elasticity, so it may make sense there, but ropes/lines in general do not. – Carl Witthoft Jun 05 '14 at 11:59
  • Thank you for the suggestion CarlWitthoft But to be able to transfer the model into biomechanics it needs to accommodate for the addition of torque (muscular force) in each joint. ---- The problem sounds "simple" to me, who has no deeper experience of solving mechanical problems. But when I try to compute how the chain of segments will move, once a torque is applied to one of them during a short time interval, I can really not make it. – cvr Jun 05 '14 at 13:48
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    may be this will help if you want to do the pendulum approach derivation: http://12000.org/my_notes/double_pendulum/main.html – Nasser Jun 20 '14 at 05:10
  • Thanks Nasser. It is definitely a very good reference. I will look into it. -- I am also starting to realize how much they can accomplish with FEM: Link 1, Link 2, Link 3. Maybe I should start there to just grasp the process and see a quick result first. (I just know too little about the differences between the FEM softwares.) But to understand what is happening in ropes, fishing rods etc, the more approaches you have, the better. Thanks. – cvr Jun 20 '14 at 05:45

2 Answers2

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To solve this problem as you have described it, you need to set up a simple system of ordinary differential equations. For each segment in your "fishing rod" you just need to use conservation of linear and angular momentum ($F=ma$ and $\tau = \frac{dL}{dt}$). Each segment will experience forces and torques from its neighbors. There are many ways to formulate this. And many techniques to solve the resulting system of ODEs.

As a starting point, I would suggest attacking a simpler problem that will give you an idea of what's required: a double pendulum. There are many online demonstrations that solve the double pendulum problem including a detailed discussion of the math here, a Flash implementation here, a javascript version here, and a MATLAB version here. Also, some implementations place masses only at the joints while others have the mass distributed evenly along the segments so you might focus on the one you prefer.

Once you understand the double pendulum problem, it can be very easily extended to any number of segments. Adding a force at a given segment just means adding an additional force term to the acceleration equation for that segment and is very easy to achieve. The last step for your problem would be to include torques via conservation of angular momentum. I suggest implementing everything you need up to that point and then come back and ask more specific questions about implementing the torques if you need help once you're there.

Doug Lipinski
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  • Thank you DougLipinski for a very clear reply. I understand the reply and I can follow the mathematics of the Wikipedia article on the double pendulum. Studying the double pendulum seems to be a good approach for me to get a grasp on how to compute what is moving "between the time frames" of the simulation (the ODEs). --- For me it is still a complex problem and I may have to come back soon for more advice. Any kind of further comments appreciated. Thanks. – cvr Jun 05 '14 at 15:47
  • Hmmm... this now reminds me of a partly unsolved problem: why do dry stalks of spaghetti break into 3 pieces when bent? Turns out there are travelling shock waves. Should be some good articles via Google on that. – Carl Witthoft Jun 05 '14 at 15:50
  • To add to CarlWitthoft. I have also heard (but not verified) that pole vaulters can suffer fractures in carpal bones (wrist) if the pole breaks during a jump. Presumably also due to shock waves. – cvr Jun 05 '14 at 16:07
  • @ycc_swe Glad to help. If you get stuck, come back and ask more questions. People here are very eager to help, especially if you show equal effort and eagerness on your side. – Doug Lipinski Jun 05 '14 at 20:11
  • Thanks. I appreciate. Also good fun for me to look into. I assume the Hooke's spring constants will go into a new term forming the potential energy in the Lagrange (comparing to the double pendulum). The gravity potential energy term will have to go at first, the fishing rod will be for outer space. Much new interesting stuff for me to try to grasp. (But how the derivation should be generalized to n segments looks a little rough on me now. Will probably start with just two spring loaded segments.) – cvr Jun 06 '14 at 04:52
  • What software could be suitable? I am used to C syntax, but I used many others long time ago. Right now I just find the "Borland C++ builder" from 1998 on a CD at home. Add ons come on a floppy! (I used it for a simple gliding flight simulator then.) I am not sure it would even install under Win Vista in my HP Pavillion laptop now. So far this is just a small personal program so I appreciate if the software is free or not too costly. And also quick to install and learn, of course. Maybe this is a question for another thread? – cvr Jun 06 '14 at 04:53
  • I just installed the old Borland C++. it works fine under Vista. That will do. The equations will be my challenge for a while. Thanks for the help. – cvr Jun 06 '14 at 09:35
  • @ycc_swe I'd still start with the basic double pendulum so you have verified codes to compare with. If you don't want gravitational potential energy you can take it out later. The springs will store potential energy in a very similar way. C++ will obviously work and there are free compilers available for C/C++ on all platforms (see https://gcc.gnu.org/). An interpreted language might be easier to use for a problem like this that won't be too computationally intensive. Python is a very popular and good free option. – Doug Lipinski Jun 06 '14 at 15:40
  • Thanks DougLipinski. The double pendulum feels like the right track. Here is a preliminary of it: https://www.dropbox.com/s/48pksy0kl8mti40/20140606_224047.mp4 But I can't really say I feel confident in computing the corresponding equations for the plate springs. I want (optional) gravity, I just thought it might complicate. I will start trying to find the motion equations soon. But I am not sure I can make it. Any advice appreciated. (Should also try to fix a few things with the Borland builder. It works fine, but small text for my eyes, wrong folder for include files etc.) Thanks again. – cvr Jun 06 '14 at 20:52
  • This is the executable for the double pendulum, 240K. https://www.dropbox.com/s/navyqvknkce04fu/CANVAS.exe Over many iterations the momentas seem to accumulate, but I think it is just scaling. – cvr Jun 06 '14 at 21:18
  • @ycc_swe For obvious reasons, I'm not in the habit of downloading and running executables posted in the comments (and I don't have a Windows machine). I'd suggest asking a new question with specific problems you might be having. The more specific you can be, the more easily someone can help. – Doug Lipinski Jun 06 '14 at 22:40
  • @DougLipinski I agree with all you say. I just put the executable together with the video since the video became so large. (One reason I am back to Windows on this machine is that in Sweden, the national system for secure bank log ins have stopped supporting Linux! Bad.) I will try to compute the ODEs for the springs myself. If I can't make it I will as a new question. Thanks a lot for pointing out the double pendulum. A good first start on modeling a fishing rod. – cvr Jun 07 '14 at 00:00
  • @ycc_swe - You might find the scientific Python stack to be a little more productive to work with than C. There are a number of free installers available for Windows, including Continuum's Anaconda and Enthought's Canopy. – Aron Ahmadia Jun 10 '14 at 19:36
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Just to point out to a great free Open Source software used exactly for the purpose of modeling of a multibody system, just like your fishing rod. It's called MBDyn, and I've used it to model the dynamics of multicomponent airfoils. There is ample documentation available, and also slides that describe the physics. See for instance slide 25 of this presentation, the mutually connected deformable elements correspond exactly to the fishing rod.

I would suggest that you go through the tutorials and join the mailing list for questions. I've seen a presentation of prof. Masarati where he showed how a large part of the dynamical system of an entire helicopter (blades, rotor transmission, the whole deal) was modeled and analyzed using MBDyn, so I am fairly sure that the people on the list will be able to guide you with your model. This way, you won't have to build a framework just for yourself, that is later maybe stiff when it comes to modifications and extensions.

tmaric
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  • Thanks, very useful. I signed up for the mailing list now. I might get further using ready made software. I must just learn more about it. Is it possible to input variable forces etc? -- There is also the Finite Elements Method. I don't know yet if Multi body system or Finite Elements would be the best software for me to use? – cvr Jun 19 '14 at 04:07
  • Glad to be of help. I have only used rigid bodies, but elastic bodies can be used and they are modeled with FEM in MBDyn. – tmaric Jun 19 '14 at 08:22