Instant Center of Rotation Flow - How does the I.C. move during a cast?

[gordonjudd]

The actual path for the space-centroid (explanation given at Wikipedia) Would be interesting to see, and is something that Grunde could do by analyzing the velocity of two or more points near the butt of the rod on his slow motion videos.

You might first check out a video that shows a typical instantaneous center flow before you try to plow through the details given below.

This may be something of interest to just Bob and me, as it involves a concept in rigid body dynamics that most non-technical readers will just have to take on faith. However, it was a chance for me to learn something about video processing, and the result may be illuminating to many readers.

Most people are probably not interested in the dynamics principle involving the instantaneous center derivation, but it is a handy way to look at the velocity values at different points on a rigid body that is undergoing both rotation and translation. The instant center (I.C.) of rotation is the point in space about which all points on the rigid body are revolving around at one instant of time.

Thus the velocity of any point on the body can be determined from Vp=omega x r, where omega is the rotation rate about the I.C. axis in radians/sec and r is the vector from the I.C. to the point on the body. This cross product will give the direction of Vp (it will be perpendicular to the direction of r) in addition to its magnitude omega*r.

If the body is just rotating (such as a freely spinning wheel) then the I.C. will be located on the object. If the body is undergoing pure translation the I.C. will be located at infinity. If the body is undergoing both rotation and translation then the I.C. will be at a finite distance from the body, but in general will not be located on the body itself.

The butt of a fly rod is not strictly a rigid body since it can bend somewhat, but the butt is rigid enough that we can apply the I.C. of rotation concept to see how the effective rotation center of the rod varies during a cast.

Generally the I.C. is determined by finding the intersection of two vectors that are taken at right angles to the velocity vectors (v has a direction as well as a magnitude) measured at different points on the rigid body. Similarly, it can be found by finding the perpendicular bisector of two points on the body taken at two different time points as shown in diagram below that was used in the Wikipedia article.


This bisector approach is what I used to find the I.C. of the rod rotation since it was a more direct way to analyze the spatial data taken from individual video frames. For the few people that might be interested in the details of finding the I.C. here how it was done.

First I digitized three different points near the butt of a high speed video as they moved from frame to frame on the video data. The points I used were the butt end of the rod, the top of the grip, and a point .45 m up from the grip. Then I computed the normal to each of those curved paths. From there I computed the three intersection point s of the normal vectors on a frame by frame basis to determine how the I.C. moved during the cast.

An example of determining the I,C. at one point in time with the bisector approach is shown below. I used three points instead of just two, as an accuracy check, and found the resulting intersection points to be surprisingly close to each other as shown in the figure. The final I.C. value I used was set equal to the average of the three points determined above for each video frame.



The blue curve in this plot shows the path of the .45 m marker on the rod. The red curve shows the path of the top of the grip, and the green curve shows how the butt of the rod moved during the cast. The (0,0) reference point for this plot was at the center of the shoulder, so you can see that at this point in time the I.C. was located .5 meter ahead and .2 meter below the shoulder.

A video of a 40 foot cast that shows the movement of the rotation center of the rod with a nominally vertical casting plane is shown at Vimeo. As noted on the video file, the red dot shows the location of the I.C. for a given frame. The blue line shows the hand path during the cast.

From this video you can see that for my casting style (and your results would certainly be different) the I.C. is out of the frame of the video at the beginning of the cast where most of the movement is due to just translation with very little rotation.

As the rod begins to rotate the I.C. is out of frame and then begins to move behind me and then towards my shoulder. As the angular velocity is increased, the I.C. moves down through the bicep, and then through the forearm. It ended up near the marker at the top of the grip as the rod approached RSP.

I am sure the path of this space centroid (definition is in the Wikipedia article) would be different for different casting styles, but it shows that the translation of the rod butt shifts the I.C. of rotation quite a ways from the shoulder, elbow, and grip at the start of the cast. It is interesting to see that combination of rotations coming from the shoulder and elbow cause the I.C. to run down the bicep and forearm, and then as those two joints stop rotating at the end of the cast the I.C. is near the grip as the rod approaches RSP.

For any given frame this shows that the rotation center is quite a distance from the grip during most of the cast, and would need to be taken into account in determining the actual MOI of the rod and reel. At the beginning of the cast; the large mass and distance of the reel from the I.C. would dominate the total MOI. The MOI of the reel would continue to be significant for much of the cast where the I.C. is at some distance from the center of the reel. This larger rotation distance would also cause an increase in the MOI of the rod as well.

Gordy

[Bobinmich]

Gordy,

Very, very, very nice piece of work. It will take me a while to adsorb all you have learned here.

Two points strike me immediately though. Even though some will take this as self evident from their experience:

1) The effect of the MOI of the reel varies markedly throughout the cast.

2) The effect of the reel is very casting style dependant.

Both of these conclusions are in your disertation but I am particullarly attentive to them now. The plot I made originally - seems like long ago - was at a point near maximum rod deflection. For my style (stiff wrist) the rod handle would be 10 to 20 degrees from vertical. I do not bring the rod down as much as you do. This would have a significant influence on i.c. The fact that the i.c. changes so much throughout the cast means that the plot I made may not be where the effect of the reel mass is most influencial (felt most ) to the caster. I wonder if we could get Noel to set up a rod with accelerometers and calculate the i.c. effect throughout the cast. But then, that would probably only be of interest to you and me. Guess we are geeks of a feather.

Again, very cool piece of work. My hat is off to you.

Godspeed,

Bob

[gordonjudd]

For my style (stiff wrist) the rod handle would be 10 to 20 degrees from vertical. I do not bring the rod down as much as you do. This would have a significant influence on i.c.

Bob,

So where do you think the I.C. for a stiff wrist casting style would be and how would you expect it to vary?

I think looking at the video (I am using a stiff wrist over much of the cast) I don't think it is going to be in line with the axis of the rod.

Gordy

[Bobinmich]

Gordy,

Okay, and?

The original discussion was on whether the reel had any effect on the cast. I said it did but not as much as the line and rod upper. Is that not still relavent?

I would love to have the equipment and ability to analyze many different casters and casts. Don't let any dust gather on that. It is really cool.

Bob

[gordonjudd]

Okay, and?

Bob,
The answer to the first question is:
So where do you think the I.C. for a stiff wrist casting style would be and how would you expect it to vary?

As for the second:

The original discussion was on whether the reel had any effect on the cast. I said it did but not as much as the line and rod upper. Is that not still relevant?

Since this thread is about the flow of the I.C. during a cast I am not sure what you mean by "the original discussion", but if you mean to compare how the MOI of the reel, line, and upper section compare then you have to specify the radial distance to each of those masses to the I.C. at a particular point in time. Thus rather than using a fixed pie chart you need to plot the MOI of each component as a function of time to show how that relationship changes during the cast.

As you know using the parallel axis theorem the MOI is going to be the MOI of the object about its center of gravity plus the mass of the object times the square of the distance to the I.C.



As shown in the graph above, in the early part of the cast the I.C. is a long way from the reel (the reel would be close to the green curve for butt end of the rod) thus the m*r.^2 term for the reel is going to dominate the total MOI of the rotating components early in the cast since its mass is so big.

Consequently unless you specify a moment in time for the relative position of the I.C. and the components in question the pie chart you showed in your write-up is not relevant because you did not use the correct position for the changing I.C. and a fixed chart does not reflect what changes are going on during the cast.

Gordy

[Bobinmich]

Gordy,

Okay, that's all fine. Maybe you should integrate the work done on the various parts of the cast to make a proper pie chart. For my style of casting with the rod handle close to vertical, my pie chart is somewhat close. And it's the only one I have seen attempted. But maybe I cast funny. Or maybe you do. We certainly do not cast the same. And as I originally said, when you go for distance, the whole picture will change.

Having accepted the i.c. concept, I think you can use it to provide insight into so much more. I am only urging you not to waste it. And rather than spending time talking about the lack of relevance about what I did, why not do it better? We would all love to see it. And I am not sensitive about doing something that is not quite right if it inspires someone to do better.

Godspeed Gordy,

Bob

[Bobinmich]

Thought some more about this overnight. If you could rovide work integral charts of different types of casts showing where the energy was really going, it would be possible to analyze concepts like "late rotation" with real numbers to see if all the energy possible was going into the line instead of being wasted other places. It could also be related to that bad word "feel" to see if it had relevance there. Maybe there is another level of learning here.

Bob

[gordonjudd]

If you could provide work integral charts of different types of casts showing where the energy was really going, it would be possible to analyze concepts like "late rotation" with real numbers to see if all the energy possible was going into the line instead of being wasted other places.

Bob,
This may not be exactly what you were looking for, but the work integral comparison done from a rotational analysis standpoint is at the Angular acceleration used by distance casters thread.

In a rotational system the relevant work integral is related to torque over angle rather than the force over distance integral used in a rectilinear measurement frame. As shown in the other thread, casts made with exponentially varying acceleration ( typically used in casts made with late rotation) was shown to have much higher energy levels than could be achieved with casts made with constant angular acceleration.
Gordy

[Bobinmich]

Gordy,

Been thinking some more. I waded into the late rotation thread a bit and I have some thoughts. All this is in the area of pure speculation so it may not sit well with you initially, but bear with me a minute and I will try to bring it back to the thread at hand, i.e. instant centers.

Your previous work shows an energy advantage to late rotation. I am not a good distance caster but the whole subject interests ne from a analytical viewpoint. I will walk out on a limb a bit here so those who are more familiar with the subject, feel free to saw away.

The main purpose of the body movements in an all out cast is probably to get as much energy from various muscle groups into the line as possible. Secondary but equally important is controlling those movements to keep the motion of the line going in the proper direction and to create a proper loop. Looking at where the energy goes from each of the muscle parts of the body, a lot of energy is used up in accelerating other stuff than the line. This includes body parts, the rod parts, the reel, and the air resistance to motion in general. Different muscle groups have varying amounts of body parts to deal with and varying ability to deliver energy by virtue of each muscle group’s own physiology.

Late rotation, I would suppose, involves the muscles of the forearm more dramatically that a cast where the wrist is held more rigid and acceleration is controlled more by body, shoulder, and upper arm. I am making an assumption here because in videos I look at with pronounced late rotation, it seems so. Interestingly, while being considerably weaker than torso muscles, the muscles of the forearm have less body mass to deal with in transferring energy to the hand.

Case 1) Let’s speculate a bit on instant centers. If you look at your video at the beginning of this thread, and ignore for the moment that this is not a distance cast, much of the rod rotation at the end of the cast is caused by wrist movement. Note that because of this, the I.C. is very close to the wrist – as you would expect. Now the muscles of the forearm are working almost exclusively on the upper rod and line because the polar moment of the reel handle and reel are very low by virtue of their proximity to the I.C. The acceleration of the lower rod and reel is done predominately by the upper arm and body where it’s increased polar moment is more than compensated for by upper body strength.

Case 2) Let’s further speculate the cast was accomplished as is taught by many instructors in FFF’s booklet, “The Essentials of Fly Casting.” A quote from this book is “We recommend that most of the movement come from the forearm and upper arm, with an almost stiff wrist playing only a minor role in turning the rod over.” In this case, the I.C. could not be at the wrist because it is not bending. It would have to be lower. Suffice it to say, there are reasons for this but I would suggest also, this is not the case for all out distance casting. Here’s why.

If the I.C. for Case 2 would be well away from the reel and rod handle. Therefore, the muscles of the forearm would be working against a much higher polar moment and less energy would go into the line. In Case 1, the muscles of the forearm would result in more energy transfer to the line.

Okay, I have nothing to support these conclusions. But by using the I.C. concept, and studying energy transfer from the muscles themselves, it might make sense out of the late rotation thing. I think it would be cool to redo the energy study using true I.C for the calculation of the polar moments for both casts. Easy for me to say since I don’t have to do it.


Bob

[gordonjudd]

But by using the I.C. concept, and studying energy transfer from the muscles themselves, it might make sense out of the late rotation thing.

Bob,

Maybe without your realizing it, I think your intuition has laid the groundwork for the principles involving the kinetic sequencing concept in sports movements.

Walter started a thread on this earlier, and the primary thing that came out of that discussion it is that different styles can utilize different forms of kinetic sequencing. Some analysis will show a proximal to distal flow and others a distal to proximal direction for executing the penalty throw in the sport of team handball for example.

Consequently the concept is more complicated than it would first appear, and most the earlier discussion on how it applies to casting soon became an exercise in unsubstantiated hand waving (especially from me because of my limited knowledge of the subject).

However, since I also am interested in the physics of the golf swing I think that a lot of the work done with coupled pendulum models of the golf swing could be applied to casting as well. Here is a simple description of how kinetic sequencing would be used to optimize club head speed in a golf swing that was taken from Search for Perfect Golf Swing



In applying this concept to casting you could look at cylinder A as being the torso, cylinder B the shoulder, cylinder C the elbow and the final hinge being the wrist.

The changes in the I.C. location that was shown in the first post shows this kind of flow, and supports a proximal to distal chain sequence that was debated in the other thread.

Just as in golf, in order to produce the maximum rod tip speed, you want to hold off in releasing the wrist angle as long as possible so that you can apply maximum torque over the longest butt angle range as possible.

This was the main conclusion of the acceleration thread, and I think the I.C. flow shown in the video supports that contention as well.

Gordy

[Bobinmich]

Gordy,

Cool!

But why is it that when I get somewhere, everyone else has already left?

BTW, all this is making me wonder why they teach the stiff wrist technique. But then, that's a different thread.

Godspeed,

Bob

[gordonjudd]

If you are interested the flow of the center of rotation in Chris Korich's tournament casting stroke check out this video

You can see that he uses a lot of shoulder rotation that moves to a point near his elbow when he uses the big muscles in his shoulder and elbow to accelerate the rotation of the rod to its maximum angular velocity point.

The rotation point does not move out to his wrist until the
very end of the cast.

Here is a plot of the butt phase angles and angular velocities for that cast.



The time counter on the video corresponds to the time scale on this plot so you can compare where the I.C. is located for different angular velocity values.
Gordy

[Bobinmich]

Wow Gordy! Good memory. I'd forgotten all about this thread.

My problem has always been that I tend to think of these things in my own experience. Most of the models I have built are for normal ( for me) stream casts and using the style of casting I was taught. I was taught to cast with a straight wrist and with my arm more parallel to the rod than that clip. So when I chose an instant center just below my elbow, it probably was close enough for government work for the type of casting I do.

But there are nearly as many casting scenarios as there are people, or maybe as there are teachers anyway. A lot of the discussions here on this site are about distance and tournament casting. The experts here use markedly different styles and each is constantly modifying his or her own style as they evolve. I soon realized that trying to mimic any single cast or caster with a model was doing the greatest disservice to all the rest who are successful with a different approach. The model and analysis would only be good for that cast and may be misleading to what is really going on.

So I turned away from taking a set of data on a single cast and trying to make my models and analysis match it and tried to model a system response with a given force applied to the handle. That way I could see what is going on at the caster's end to achieve a certain result at the line end. I was able to get a piece wise linear solution using a spread sheet and applying the force over .01 sec intervals and calculating new positions for all the components for the next .01 sec interval. Each .01 sec interval would generate a new free body diagram for the following calculation.

This was a simple model using statically determinate FBD's and representing the rod deflection with a simple quadratic equation determined from a curve fit of the measured deflection. The next step was to incorporate the rod force on the line as a function of the applied angle. I wanted to incorporate the load on the line using the thinking of Don Phillips in that the rod and line are actually loaded through the guides and the left hand of the caster. Using this approach would also allow for hauling in the model.

But low and behold, the rod is no longer statically determinate. So for every single free body diagram, an iterative solution would be required. I think I can do it but I am not sure I really want to try.

I had an excellent analytical group at GM. If I had such a group now, I wouldn't hesatate. Just build a FEA of the rod and iterate for convergent solutions. Piece of cake.

But why? At the end of the day, you would have an electronic digital rod you could cast but what then? You would still have to cast until you matched someone else's style anyway. So just measure their style and analyze that. Just don't expect it to yield universal truths.

I gave up trying.

Godspeed,

Bob

[gordonjudd]

I was taught to cast with a straight wrist and with my arm more parallel to the rod than that clip. So when I chose an instant center just below my elbow, it probably was close enough for government work for the type of casting I do.

Bob,

If you have a video clip send it to me and we will find out how your I.C. varies. No need to guess, when it is a straightforward thing to measure.

Gordy

[Bobinmich]

Gordy,

Thanks for the offer. That is kind or you. But I just picked up a contract for my LLC. First work in two years. Good thing I have a pention or I would starve to death. Anyway, I'll be busy for a while. But I don't think I'll try to get back into the casting modelling stuff. I would have to upgrade my computer and buy a good FEA program. And I am getting too old for this stuff. But even if I did, what would I have? It would still boil down to the casters style anyway. The way we would handle a problem like this in the industry is to clinic it through a whole gob of casters using a fully instrumented rod and high speed video. Then you could establish a mathematical mean to model to.

I think Noel and his whiz kids could do this. He has the manpower and computer power. But of what use would it be to the betterment of mankind? So why do it?

Godspeed,

Bob