Using pulley systems to redirect and reduce forces required to move loads
Simple pulley systems using a single pulley can be used to redirect forces. More complex pulley systems using two or even four pulleys can be used to reduce the force necessary to move an object by increasing the distance that force is exerted across.
With a simple pulley attached to say an overhead beam, force can be redirected. To lift an object up, we pull down on the rope, (1).
While this type of system can redirect force, it doesn't reduce it. If the object weighs 100 lbs we have to exert 100 lbs of force.
If we add an additional pulley to the object we are lifting, we can now use 50 lbs of force to lift the same 100 lb object. This pulley system redirects force and reduces the force required to lift the object, (2).
The trade off is that when we pull the rope a distance of 4m the object only moves 2m.
If we add two additional pulleys, we can now move the object with only 25 lbs of force. However now when we pull the rope over a distance of 4m the object only moves 1m, (3).
Work is Force times distance
In physics, work is equal to force applied over a distance. Pulley systems don't reduce work. They reduce the force required at the cost of having to apply that reduced force over a longer distance.
Exerting the same force to lift different weights
Say we had 4 different objects, each with a different weight.
The first one weighs 50 lbs. We can use the first system, a single pulley, and exert 50 lbs of force over 4m to move the object 4m, (1).
The second object weighs 100 lbs. Now we use the second system. We again exert 50 lbs of force over 4m but this time we only move the object 2m, (2).
The third object weighs 200 lbs. Now we use the third system.
We again exert 50 lbs of force over 4m. Now we only move the object 1m, (3).
While the distance that work is done across increases, in each case the force applied across each rope element is the same.
If you sum the force across all supporting rope elements (not including the end of the rope that is "pulled"), then you get a force that is equal to the force exerted by gravity on the object.
Pulley systems reduce friction
Obviously our body isn't equipped with pulleys. So what is the point at looking at pulley systems?
Pulleys and systems of pulleys redirect forces and they do this with minimal friction. It's the ability to redirect forces with minimal friction that makes pulleys useful.
The frictionless (or friction reducing) quality of pulleys allows them to distribute forces evenly to ropes on either side of the pulley.
So now let's look at how to ways to reduce or eliminate friction. The idea being so that we can see how we might apply this to understanding how out joints and muscles work together to bear loads without any joint or muscle bearing excessive loads.
Aquaplaning reduces or eliminates friction
Aquaplaning or hydroplaning is where the wheel of a car, truck, or airplane (or motorbike) is lifted off of the surface of the road by a thin layer (or wedge) of water. It occurs on wet road surfaces when moving above a particular speed.
When driving on wet road surfaces, a wedge of water builds up in front of where the wheel meets the road surface. At low speeds, the wedge of water can be dispersed by the rotating wheel. As speed increases above the speed where aquaplaning occurs, the water that makes up the wedge is not dispersed fast enough and so the wedge of water inserts between the road surface and the wheel, jacking the wheel off of the road surface.
Note that with "normal" aquaplaning, a layer of water as thin as 3mm can lift all wheels of a car off of the road surface. Aquaplaning can affect things as big as jet airliners.
Viscous aquaplaning can occur at much lower speeds and relies on a smooth road surface. A thin film of .025 mm is all that is required in this case. And this may be the same phenomenon that causes a glass to be lifted off of a table top by a thin layer of water.
Aquaplaning eliminates friction
The important point about aquaplaning is that it reduces or eliminates friction.
This is bad when you rely on friction for steering and speed control. When a vehicle aquaplanes, the driver loses the ability to control direction and it's also very difficult to reduce speed. All of this is because the wheels are no longer in contact with the surface of the road.
Aquaplaning causes this loss of grip or "friction" by drawing a layer of fluid between the wheel and the road surface so that they are separated.
Aquaplaning is good when you want to prevent friction.
If a thin layer of water can "lift" a jet airliner and so eliminate friction, imagine being able to use a similiar principle within our joints.
Imagine if our joints could draw fluid between mating surfaces so that our joints effectively became friction free.
In lubrication engineering, a lubrication method that relies on a similar affect to aquaplaning is called hydrodynamic lubrication.
The advantages of friction-free joints
Our synovial joints are filled with fluid. If the equivalent of "aquaplaning" could occur in our joints so that friction free (or at the very least, "reduced friction") connections are created, what might the advantages of doing so be?
- Using a single pulley, we effectively had one section of rope supporting the weight.
- Using two pulleys we had two sections of rope bearing (and thus sharing) the weight.
- Using four pulleys we had four sections of rope bearing the weight.
Something important to bear in mind is that even if the system is stationary (with the weight supported by the ropes), those forces are still being exerted.
If joints did act in a way similiar to pulleys, then when dealing with more weight, we can use muscles on both sides of the joint to share the load. With multiple frictionless joints as intermediaries, groups of opposing muscles could work together to share loads.
Single joint and multi-joint muscles
Note that there are single joint muscles. There are also multi-joint muscles that span more than one joint.
For relatively small forces, the single joint muscles may be sufficient. When more weight is added, longer muscles can then come into play, acting both on the target joint but also the other joints they cross.
In this way the load is shared not just by muscles, but by joints also.
As more muscles come into play, these muscles affect not just the initial joint, but neighboring joints. As a result, the heavier the weight, the more we have to "integrate" our body or use more of our whole body with the advantage that instead of one set of muscles muscle and one single joint working really hard, lots of muscles and joints work together to share the load.
For muscles to be able to work in this way easily (and at the same time for them to be easily and simply controllable), we need friction reducing joints. If you have friction (or "excessive" friction), then you lose the ability for muscles and joints to work together to distribute load.
How could this be achieved?
Alternatives to aquaplaning for creating friction free joints,
Injecting synovial fluid in-between joint surfaces could happen relatively easily using a principle similiar to aquaplaning when doing repeated movements (like running) that involve repeated constant changes in acceleration. So for example, a leg swing forwards at the hip followed by a straightening of the knee could result in a cushion of fluid being built up between joint surfaces just prior to impact. The same thing can occur during the back swing so that joints are constantly cushioned during changes in acceleration.
We'd need another mechanism to inject synovial fluid at low speeds or in static weight bearing positions.
Here viscous aquaplaning may be a possibility. But another possibility is to pressurize the synovial fluid mechanically.
Pressurizing synovial fluid for friction free synovial joints
Synovial joints include a joint capsule that contains synovial fluid. If we make the tension of the joint capsule variable and controllable, we then have a mechanism for pressurizing synovial fluid.
Why pressurize synovial fluid? So that it can be forcibly injected between the articulating surfaces of mating bones, preventing them from touching and thus creating a friction free joint.
To account for different joint positions and different load magnitudes, the tension in the joint capsule would need to be variable and controllable.
- In joint positions where one side of the joint is open or "stretched" the stretch induced connective tissue tension could in part be used to control joint capsule tension.
- On the side of the joint that is "closed" tension could be provided by muscle activation.
- In joints that are relatively neutral (i.e. not bending or rotating one way or the other) muscle activation could be used on all sides of the joint to add tension to the joint capsule.
The idea proposed here is that muscles (and their connective tissue connecting elements) not only move the body (or resist it being moved), they also help control synovial fluid pressure via control of joint capsule tension
If this seems strange, it's no different than in an engine where the movement of the parts of the engine are used to drive an oil pump which in turn circulates oil, keeping the engine lubricated so that it continues to function.
Does our body come equipped with a oil pressure warning light?
On a side note, one of the most important warning lights on an engine is the oil pressure warning light that tells us when oil pressure is low. This means either that the oil level is low or it isn't being pumped. So we either have to add oil or get the oil pump fixed (or if there is pressure leak, get the leak fixed).
What if lubrication where equally important in our joints? In this case, muscle power can be used to maintain joint fluid pressure so that joints can be acted on by muscles. The failure of a muscle to operate when required would lead to a possible lubrication failure. How might our brain signal this problem or work towards preventing the problem form worsening?
It could use pain as a signal. Or it could use muscle control to prevent (or try to prevent) particular ranges of movement.
The implications here are that if you are dealing with pain, lack of flexibility or lack of strength, then working on muscle control (which in turn means joint control) could be one way of dealing with all of these issues.
Lifting heavy stones and preventing them from falling
Apart from the use of pulleys, an interesting aspect of cranes is the use of different methods of attachment to the object being lifted.
Observing holes in line with the center of gravity in massive stones that were used in the construction of ancient temples, researchers summize that a device called a Lewis or Lewison or Lewis irons was used in the construction of some of these temples.
What's a Lewis?
Lewis irons are basically a "reverse" scissor mechanism that are inserted into the hole of a stone. They are a means of securing the stone to a rope so that it can be lifted.
When the protruding ends of the lewis are closed or pulled towards each other, the ends inside the hole press outwards against the hole, gripping the stone from the inside and helping to lock the lewis in place.
If ropes are attached to the protruding arms of the lewis, an upwards pull on these ropes can pull the arms of the lewis inwards (as well as upwards), locking it in place. From there, a further pull on these ropes can be used to lift the stone via the friction locked lewis.
When the stone is lifted, via the same ropes attached to the long arms, the outward pressing force against the sides of the hole is enough that friction prevents the stone from slipping off of the lewis.
Using a lewis, Don't bump the wall!
Using a lewis, the weight of the stone itself helps to friction lock the lewis. The greater the weight, the greater the friction and the better the stone is held in place. So what happens if the stone bumps into a wall?
The interesting thing is, if the stone, while being lifted, bumps against a wall, this reduces the downwards force on the lewis. This in return reduces the outwards force against the sides of the hole. Friction is thus reduced and the stone can fall.
So for this device to be useful it has to be working against the full weight of the stone.
Using more force to prevent the stone from falling
If the stone did bump into a wall, how could it be prevented from decoupling from the lewis?
By creating an additional downwards pull on the stone.
You could get someone to stand on it. Or you could attach ropes and pull down on the block even as it is pulled upwards.
With sufficient downward force, the lewis has enough friction to keep the stone in place even if it does inadvertently bump into a wall.
This comes at a cost though.
Now, with ropes creating an extra downwards on the block (or someone standing on it to have the same affect), now the crane has to do more work to lift the block. And so one way to avoid this is to pivot or otherwise align the rock as it is being lifted so that it doesn't bump into anything.
If a block can be lifted without bumping into any walls, then the force required to lift it is minimized. You aren't dealing with the friction of it rubbing against a wall. Nor are you dealing with the opposing force necessary to prevent the block from slipping off of the lewis.
Using joints efficiently
The idea in bringing up the idea of lewis irons is to suggest that with synovial joints acting as frictionless pulleys, if space is maintained within the joint, so that no friction occurs, then the joint can work more efficiently. The key is to maintain space within the joint so that no friction occurs. And for that to happen we need to control tension in the joint capsule.
What happens to joints and muscles if friction prevales
Having talked about the problems that can occur if you bump a stone into a wall while using a lewis, it might help to have some idea of what can happen if in a pulley system, a pulley gets jammed. This would be roughly equivalent to a joint capsule not being fully tensioned resulting in loss of fluid pressure and assuming back up systems (boundary layer lubrication) has failed.
In a pulley system that normally halves the working load, if the load attached pulley fails completely, then as the weight is pulled higher and higher, tension is sustained in only one rope element (1). As a result the advantage of using the pulley system is completely lost.
In a pulley system that normally reduces the force required to lift the load to a quarter, if one pulley fails, then as the weight is lifted higher the rope element on the other side of the broken pulley ceases to work. As a result load is now shared by only three rope elements. Depending on the configuration of the pulleys, and how they line up with the center of gravity of the object being lifted, the load may tilt. In any case, now instead of the load being reduced to a quarter, it is now a third (2).
Understanding and controlling synovial joint fluid pressure
At this point it could be helpful to have a rough understanding of the interaction between joint fluid and joint capsule. While the joint capsule can be used to pressurize joint fluid, joint fluid pressure will also have an affect on the joint capsule. This relationship can be roughly understood via balloons.
The interplay of pressure and tension in balloons
It's been a while since I studied physics and one of the problems I've had was trying to remember whether tension throughout a joint capsule would be the same or not.
As a side note, I used to work on motorcycles. Reading advertisements for particular models of brakes I would laugh at the idea of braking systems with multiple pistons with "differential pressure" or some such term. The idea in these systems with multiple pistons pressing on a brake pad was that the pistons near the leading edge would press with less force than those away from the leading edge. While it sounded technical, all it involved was different diameter pistons.
Smaller diameter pistons would press with less force than large diameter pistons.
The brake fluid pressure acting on these pistons would be the same, but because of their different diameters, the force they would exert would be different.
Anyway, reading an article about pressure and tension in an inflated balloon, I learned that with a typical balloon, the rubber at the neck tends to be softer than at other parts of the balloon. As with the braking system outlined above, pressure within an inflated balloon is the same throughout. It's constant. So why is is the skin of the balloon softer, more pressable where it is narrower? Because the tension in the skin of the balloon varies according to the radius of that portion of the balloon.
Assuming the balloon is inflated and pressurized to some degree, parts of the skin of the balloon with different diameters will have different amounts of tension.
Tension varies, pressure is constant
Assuming the fluid within a joint capsule is pressurized, that pressure will be the same throughout the body of fluid. However, tension throughout the joint capsule won't be equal. Some areas will have greater tension, other areas less.
For an interesting overview of this check out http://hyperphysics.phy-astr.gsu.edu/hbase/ptens.html
Note that I haven't provided a direct link because the linked to site isn't https.
An illustration I thought of before remembering my thoughts on motorcycle differential braking systems was of two slack lines, one twice as long as the other. Using people of equal weight, with the short line you could, say, place 10 people on the line. With the long line you could place 20 people. The reason I specified that each person be of equal weight is that this would simulate even pressure acting on surfaces of varying area. So even though the two lines are subject to even pressure, each person weighing the same, the longer line is subject to twice as much force as the shorter line.
If a joint is configured so that opposite sides of the capsule are at different lengths, say one side twice as long as the other, then the two sides with be subject to the same pressure but be subject to different forces.
If you look at units of pressure they are expressed as force per unit of area. So in imperial, pressure is pounds per square in. What this means is, the greater the area, the greater the total force.
How do joint capsules deal with differences in load and configuration?
So how would a joint capsule change tension to deal with these different load requirements?
- One way to meet these varying force requirements is from stretch induced tension of connective tissue.
- Another is to use forces derived from muscle activation.
This latter case is perhaps the most important because it is easier to vary and control and because it can drive the former. In addition, since muscles are responsible for moving and stabilizing our body in the first place, why not also use them to provide the force necessary to keep joints friction free (or "lubricated").
The advantages of having joint capsules with controllable and variable tension
Two main advantages of having joint capsules with controllable tension that is independent of joint position is that joint capsule tension can be controlled in any joint position. As well, joint capsule tension can be varied to suit the load that the joint is under.
In each case, the tension would be varied to pressurize synovial fluid to a great enough extent that it resists joint surfaces from touching, thus minimizing friction.
Using the knees as an example: standing on both legs, each knee is dealing with half the weight of the body (less the weight of the lower legs.) With straight knees, it may be possible that the natural resilience of connective tissue provides enough tension. On one leg it may be more critical that muscle activation is used to add tension to the joint capsule.
Note that another possibility is that in static positions, it's all right for joint surfaces to make contact. In lubrication science this is known as "boundary layer lubrication".
Sharing load between multiple (and opposing) muscle fibers
Assuming that joint systems can be configured so that joints become essentially frictionless, what this then means is that muscle tension applied to one side of a joint can be matched by applying equal tension to the opposite side of the joint.
With greater loads, the first task is to add appropriate tension to the joint capsule to maintain the friction free state of the joint. With movement under greater loads the task is to maintain joint capsule tension while at the same time using muscle control to create the desired movement.
With the friction free state maintained, large loads can be distributed on opposing sides of the joint so that load is shared among multiple muscle strands and the associated connective tissue elements.
So how can we use this understanding, assuming that it is actually the case? (Put another way, how can we test out this theory to see if it holds true or not?)
In an article on slack lining, a researcher placed a force measuring instrument in line with the slack line. As slackliners jumped or bounced or hopped on the line, the researcher could see the changes in tension in the slack line via their computer as those changes in tension happened. It the slack line had been slack, then the weight of the line could have caused some reading. Imagine if the line was effectively weight less. Then someone could step on the line, while it was slack, and only at the moment when the line became tight would a change be registered.
The point here is that with sufficient tension, changes in tension in a slack line can be instantly detected and measured.
Say you used a motor driven winch to tighten the slack line. As the slack line gets tighter, the amount of power required to further tighten it could be registered by the load on the engine. The harder the engine is working, the tighter the slack line is. Now, imagine that the engine was such that it had to be kept on in order to keep the slack line tight. (For pollution control, lets say the motor is electric. An advantage here is that we can measure the current draw of the motor as a way of measuring how hard the motor is working.) So, the tighter the line is, the more the motor has to work to tighten the line further and we can measure this by the increase in current draw.
As with measuring changes in tension, changes in motor output can be registed instantaneously.
As an example of this, if while driving the road gets steeper but you don't change accelerator pedal pressure, the engine note will become higher because the engine is working harder. As a result, simply by listening to engine pitch, you can notice changes in how hard the engine is working.
In our body, our muscles are the equivalent of engines. They give out sensations that tell us exactly how hard they are working. At the same time, connective tissue, when tensed, tells us how much stretch it is under. Both of these signals happen in real time. And not only can we use these signals to "feel" our body (in real time, no less). We can also use them to infer the state that our joints are in.
Feeling our body via muscle activation and connective tissue tension
When active, muscles generate a pulling force. When active, they also generate sensation and this sensation is directly proportional to effort and inversely proportional to length. So the more a muscle exerts, and the shorted the length, the greater the signal. If length is increased as the muscle exerts, the signal decreases.
In addition, connective tissue gives out a stretch signal that is proportional to length. The greater the length, the greater the stretch signal. Both of these signals are detectable as they are applied and only detectable as they are applied.
Our brain, can read these signals. The two types of signal may be how our brain senses how the parts of our body are related. What this means is that our brain can detect when a muscle isn't working.
Just as importantly, we can read these signals directly as muscle effort and connective tissue stretch.
Why might we want to do this?
We can feel whether muscles on one side or both sides of a joint are active.
We can notice things like connective tissue tension, whether it is tension in investing fascia (the connective tissue within a muscle), in tendons or ligaments. Via these we can also get a sense of our joints.
Part of controlling muscles is being able to feel when they are active and when they are relaxed. Noticing muscle activation sensation and connective tissue tension, we can improve our ability to control our body.
Clear references for controllability
With pulley systems, it's generally pretty clear what parts are meant to move and what parts are still. With a pulley attached to a ceiling or overhead beam, we generally assume that the ceiling or beam will remain still. Then as we pull on the rope, we lift whatever we are trying to lift. It moves relative to the fixed point on the ceiling or overhead beam.
When our brain controls our body, its a relatively safe assumption that it needs some sort of reference system. It uses a set of muscles to move one bone relative to anther or to keep one bone stable relative to another. One bone acts as a reference for the other bone. Using clear references is an essential element whether measuring or creating a deliberate change.
Sometimes pain, or poor function isn't a result of injury. It's simply the brain not having a clear reference for a movement.
Muscles need fixed end points
Along the same lines, when focusing on the activation (or relaxation) of a particular muscle, it is extremely helpful to have give that muscle a fixed end point. This means anchoring or stabilizing one of the bones to which that muscle attaches.
How non-functional muscles can negatively affect a joint
So what can happen if a particular muscle isn't functioning, due to injury or neural inhibition (the brain isn't turning it on)? Not only can this inhibit certain movements, it can also inhibit the joint capsule tensioning. If all parts of joint capsule can't be tensioned, the joint capsule won't be able to maintain fluid pressure which means that joint surfaces contact.
Over the short term this may not be a big deal. But if the joint loses its ability to eliminate friction while joint surfaces are in contact, this means that bones can't adjust relative to each other and this can cause a rupture of the joint capsule which would be catastrophic.
With a non-functional joint capsule, lubrication is lost which means that load sharing on either side of the joint is no longer possible.
Because our body has single joint and multi-joint muscles, as more joints and muscles are called into play, then the ability for all muscles, and joints, to function becomes more critical. In extreme stretches, or where heavier loads (or both) are being dealt with, in either case the brain may limit function via pain or other methods to limit movement in order to keep joints protected.
Inhibiting muscle activation directly or via pain to protect joints
One way to possibly avoid this eventuality is to use pain signalling to prevent joint endangering movements.
Where possible, muscle "locking" may also be used. This is where muscles become so tight that further lengthening of that muscle feels impossible.
When lifting heavy loads above a certain weight, muscles may simply not function so that the necessary strength to lift the load simply becomes absent.
The point here is that pain and/or poor function can be a symptom of your brain protecting your joints.
Because we can feel (or learn to feel) muscle activation sensation and connective tissue tension, we also have the tools for fixing pain, lack of flexibility and lack of strength. Assuming that injuries are no longer an issue (i.e. enough time has passed for any injury to heal) the task then is learning to control muscles in such a way that joint capsules can be sufficiently tensioned to protect the joint and keep it friction free so that loads can be effectively distributed on opposing sides of the joint.
The idea here is to figure out ways of telling the brain that particular muscles are fit to function.
And that to me is what "muscle control" is all about.
Odds and ends.
Note that in the case of dealing with impact, non-contacting joint surfaces may allow for shock dissipation via tensioned joint capsules.
When dealing with ballistic or accelerated movements, opposing forces can come from the mass of the accelerated part of the body.
For detecting and subsequently reprogramming "poor" muscle control patterns, slow/smooth repeated movements may be helpful, in particular when movements are isolated to various degrees and when focus is on the bones, joints or muscles in question.
While I talked above about maintaining fluid pressure by varying joint capsule tension, another mechanism for varying fluid pressure is to actually vary the amount of fluid inside the joint capsule. With the knee joint in particular, this can be achieved via bursae which connect to the main joint cavity and that are directly acted on by tendons and/or ligaments.
Note that there are also bursae situated between ligaments and tendons and so for ligaments which aren't directly affected by muscle activation, these bursae offer away of varying ligament tension indirectly.
Note that some or all of the above may be wrong.
that being said, these are the assumptions I've used or built upon in order to learn my body while experiencing it and to help me solve problems like joint or muscle pain, and problems with lack of strength or flexibility.
In turn it also parts part of the framework for understanding how we can feel or proprioceive our own body.
With this understanding, or working towards this understanding via the experience of your own body you can eventually learn to teach yourself.
At the very least you can use it to learn your body well enough that when learning new skills, what you can focus on is the skill itself versus learning your body and learning the new skill.
Driving Lessons for Your Body
For more on learning to feel your body and control it, Driving Lessons for your Body is a series of online video courses with exercises for improving body awareness (proprioception and kinaesthetic awareness) and muscle control.
Improve spinal posture, breath control, ribcage control, core control and spinal erectors.
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Simple hip flexor activation drills so you can stretch them, feel them, use them.
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Hamstring anchoring and activation for easier hamstring stretching and strengthening.
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Feel and control quads, inner/outer thighs, knees and hips, fine tuning adjustments.
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Long thigh muscle control, Shin and knee rotation, hip bone stabilization and control
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Integrated leg, hip joint, hip bone, SI joint, spine, spinal erector and ribcage control.
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Simple gluteus maximus activation, deep hip muscle control, front and side splits.
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Basic shoulder control, pressurized shoulder activation, hand pressure awareness.
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