1. Knee Complex in Involution and its implication on how to avoid graft  impingement
Wangdo Kim1,*, Antonio Veloso1, Duarte Araújo3, Maria Machado1, Veronica Vleck2, Liliana Aguiar1, Silvia Cabral1 and Filomena Vieira1
1 Biomechanics Laboratory
2 CIPER (Center for the Interdisciplinary Study of Human Performance)
3Sports Expertise Laboratory Faculty of Human Kinetics
Technical University of Lisbon

2. Impingement of the graft
A tibial tunnel that anterior to the tibial intersection of the slope of the intercondylar roof allows the distal half of the roof to impinge on the anterior surface of the graft (arrow). Complications caused by roof impingement include antior knee pain, effusions, flexion contractures, and recurrent instability. These complications can be prevented by careful surgical technique.
Kinematically, roof impingement occurs when an anterior cruciate ligament graft prematually contacts the intercondylar roof before the knee reaches terminal extension. Abrasion of the graft is caused by elevated pressure between the intercondylar roof with the graft under tension.
Reconstruction of a torn anterior cruciate ligament cannot be successful without a properly placed tibial tunne.
A surgical technique is presented which consistently places the tibial tunnel in the pathways of the normal ACL (anatomic placement) and avoid roof impingment.
With more than three decades of experience as a clinician, researcher, and innovator in total knee replacement (TKR), anterior cruciate ligament (ACL) reconstruction, and meniscal injury, Dr. Howell’s clinical practice focuses on the treatment of degenerative processes and sports-related injuries to the knee. He performs over 450 TKRs and 100 ACL reconstructions per year.
fff(Reprinted with permission from Stephen M. Howell

3. The lateral roentgenogram of the knee in maximum passive extension is a sensitive and inexpensive method for diagnosing roof impingement.
Roof impingement can also be diagnosed by magnetic resonance imaging (MRI). Pathognomonic findings include an increase in signal confined to the distal two thirds of the intra-articular pathway of the graft and posterior bowing of the graft caused by contact with the intercondylar roof.
Severe roof impingement occurs when the surgeon places the tibial tunnel antirely anterior to the slope of the intercondylar roof.
Moderate roof impingement occurs when the surgeon places the tibila tunnel partially anterior to the slope of the intercondylar roof
A graft is unimpinged when the surgeon places the tibila tunnel entirely posteior and parallel to the slope of the intercondylar roof.
An unimpinged graft has a row, uniform signal intensity on MRI.
Howell SM Principles for placing the tibial tunnel and avoiding roof impingement during reconstruction of a torn anterior cruciate ligament. Knee Surgery, Sports Traumatology, Arthroscopy 6:S49-S55.

4. Two prominent surgeons, Freddie Fu and Charlie Brown, have been working on the idea of anatomical ACL reconstruction. They would stand up at meetings and say “I’ve done 5,000 ACL reconstructions and looking back at what I was doing I now think that I put 5,000 ACLs in the wrong place because we now know that we have been putting it in the wrong place. Although we can get an excellent clinical result, almost everyone that has an ACL reconstruction will eventually go on to develop osteoarthritis.”
Freddie Fu and Charlie Brown have been doing a lot of work on “Where’s the right place to put the ACL?”  in particular – really hard at the anatomy again in the lab, in the cadavers, on CT, on MRI and so on, restoring anatomy may be the key to success (Fu and Karlsson, 2010), and what they have discovered is that we have been way out on our tunnel positioning on both the tibia and the femur. So there was this vogue to do double-bundle procedures – two tunnels on the tibia and two tunnels on the femur – to recreate a more anatomical ACL (Araujo et al., 2014; Desai et al., 2014; Hofbauer et al., 2014; Middleton et al., 2014) but that procedure has not really taken off as no one can show at the moment a clinical advantage to the patients either in the clinic or there is no way of testing to say if it is any better than single-bundle (Jarvela and Suomalainen, 2011; Gobbi et al., 2012).
Double bundle or double trouble? In this issue of Arthroscopy, a new technique of double-bundle anterior cruciate ligament (ACL) reconstruction is presented by Yasuda et al.1 This well-designed multidisciplinary study included an initial cadaveric phase prior to clinical application. The goal of this procedure is to more accurately reproduce the anatomy of the ACL. This technique involves the drilling of two tunnels in the tibia and femur using a transtibial technique. Although the concept of double bundle has been described by several other surgeons, Yasuda’s approach specifically addresses the true anatomic insertions of the anteromedial and posterolateral bundles with promising two-year results.
That is a very anatomical way of doing the surgery as it is re-creating the anatomy by replacing the two ruptured bundles of the original ligament with two new bundles (Fu and Karlsson, 2010). However, which, if any, of these recommended placements results in the goal of obtaining an isometric graft remains uncertain (Grood et al., 1989; Hefzy et al., 1989).
Freddie H. Fu, M.D.,(傅浩強; pinyin: Fù Hàoqiáng) is a pioneer and authority in sports medicine and recognized as a preeminent leader in orthopaedic surgery and sports medicine across the globe

5. Aims Observations on active touch
The difference between active touch and passive touch is very important for the individual but it has not been emphasized in sensory psychology, and particularly in the experimental literature.
Active touch referes to what is ordinarily called touching. This ought to be distinguished from passive touch, or being touched. In one case the impression on the skin is brought about by perceiver himself and in the other case by some outside agency.
More exactly, variations in skin stimulation are caused by variation in his motor activity. Such movements are not the ordinary kind usually thought of as responses. They do not modify the environment but only the stimuli coming from the environment.

6. James Jerome Gibson (January 27, 1904–December 11, 1979), was an American psychologist
Edward S. Reed (November 20, February 14, 1997) was a philosopher of science and an ecological psychologist in the vein of James J. Gibson.
Movements and postures are controlled and coordinated to realize functionally specific acts based on the perception of affordances (that is, possibilities for action (Gibson 1979)
Gibson (Gibson, 1966, 1979) promoted a related idea. He argued that, in contrast to its use in communication theory (Shannon, 2001) as the uncertainty of the specific, information should be construed as control strategies of human locomotion as specificity of the useful and as a process that is distributed over the performer-environment system, i.e., rather than being localized in an internal structure associated with performance−a better posed scientific problem because commensurability is assured (Shaw and Turvey, 1999); it replaces mind-matter dualism with animal-environment duality because the former problem precludes a solution to the degrees-of-freedom problem because of its incommensurability. Gibson conceived of a perceptual psychology very different from that taken by mainstream research work. Placing psychology in a biological and mechanical context and avoiding traditional disciplinary definition, Gibson outlined a mechanics relevant to animate life (Nakayama, 1994).
Placing psychology in a biological and physical context and avoiding traditional disciplinary definitions, Gibson outlined a physics relevant to animate life.
His preoccupation with surface , and his interest in animal locomotion.
Eleanor J. Gibson (December 7, 1910 – December 30, 2002) was an American psychologist

7. The Basic Orienting System
The primary kind of orientation is to gravity.
Most of the multicellular animals have developed a special organ for detecting the direction of gravity when resting. In its simplest form it is called a statocyst.
At the top of this highly simplified animal is a sac filled with fluid and line with mechanoreceptors of the ciliated type, the hairs being stimualted by a weight which can be displaced relative to the sac.
Gibson JJ The senses considered as perceptual systems: Houghton Mifflin.

8. The Statocyst in Relation to Other Organs
This organ yields its possessor an index of the direction “down”, it yields informaion in terms of the possible range of patterns of hairs excited.
If the animal happens to be tilted to the right, the stimulation makes one pattern; if to the left, another. If different patterns of input cause different patterns of output to motor organs of the animals, compensatory movements can occur which will keep the animal upright.
The movements are such as to normalize the pattern of input.
Left:
If the ground is level, its force against the skin will be in the opposite direction to the force of the force of the statolith on the lining of the statocyst.
The two will necessarily vary together. They yield both concident and covariant information.
Right:
What if the substratun is not horizontal? Angle of discrepancy is the slope of the ground.
They ae no longer coincident. In this case the discrepancy is information, however, and it will be constant over time, for any posture of the animal.
These are experiments in psychology of this sort.

9. The Limitations of the Vestibular Apparatus
The Limitation of the vestibular apparatus
The statocyst was said to be an unfailing indicator of the direction “down.”
And so it is, except whn subjected to a constant and sustained horizonal acceleration.
The statocyst cannot be expected to seperate a gravity from a sustained inertail forces. The situation is diagrammed in figure.

10. The frog never falls into the water
Recalling our frog pond, we can picture a game where the player receives an amount of money R ij if the frog jumps pad i to pad j. As some of the R ij might be negative, the player on occasion would have to contribute to the pot. Although his jumps may be random, the frog never falls into the water.
In probability theory and statistics, a Markov process or Markoff process, named after the Russian mathematician Andrey Markov, is a stochastic process that satisfies the Markov property. A Markov process can be thought of as 'memoryless': loosely speaking, a process satisfies the Markov property if one can make predictions for the future of the process based solely on its present state just as well as one could knowing the process's full history. i.e., conditional on the present state of the system, its future and past are independent.[1]
Ronald A. Howard Dynamic Programming and Markov Processes, The M.I.T. Press, 1960.

11. Touch and Posture are Covariant
As shown in Figure 6, a thin rectangular plate is supported on a frictionless horizontal plane (z = 0) with four circular shaped pegs arranged in configuration (a), (b) and (c). The contact between the plate and the peg is assumed frictionless point contact.
Determine the wrench (force/torque) exerted on the plate by the four pegs respectively and write the four wrenches in a 6 x 4 matrix for configuration (a), (b) and (c) respectively.
(6 marks)
The plate is allowed to move only on the horizontal plane. Based on the configurations of the pegs, determine the directions of the unconstrained instantaneous motion (the directions of the twist motion) of the plate for configuration (a), (b), and (c) respectively, if there is any.
For case (a), 4 wrenches can only constrain the plate in X- and Y- direction.
It cannot constrain the rotation in Z-direction, i.e., the reciprocal twist motion is in [0,0,0,0,0,1].
For case (b), the 4 wrenches can partially constrain the plate in all 3 directions. However, as the peg are arranged in such a way that a twist motion in the CW Z-direction rotation cannot be constrained. This can be reflected in the linear combination of the 4 wrenches that the torque in Z-direction is always positive.
For case (c ), the 4 wrenches can fully constrain the plate in 3 directions. Hence, there is no unconstrained twist motion.

12. "You think too much."

13. Neue geometrie des raumes
The lack of duality
The concept of “aggregate”
The concept of “aggregate” was used to identify the lines as how it corresponds with the linear range of points and to identofy the splines as how it corresponds with the pencil of planes.
In the mirroe, the points trade position (reflect) along the line, but the planes of the pencil do not. The force and rotation are therefore dual and do not represent the same thing.
Griffis M, Rico JM The nut in screw theory. Journal of Robotic Systems 20: Plücker J, Klein F Neue geometrie des raumes gegründet auf die betrachtung der geraden linie als raumelement Erste-[zweite] Abtheilung. In. Leipzig: B. G. Teubner.

14. The stimulation produced by sense-organ adjustment:∞3 the linear line complex (LLC)of an Instantaneous screw
If any screw motion about a certain axis be given to the lines forming a linear complex, these lines still remain within the complex.
If all the lines of a complex are subjected to a screw motion about the axis, the complex itself is not altered.
Huang C, Kuo W, Ravani B On the linear line complex and helicoidal vector field associated with homologous lines of a finite displacement. Mechanism and Machine Theory 43:

15. Fiber tractography imaging and LLC
Fiber tractography imaging of a portion of the gastrocnemius lateralis muscle generated in a healthy subject. The images were generated with one region of interest, correspondent to the muscle boundary where the anatomical cross-section area was maximal. The subject’s leg was placed parallel to the magnetic imaging field. The pole and pole plane within a single muscle fiber are shown. Adapted from the original figure published in Kim et al. (2013a).
This is an articular sense, not a muscle sense, and the knee joint yields information about joint position as well as joint rotation. Probably there is no “sense” of muscle contraction as such, the joint initiating the spatial information and the muscle spindles having only reflex coordinating functions.
Note also that the movements made do not always depend on the particular muscles at work. The movement systems are characterized by “vicarious action” of different muscles. The classification above is not based primarily on the anatomy of body members but on purposes. This is especially true of the performatory system. Just as perceptions do not depend on specific sensations, so motor actions do not depend on specific muscles.
Kim W, Espanha M, Veloso A, Araújo D, João F. 2013a. An Informational Algorithm as the Basis for Perception-Action Control of the Instantaneous Axes of the Knee. J Nov Physiother 3:2.

16. Original system of knee complex in involution as the organs of sensitivity
A reciprocal connection scenario compatible with a single DOF of the right knee joint about $. Here the vectors associated with the five constraints $i´ intersect the axis of $. The five intersections are indicated by the markers. In this model, for simplicity, the LCL as indicated is not included. (Kim and Kohles, 2011) Original system of knee complexes in involution: Five constraints s are collectively reciprocal to the instantaneous screw , indicated as . That the virtual coefficient should vanish is the necessary and the sufficient conditions (Kim et al., 2013e), or the pair ( and ) are in involution,
The instantaneous axis of the knee (IAK) is guided by the constraints of the anterior cruciate ligaments (ACL), posterior cruiciate ligament (PCL), medial collateral ligament (MCL), and articular contact in the medial (P1) and lateral (P2) compartments. Note that no combination of the constraint forces that might be generated at the will result in a turning at the and no angular velocity at the will cause the constraint force to do any work at the points on medial and lateral contacts. In the language of Plűcker a system of lines in involution forms a linear complex as defined in Figure 2. Note that a system of lines thus defined belongs to a screw five-system, when six lines, , are so situated that forces acting along them equilibrate when applied to the knee joint, which is free to twist about the IAK. We speak of the six lines so related as being in involution. (The figure was originally published by Kim and Kohles (2011)).
Kim W, Kohles SS A reciprocal connection factor for assessing knee-joint function. Computer Methods in Biomechanics and Biomedical Engineering 15:

17. The relation of touch to kinesthesis
The knee joint provides the instantaneous screw which is reciprocal to the impulsive ground reaction force . No combination of angular velocity about the axis will cause instantaneous translational movement, while any force at the ground contact will not cause a rotation about . The reaction forces (and torques) of the GRF will then be taken up by the musculoskeletal structures with the limb. Muscle contraction and GRF are compounded into a wrench, which is limited to a plane of COP and reciprocal to the IAK. The reciprocal forces reside in the plane is resolved into component wrenches belonging to the reciprocal screw system of the five components as indicated in the Figure 1. We established a framework for the estimation of reaction of constraints about the knee, in vivo medial and lateral contact force, using a process that is simplified by the judicious generation of IAK for the first order of freedom in equilibrium. Adapted from the original figure published in Kim et al. (2013a).
An organ of the body is being adjusted for the registering of information. The limbs and extremities are, of course, motor organ as well as sensing organs, whereas the eyes are only sense organs, but the function of motor performance can be subordinated to the function of exploratory adjustment in the case of the limbs.
Kim W, Veloso A, Araújo DK, SS Novel computational approaches characterizing knee physiotherapy. Journal of Computational Design and Engineering 1:55-66

18. The Ball–Disteli diagram and its relevance to instantaneous axis of knee
Composition of twists and wrenches
The position attained could have been arrived at by a single twist about some third screw. We always to remember that the amplitude of the twists are infititely small quantities, virtual displacement near equilibrium status.
Sir Robert Stawell Ball ( )
Martin Disteli, ( )
Dresden, Karlsruhe
Ball R A treatise on the theory of screws: Cambridge University Press. Jessop CM Treatise on the Line Complex: American Mathematical Society.

19. The Ball-Disteli diagram
Since shank S and thigh T are appropriated to two different elements of the mass-linkage (Figure 5), no kinematic significance can be attached to the composition of the two twists on S and T. If, however, the two twists on S and T, having the proper ratio of amplitudes, had been applied to a single rigid body, the displacement produced is one that could have been affected by a single twist about a single screw, IAK, on the cylindroids (S, T).
In the section 2.3, when a knee is capable of being twist about the two screw on S and T, it is capable of being twisted about every screw on the cylindroids (S, T); Knee motion is believed to occur about two dominant axes (Bonny et al., 2013), therefore two DOF knee model has been constructed. However, if S and T undergo the same transformation of coordinates, the mutual invariant of Equation 12 vanishes and then it follows the complexes of the linear combination of S and T are in involution with the specific ratio being assigned due to the Equation 11.

20. Observation of the act of touching
twist about the two screw on S and T on the cylindroids (S, T)
by a single twist about a single screw
The complexes are said to be themsleves in Involution
A system of lines in two LLC in involution forms a LLC
The upward pressure of the surface of support on the ventral side of the foot provides, for every terrestrial animal, a constant background of stimulation. It is covariant with the continuous input of the appropriate receptors of the articular motion in the knee joint already mentioned. Together they provide what the ordinary person calls the “sense of support.” The axis of gravity and the plane of the ground provide the basic frame of reference for tactual space perception. Active touch, as will appear, yields clear perceptions of environmental space in the absence of vision.
Kim W, Veloso AP, Araújo D, Vleck V, João F An informational framework to predict reaction of constraints using a reciprocally connected knee model. Computer Methods in Biomechanics and Biomedical Engineering:1-12.

21. Relationship between two bodies in contact for motion transmission between parallel axes
Uniform motion transmission between two parallel axes is possible only if the line of action passes through a fixed point, know as the pitch point.
Dooner DB On the Three Laws of Gearing. Journal of Mechanical Design 124:

22. The position and size of drilling of the tibial femoral tunnel can be customized
Because of wide variabilities in knee extension and roof angle between patients, there is not one ideal tibial tunnel placement for all knees.
Customized placement of the tibial tunnel to account for anaomic variability places the graft anatomically, fro a more conservative roofplasty to prevent roof impibgement, and improves the function and stabilty of our pataient’s reconstructed knee.

23. Reconstructed system of knee complex in involution
Tibial Tunnel Enlargement 

24. Conclusion
The layout of physical surfaces, according to this theory, is perceived by the way of the disposition of body members when touch and posture are covariant.
The units of anatomy are not the units of function. The movement systems are characterized by based primarily on purposes.

25. Acknowledgement: a simple spring-mass system
Leg stiffness is not directly related to hopping mechanics, but, rather, to the hopping environment.
Claire T. Farley
Kim W, João F, Tan J, Mota P, Vleck V, Aguiar L, Veloso A. 2013b. The natural shock absorption of the leg spring. Journal of Biomechanics 46:

26. Thank you!
The world is a meaningful environment of an animal.