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steve laslovich
05-16-2011, 07:30 PM
The literature often refers to rolling of the convex surface of a diarthodial joint when describing motions involving convex concave articular surfaces. Rolling is defined as a combination of pure rotation and pure translation. The ratio of pure rotation to pure translation that occurs during individual movements is reported to vary depending on joint geometry as well as via passive and active mechanisms involving muscles, ligaments, and capsules, etc.

1. My first question is that if no translation is occuring (rolling with slipping) of a convex member's articular surface on its mated articular surface should we always refer to this as spin and therefore not ever consider this as rolling. My problem is with understanding the terms when considering the location of the purported mechanical axis for rotation. If pure rolling occurs, and depending on my reference plane, the axis for rolling would occur at the contacting articular surfaces. Most of the literature refers to the mechanical axes lying within the convex members of most human diarthrodial convex concave joints some distance from the articular surface. If the axis is not at the surface and no translation occurs why do we still call this rolling? For example, in spite of the research which shows very little translation of the humeral head during frontal plane motion of the humerus (abduction) we still say the humeral head rolls upwards and slides downward (based on lever system mechanics). It would seem that this is just describing rotation. If the mechanica axis occurs at the joint surface then lever laws to create obligatory opposite translation to the direction of a convex's member's roll do not apply. Is there a mathematical relationship between how far the mechanical axis (lets say within the humeral head during abduction) lies from the surface and the degree of rolling (rotation with translation) that potentially occurs on a surface where friction between the two is present?
2. My second question involves more about rolling. Since the articular surfaces generally exhibit an extremely low coefficient of friction how could true rolling occur unless there is a force that creates translation. Is it absolutely necessary to have static friction to initiate rolling of a convex surface in human joints? If a force is applied to a bone with a convex joint surface and friction is essentially minimal would the convex member simply spin. It seems to me that to create a rolling motion on a nearly frictionless surface I need both a linear and rotation force to create a roll. If an upward roll occured during humeral abduction I need a linear force that creates an upward translation if friction is minimal or absent. Can someone please explain what I am missing in my understanding?

3. I have been told repeatedly that for rolling to occur in a joint with a very low coefficient of friction that the joint surfaces must be incongruent. I do not see the mechanics of how incongruent surfaces create rolling. Can someone please explain this?

Steve Laslovich
University of St. Augustine for Health Sciences
San Diego, California

ecattrysse67
05-18-2011, 11:10 AM
Hello Steve,
the convex-concave 'story' and its relation to 'rolling and gliding' is a long existing one and has been put forward by Kaltenborn (orthopaedic manual therapist) from a clinical perspective (i.e. non mechanical approach). These (2D) rules have been questioned several times (e.g.Baeyens JP, Van Roy P, Clarys JP (2000) Intra-articular kinematics of the glenohumeral joint in the late preparatory phase of throwing: Kaltenborn's rule revisited. Ergonomics 43 (10):1726-1737)which has lead to controversies in the clinical field ( see Schomacher J (2009) The convex-concave rule and the lever law. Man Ther 14 (5):579-582. doi:10.1016/j.math.2009.01.005). It is clear that joint kinematics can not be explained by simple joint surface morphology. active (muscles) and especially passive stabilising structures (ligaments) play a major role, and kinematics are often position and movement specific (Cattrysse E, Baeyens JP, Van Roy P, Van de Wiele O, Roosens T, Clarys JP (2005) Intra-articular kinematics of the upper limb joints: A six degrees of freedom study of coupled motions. Ergonomics 48 (11-14):1657-1671).
therefore, I agree completely with your statement(s) that translations should be considered for the centre of rotation (2D) or the axis of rotation (3D). Moreover, it is clear that these centres/axes are not stable which makes the story even more complex. only when one would like to analyse/study joint surface contact points/areals another point of view could be considered.
I'm less experienced in friction issues, however, friction in human joints is dependent on the speed of movement and the influence of active stabilizing systems. it seems to me that some kind of static friction may be present. Referring to the influence of ligaments and joint capsules it is clear that these might generate the external forces you refer to as necessary to create translation in a nearly frictionless condition.
Unfortunate I have no creative comments on your third question on congruence. I can only remark that cartilage ,although it looks absolutely flat, from a microscopic point is very incongruent.
kind regards
Erik Cattrysse (PhD)
Vrije Universiteit Brussel
Brussels -Belgium

bogert
05-18-2011, 05:41 PM
Great discussion.

Regarding the third question (relationship between congruency and rolling): Steve is right that incongruency does not create rolling. Incongruent joint surfaces can do any combination of gliding and rolling. The combination that actually occurs will depend on ligaments, muscles, and external loads.

But what he has been told is still correct, I think. Incongruency is needed for rolling because congruent surfaces can only glide or dislocate, there is simply no space for rolling to occur. That is of course in an ideal geometry. In the real world, as Erik noted, nothing is perfectly congruent.

In mathematical terms I would say: incongruency is necessary, but not sufficient, for rolling to occur.

Regarding friction. The term "rolling" is just a description of the kinematics. While it is unlikely that pure rolling occurs without friction, it is not impossible. It is theoretically possible that there is a very precise combination of muscle forces or external forces that creates pure rolling, even when there is no friction. Unlikely, though.

Ton van den Bogert

tphilippe
06-08-2011, 08:13 AM
Very interesting subject, I recently finish a thesis about convex rule modeling.
I prefer to use another rolling definition: rotation motion with the instantaneous center of rotation in the point of contact and the mechanical axis parallel to the other joint surface. Also rollins is a rotation without glidding.

First question: If no translation is occuring, could be different solutions: 1) No movement at alll :) 2) Spin motion 3) Roll and glide (exactly the same trasnlation produced for the rolling must have a glidding in the oppsite direction)
Also you must to consider that rolling is a swing motion, never could be spin motion!

Second Question: Yes, theres forces that produces the translation: capsule restriction and local muscle stabilizing the joint. Alot of research have talk about these forces.

Third Question: Incongruent surfaces does not produce rolling motion! I think that these missunderstanding result from the next fact: Congruent surfaces reduce and sometimes avoid the rolling motion (think in a rolling sphere inside a ball and socket joint... is impossible!), but that does not mean that incrongruent surface produce rolling motion! We could say that: rolling motion occur with more frequency and ease in incongruent surfaces.