Convex-Concave Rule (and concave-convex rule)
Convex-Concave Rule (and concave-convex rule): These rules describe an arthrokinematic pattern that minimizes the inherent migration of the center of the axis of rotation of a joint, in the direction of arthrokinematic roll. Note, these rules were developed with the intent to aid in teaching, specifically to assist with “visualizing” joint motion. They were not intended to dictate the direction of joint mobilization or manipulation techniques (although they can aid in decision-making).
- The concave-convex rule implies that when a bone ending in a concave surface (e.g., the humeral head) is moving on a convex surface (e.g., the glenoid fossa), that glide will occur in the opposite direction of the roll.
- The convex-concave rule implies that when a bone ending in a convex surface (e.g., the mortise of the ankle) is moving on a concave surface (e.g., the dome of the talus), that glide will occur in the same direction as the roll.
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Related Terms:
Semantics and Contemporary Use: Although often attributed to Kaltenborn, the origins of these rules date back to the 1950s and 1960s, with key contributions from MacConaill, Maitland, Basmajian, and Steindler. The terms are now commonly used in physical therapy education, but they are often oversimplified and taught as the only correct motion, rather than a trend or a general relationship between osteokinematics and arthrokinematics. Contemporary clinicians and educators should emphasize that these rules are a learning tool and a heuristic to help visualize the motion of joints. A failure to do so can lead to flawed assumptions in manual therapy, particularly when joint shape, passive restraints, and muscular control are not taken into account.
Applied Example: During glenohumeral abduction, the convex humeral head rolls superiorly on the concave glenoid fossa, while gliding inferiorly to maintain joint congruency and avoiding abutting the acromion shelf. If this relationship is altered, a change in arthrokinematic motion may lead to increased stress on tissues and potentially result in pain and dysfunction.
Frequently Asked Questions:
What is the convex-concave rule in arthrokinematics?
It’s a principle that describes how joint surfaces glide relative to each other during roll:
- Convex-on-concave: Glide occurs in the opposite direction of the roll.
- Concave-on-convex: Glide occurs in the same direction as the roll
Why are these rules important in physical therapy?
- They help therapists visualize joint motion, to aid in choosing techniques that may optimize arthrokinematic glide.
Do the convex-concave rules determine mobilization direction?
- Not strictly. They are a heuristic for understanding joint mechanics, but actual mobilization techniques should be based on clinical findings, patient response, and other factors.
Are there exceptions to the rule in shoulder mechanics?
- Yes. For example, during external rotation of the GH joint, some studies found posterior glide, despite the rule suggesting anterior glide. This highlights that joint behavior can deviate in living subjects.
How do the convex-concave (and concave-convex) rules apply to the motion of the ankle ?
In talotibial dorsiflexion and plantarflexion, the convex talus moves on the concave tibial mortise. According to the convex-on-concave rule:
- Dorsiflexion involves an anterior roll and a posterior glide of the talus.
- Plantarflexion involves a posterior roll and an anterior glide of the talus.
How do the convex-concave rules apply to the thumb?
At the first carpometacarpal (CMC) joint, the direction of glide depends on the plane of motion:
- In abduction/adduction (sagittal plane), the convex metacarpal moves on the concave trapezium → glide opposite roll.
- In flexion/extension (frontal plane), the concave surface of the metacarpal moves on the convex trapezium → glide in the same direction as the roll.
How do the convex-concave rules apply to the spine?
The spinal facet (zygapophyseal) joints are oriented differently at each level, but in general:
- In the lumbar spine, the inferior articular process of the superior vertebra moves on the superior articular process of the inferior vertebra.
- These joints are typically concave-on-convex, so glide and roll occur in the same direction, though the rule is harder to apply due to joint orientation and coupled motion.
Example of Convex/Concave Rules in a Course
Course: Infraspinatus and Teres Minor
Optimal arthrokinematics of the shoulder can be summarized as "slide opposite roll" with the intent of maintaining the humeral head center in the glenoid fossa. That is; ideally, abduction of the shoulder would involve a superior roll of the humeral head and inferior glide. Flexion would result in posterior spin and anterior translation that should be accompanied by posterior glide. Internal rotation of the shoulder is accompanied by anterior roll and posterior glide. It is worth noting, that there is more to these opposing translatory forces than simply overcoming the roll that accompanies osteokinematic motion (flexion, abduction, internal rotation, etc.). All muscles create not only osteokinematic motions but may create force vectors that exaggerate the translation of the humeral head. For example, the deltoid not only creates a force on the humerus that results in abduction, but the fiber direction also pulls superiorly, contributing to superior glide and roll of the humeral head. The forces that help to maintain the humeral head center in the glenoid fossa are likely the result of resistance to stretch from passive structures and active resistance via co-contraction of the functional antagonists. The passive structures involved in providing an opposing translatory force include the joint capsule and ligaments, as well as, the tonicity of muscles not actively involved in the joint motion (for example, the latissimus dorsi and teres major may assist in creating an inferior force, opposing the superior role noted during abduction due to their inherent tone and passive resistance to stretch) (3). The active resistance to translatory force is generally created by co-contraction of antagonists proximal to the joint itself. This active resistance to translation is likely the primary role of the rotator cuff muscles, along with compression to aid in glenohumeral stabilization. The rotator cuff may be viewed as tiny boosters attempting to maintain the humeral head in orbit (centered in the glenoid fossa) during functional activities throughout the large range of motion of the humeral head.
Additional Reading:
For more information, we recommend the following publication: The convex-concave rules of arthrokinematics: flawed or perhaps just misinterpreted?
An example from this publication:
“…consider an adult-size humeral head with a circumference of 16 cm. A motion of 90° of GH joint abduction occurring purely due to a rolling motion (with no concurrent inferior slide at the articular surface) would theoretically cause the humeral head to roll upward on the glenoid about 4 cm. Clearly, a significant, concurrent inferior slide of the humeral head must occur. This offsetting slide is an essential component of GH joint abduction, especially considering that the adult subacromial space is only about 1 cm in height.”
Although these rules are often attributed to Kaltenborn (2), their origin is likely decades older (1950s – 1960s), with references in publications by MacConaill, Maitland, Basmajian, and Steindler (3-6).
- Neumann, D. A. (2012). The convex-concave rules of arthrokinematics: flawed or perhaps just misinterpreted?. journal of orthopaedic & sports physical therapy, 42(2), 53-55.
- MA, M. (1964). JOINT MOVEMENT. Physiotherapy, 50, 359-367.
- MacConaill, M. A. (1953). The movements of bones and joints: 5. The significance of shape. The Journal of bone and joint surgery. British volume, 35(2), 290-297.
- Basmajian, J. V., & MacConaill, M. A. (1969). Muscles and movements: A basis for human kinesiology. Williams & Wilkins
- Maitland GD. Peripheral Manipulation. 2nd ed. Boston, MA: Butterworths; 1977Steindler, A. (1955). Kinesiology of the human body under normal and pathological conditions. (No Title).
- Steindler, A. (1955). Kinesiology of the human body under normal and pathological conditions. (No Title).