The instantaneous point in space about which a rigid body (for example, a tooth approximated as rigid for small displacements) rotates under a specific applied system of forces and moments; its position is not intrinsic to the body but depends on the resultant force–moment combination and the location of the centre of resistance under the current loading conditions.

Principle

For a given rigid-body force system, a unique instantaneous center of rotation exists and shifts when the applied force or applied moment changes.

Demonstration

Illustrative scenario → A single tooth is approximated as a rigid body. An off-centre occlusal force produces a net moment; the instantaneous motion is rotation about a point (the COR) whose position relative to the tooth depends on the magnitude and line of action of the applied force and any counteracting moment. Clinician alters moment (e.g., with an auxiliary) to move the COR and change the motion from tipping toward translation.

Misapplication

Treating the COR as a fixed anatomical landmark (rather than load-dependent) or equating it with the centre of resistance without acknowledging that the COR location depends on the applied force–moment system.

Consequence

Accurate identification of the COR for a planned force system permits prediction and control of initial tooth motion (tipping vs translation); assuming an incorrect COR leads to unintended rotation, undesired crown or root movement, and compromised mechanics.

Reversal

When the rigid-body assumption fails (large displacements, deformation of the tooth or supporting tissues, or changing periodontal support), the instantaneous COR concept no longer reliably predicts long-term movement because the geometry and resistance change during the process.

Boundary

Applies to small-displacement, rigid-body approximations of single-tooth mechanics under static or quasi-static loading; it does not directly apply to distributed deformable bodies, multi-tooth interactions without constraint specification, or time-dependent biological remodeling unless those processes are explicitly modeled.

Semantic Tension

Trade-off between the mechanical clarity of a load-dependent COR (useful for planning forces) and the biological variability and time-evolving support conditions that alter the COR during treatment.

Synthesis

The COR is a kinematic, loading-dependent descriptor that helps translate force–moment choices into expected instantaneous motion; it is most useful when combined with consideration of tissue behavior and evolving biomechanics over time.