● Free Educational Tool

Orthodontic Tooth-Movement Simulator

Inspect a tooth under an initial force system through a benchmarked population-reference model. See the center of resistance, center of rotation, crown and apex tendencies, and modeled PDL load distribution. Compare tipping, translation, and root-directed movement without treating the result as a patient forecast.

No install · No signup · Runs in your browser. Educational and research tool — not a medical device.

Tooth-Movement Simulator
Movement
Anchorage
Loop design
Materials
Live force system
Center of resistance
0.40 × root length
CRes
M/F ratio
Bodily translation
12:1
Peak PDL stress
Within optimal range
OK
Resorption risk
Tipping vs bodily
Watch
Illustrative — live values update as you change the force system

What you can explore

Model assumptions, cited relationships, and source-backed inputs are exposed so derived outputs can be interpreted within scope.

Center of resistance

Located for any root geometry — the point where a single force gives pure translation. See it shift as the root changes.

Center of rotation

Watch it migrate as you change the moment-to-force ratio — from tipping, to controlled tipping, to bodily movement and root torque.

M/F ratio & movement type

Dial the moment-to-force ratio and see the movement type resolve live — the core of orthodontic force-system design.

Live PDL stress

Per-patch periodontal-ligament stress against the optimal-pressure threshold — see where the ligament is overloaded.

Modeled PDL load concentration

A mechanical indicator from the reference PDL field shows where a selected force system concentrates load. It does not predict patient-specific resorption.

Crown & apex paths

Trace the modeled initial crown and root-apex paths implied by the selected reference force system.

How it works

From a force system to a moving tooth in three steps — no setup.

1

Set the force system

Choose the force, the moment, and the appliance — or start from a preset. A bracket-applied force with a chosen M/F ratio.

2

Step the reference model

The benchmarked PDL model applies the load, estimates initial ligament displacement, and recomputes as the modeled force decays.

3

Read the mechanics

Play or scrub through the model and read CRes, CRot, load distribution, and crown/apex paths at every step.

Benchmarked and traceable

The population-reference model is checked against defined analytical and literature reference cases, including center-of-resistance and M/F-to-center-of-rotation behavior. Those checks support conceptual mechanics; they are not external clinical validation or patient-specific prediction.

Who it's for

Biomechanics is abstract on paper. This makes it something you can change and watch.

🎓

Dental & ortho students

Build intuition for force systems before the clinic. See why a moment changes the movement, instead of memorizing M/F ratios.

🦷

Residents & clinicians

A fast sandbox to reason about force systems, tipping, and modeled load concentration — concept-level, never patient-specific.

🔬

Educators & researchers

A transparent teaching and research model with cited relationships, exposed assumptions, and model-dependent outputs; the engine is available as a citable library.

Frequently asked questions

What is the center of resistance of a tooth?

The center of resistance is the point at which a single force produces pure translation (bodily movement) with no rotation. For a single-rooted tooth it sits roughly 40% of the root length apical to the alveolar crest. The simulator locates it for any root geometry and shows how it shifts.

What is the M/F (moment-to-force) ratio?

The moment-to-force ratio helps determine the initial center of rotation, but the transition values depend on root geometry, support, center-of-resistance location, and point of force application. Translation occurs when M/F approaches the effective lever arm for the selected reference geometry; the simulator shows that relationship as inputs change.

Is it free? Do I need to install anything?

It's completely free, with no signup, and runs entirely in your browser — nothing is downloaded or installed.

Is this a medical device?

No. It is an educational and research simulation of general biomechanics using generic, user-entered parameters. It does not use patient data and is not intended for the diagnosis or treatment planning of individual patients.

What is it built on?

A benchmarked periodontal-ligament / rigid-body population-reference model in the Ortho-Biomechanics engine. Key assumptions and cited relationships are exposed, but the model has not been clinically validated for individual prediction.

Open the simulator

Free, in your browser, right now. Change a force, watch the mechanics respond.

Launch the Tooth-Movement Simulator →