● Free Educational Tool

Orthodontic Tooth-Movement Simulator

Watch a tooth move under a force system — step by step — through a validated periodontal-ligament model. See the center of resistance, the center of rotation, the crown and apex paths, live PDL stress, and root-resorption risk. Compare uncontrolled tipping vs controlled bodily movement from first principles.

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

Every output traces to a named equation and a published source — this is a transparent model, not a black box.

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.

Root-resorption risk

A risk index from the PDL stress field, step by step — see why uncontrolled tipping concentrates stress at the apex.

Crown & apex paths

Trace where the crown and root apex actually travel through the movement — the geometry behind the clinical outcome.

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 movement

The validated PDL model applies the load, moves the tooth by its initial ligament displacement, and recomputes until the force decays.

3

Read the mechanics

Play or scrub through the movement and read CRes, CRot, PDL stress, resorption risk, and the crown/apex paths at every step.

Validated, not approximated

The model recovers the textbook results before it draws anything: center of resistance at ~0.40 of root length, the M/F → center-of-rotation relationship following Burstone, and ~0.17 mm initial crown mobility. Uncontrolled tipping leaves the root tipped with peak apical stress; controlled bodily movement spreads the load — exactly as the literature predicts.

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 anchorage, tipping, and resorption risk from first principles — concept-level, never patient-specific.

🔬

Educators & researchers

A transparent, citable model for teaching and study. Every value traces to a published equation; 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 determines the type of tooth movement: a low ratio tips the tooth, around 10:1 produces controlled tipping, and roughly 12–15:1 produces bodily translation. The simulator shows the resulting center of rotation live as you change it.

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 validated periodontal-ligament / rigid-body tooth model, part of the open Ortho-Biomechanics engine. Every output traces to a named equation, author, and year.

Open the simulator

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

Launch the Tooth-Movement Simulator →