● Free Educational Tool

Friction & Binding Calculator

See the net tooth-moving force after friction in sliding mechanics. Cross the critical contact angle and watch binding consume the force — wire size, ligation, angulation, and lubrication all update live.

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

Friction Calculator
Friction
Loop
Movement
Materials
Sliding mechanics
Applied force
At the bracket
150 g
Classical friction
Below critical angle
Low
Critical contact angle
Onset of binding
θc
Net moving force
After binding
Drops
Illustrative — live values update as you change the inputs

What you can explore

Friction is not one number — it is a regime that changes the moment the wire and bracket bind.

Classical friction

Below the critical contact angle, resistance is the familiar wire–bracket friction.

Critical contact angle

See the angle at which the wire contacts the bracket corners and binding begins.

Binding & notching

Past the critical angle, binding dominates and can consume nearly all the applied force.

💧

Ligation & lubrication

Self-ligating vs elastomeric, dry vs saliva — see how each shifts the resistance.

How it works

From applied force to what actually reaches the tooth.

1

Set the system

Wire size and material, bracket slot, ligation method, and tooth angulation.

2

Cross the angle

Increase angulation and watch the resistance jump as binding begins.

3

Read the net force

See how much of the applied force is left to actually move the tooth.

Friction + binding, properly separated

The model distinguishes classical friction from angle-dependent binding around the critical contact angle — reproducing the well-documented result that, in sliding mechanics, binding (not classical friction) is usually the dominant source of resistance.

Who it's for

For understanding why sliding mechanics “stick.”

🎓

Dental & ortho students

Build real intuition before the clinic — change a parameter and watch the mechanics respond, instead of memorizing rules.

🦷

Residents & clinicians

A fast sandbox to reason from first principles — concept-level understanding, never patient-specific advice.

🔬

Educators & researchers

A transparent, citable model for teaching and study. Every value traces to a published equation.

Frequently asked questions

What is the critical contact angle?

It is the angulation between wire and bracket at which the wire first contacts the slot corners. Below it, resistance is classical friction; above it, binding rises steeply and can consume most of the applied force.

Does self-ligation eliminate friction?

It reduces classical friction from ligation, but once the critical contact angle is exceeded, binding dominates regardless of ligation type. The calculator shows both regimes.

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.

Open the simulator

Free, in your browser, right now.

Launch the Friction Calculator →