A rotary combination lock uses a set of coaxial wheels whose gates must align before a fence can enter them. A dial-driven cam transfers rotation through pickup components to position the wheels. This page illustrates wheel alignment and calculates a nominal count of settings; it does not estimate a particular lock’s resistance to attack.
Combination Lock Interactive Calculator
Compare the nominal setting count of a three- or four-wheel combination lock. The animation shows a drive cam picking up coaxial wheels and a common fence entering aligned gates. Dial divisions determine the ideal count; angular tolerance is a separate assumed window, not a measured security rating.
Equation Used
- All P settings are allowed independently on every wheel; repeats are allowed.
- The bit count is theoretical uniform-choice information, not a security certification.
- Angular tolerance is an assumed half-window; it does not specify physical gate dimensions.
- Generic drive-pin lost-motion model; illustrative sequence and enlarged gates.
- Fence detail only; lever nose and bolt actuation are not simulated.
Generic wheel-pack alignment detail with modeled pickup lost motion. Illustrative gate dimensions and dialing sequence, not a commercial operating procedure. Nominal counts assume independent unrestricted settings.
Wheel pickup and gate alignment
The mechanism contains a drive cam, wheel pack, drive pins, flys, gates and fence. The drive cam turns with the dial spindle. Pickup components transfer rotation to successive wheels after their angular clearance is taken up. On reversal, that clearance allows nearer wheels to move before previously positioned farther wheels are picked up again.
The animation models this lost motion around a common axis. It uses illustrative settings to bring each gate to the fence, then shows the common fence entering the aligned openings. The wheel spacing is expanded to reveal the parts. Gate cutouts and pickup clearances are drawn for visibility; they are not dimensions of a manufacturer’s lock.
This is an alignment detail. The full lever, its nose engaging the drive cam and the subsequent bolt movement are outside the animated detail. The sequence resets to its starting arrangement between demonstrations and is not an operating procedure for a real lock.
Comparing nominal settings
The calculator compares the ideal count associated with a dial having P choices and a pack having N wheels. Rotary safe locks provide one example of this broad mechanism family. Other combination locks, including independently turned number wheels, can use different internal arrangements.
A real product can exclude certain settings or combinations. Its construction and testing determine its security classification; the count alone does not establish that classification.
Counting combinations and angular divisions
With P independent allowed settings on each of N wheels, C = PN. If every such combination is equally likely, its information content is H = log2C = N log2P bits. These are ideal counting assumptions, not a model of a user’s choice habits or a lock’s physical security.
Evenly spaced dial divisions have angular pitch 360°/P. This is the pitch between marked settings, not the width or spacing of physical gates on a wheel. Each illustrated wheel has one gate.
An assumed symmetric half-window of ±tol has full angular width 2tol. That geometric width is shown separately and does not alter the nominal count. Deriving distinguishable effective settings would require a specific physical and acceptance model, which is not supplied here.
Worked nominal-count example
With 40 choices on each of three wheels, C = 40³ = 64,000 and H = log₂64,000 = 15.97 bits. The dial pitch is 360°/40 = 9°. An assumed ±1.5° window has a full width of 3°.
Adding a fourth wheel at the same 40 choices raises the nominal count to 2,560,000, adding log₂40 = 5.32 bits under the same uniform-choice assumption. Changing the assumed tolerance changes only the angular-window result; it does not turn this count into a tested security rating.
What the numbers leave out
More nominal choices or wheels increases the mathematical count. Actual usability and security also depend on which combinations are permitted, user selection, manufacturing tolerances and the complete lock design. None of those is inferred from the simple exponent.
The drawing emphasizes the coaxial pack, individual gates and shared fence. It intentionally separates the theoretical angular-window inset from the enlarged mechanical cutouts, so the tolerance slider is not mistaken for a manufacturer’s gate-width specification.
Combination-count questions
Does the bit count rate the physical lock’s security?
No. It is the information content of uniformly chosen independent settings. It does not measure resistance to physical attack or certify a product.
Why does the tolerance slider not change the combination count?
The count concerns nominal allowed settings. The angular window is a separate assumption. A model for overlapping accepted settings or real dialing restrictions would require additional information.
Why are the wheels spaced apart?
The expanded spacing makes the common axis, gates and fence visible. A real wheel pack is more compact and includes spacing and retaining components.
Does gate alignment alone show the whole unlocking process?
No. In the referenced mechanism family, it allows the lever fence to enter so the lever nose can engage the drive cam. The full lever and bolt sequence are omitted from this detail.
Manufacturer reference
Sargent and Greenleaf, Mechanical Safe Lock Guide, glossary on printed pages 5–7 defines the dial, wheels, drive cam, pickup components, gates and lever fence. The drawing shows generic wheel-pack geometry; dimensions and security features vary by product.
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