A connect gears game built on ideal spur-gear physics asks you to place every candidate gear into a fixed socket so the touching circles form one continuous, conflict-free path from a clockwise driver on the left to a target gear on the right. Gear Rotation Puzzle delivers that exact challenge across five deterministic levels, each awarding exactly 200 points for a valid train. The board calculates contacts from geometry rather than from a hidden answer list: two pitch circles create an edge when their centers are within 0.75 game units of the sum of their radii. Direction reverses at every external mesh, and angular speed propagates as omega_neighbor = -omega_current × teeth_current / teeth_neighbor. Intermediate idlers contribute one more reversal but cancel from the final speed ratio in the ideal same-module model, so the final magnitude depends only on driver and target tooth counts. Five correct layouts produce exactly 1,000 points, one full-layout failure is recoverable, and a second different failure deadlocks the run.
What the Connect Gears Game Actually Asks
A typical "connect gears" puzzle gives you a row of empty sockets between a fixed driver and a fixed target, plus a small rack of candidate gears with different tooth counts. You are not asked to rotate anything yourself; you are asked to commit an assignment of every candidate to exactly one socket. Once every socket is filled, the board performs a breadth-first propagation from the driver with signed speed +1 and assigns every geometric neighbor the opposite direction and the tooth-count-adjusted speed. If the propagation reaches the target without contradiction, the target starts turning and a board label reports clockwise or counterclockwise rotation. The target's side ledger reports the ideal target-to-driver speed magnitude.
Filling every socket is necessary but not sufficient. A placed gear must belong to the powered component, and the target must be reachable from the driver through the resulting contact graph. A layout that fills every socket but leaves one gear isolated or creates a direction conflict will not turn the target at all. The solver does not compare your layout against a stored key; it tests the geometry you have drawn and reports what the physics would do.
How Gear Rotation Puzzle Solves the Connect Gears Task
The puzzle's physical model is the same module ideal that introductory gear design references describe for first-pass reasoning: external spur gears, perfect involute teeth, no backlash, no friction, no shaft misalignment. According to MIT OpenCourseWare's gears and linkages lecture, external-mesh contact reverses rotation at every pair, and ratios telescope along a train; per the tec-science gear-stage primer, the ideal ratio of a stage is teeth_driven divided by teeth_driver, with sign changes counted along the chain. Gear Rotation Puzzle uses those rules directly and shows them on the board.
That is why the game fits "connect gears" searches exactly: you connect driver to target by building a continuous geometric path of meshed gears, the same chain an introductory mechanical-engineering problem would ask you to draw. The difference is that the answer is verified on the spot by propagation rather than by your arithmetic.
Build a Working Train Step by Step
Use this sequence for every level in Gear Rotation Puzzle:
- Inspect the candidate rack. Note each gear's tooth count and matching visual radius; the larger the gear, the more teeth it carries.
- Place the clockwise driver and the target gear mentally as the endpoints of the path you are about to build.
- Pick a candidate and place it into a fixed socket; the candidate becomes unavailable until you clear it.
- Fill every remaining socket before testing; the game will not let you submit a partially filled board.
- Press Enter to test the train. If the target rotates and the side ledger reports a non-zero magnitude, the layout is correct and you have earned 200 points.
- If the layout fails, tap an occupied socket to return that gear, try a different socket, and re-test; selecting, removing, or replacing candidates never counts as an error on its own.
- When all five levels are solved, the run ends at exactly 1,000 points with no time bonus, hidden multiplier, or random element involved.
Direction, Ratios, and Why Idlers Cancel
Every external mesh reverses rotation. If a driver spins clockwise, the gear it directly touches must turn counterclockwise, the next neighbor returns to clockwise, and so on along the chain. The signed-speed rule is omega_neighbor = -omega_current × teeth_current / teeth_neighbor. Intermediate ratios telescope along a simple train, so a three-gear chain multiplies three stage ratios, with one sign change per external contact.
An idler is a gear placed between two functional gears that carries direction and bridges a physical gap. Because it is meshed on both sides, it contributes two reversals along the chain, which is an even number, so its own tooth count does not flip the final direction. In the end-to-end ratio, the idler's teeth appear once in a numerator and once in a denominator, so they cancel. The final magnitude therefore depends only on driver and target tooth counts. This is the central physics point that makes the puzzle a thinking exercise: you can add idlers freely to fix connectivity without disturbing the final speed.
| Property | Behavior in Gear Rotation Puzzle |
|---|---|
| Contact condition | Pitch circles create an edge when centers are within 0.75 game units of summed radii |
| Direction at contact | Reversed: every external mesh flips clockwise to counterclockwise and vice versa |
| Speed rule | omega_neighbor = -omega_current × teeth_current / teeth_neighbor |
| Idler in ratio | Cancels; contributes two reversals (even) and a no-op magnitude |
| Loop parity | An odd triangular contact graph conflicts; an even square contact graph stays consistent |
The loop-parity row is worth pausing on. If three gears form a triangle of contacts and you assign one clockwise rotation, the second must be counterclockwise and the third clockwise, which contradicts the first gear's own assignment. The solver flags this as a parity conflict and refuses the layout. A four-gear square, by contrast, comes back to the starting side after two reversals, which is consistent. Cycles are the cleanest test of whether you understand the reversal rule.
Scoring, Failures, and the 1,000-Point Route
Each successful test awards exactly 200 points and opens the next fixed gearbox. Five correct layouts produce exactly 1,000 points. There is no time bonus, random level, adaptive difficulty, hidden multiplier, or score penalty for exploring placements. Submitting a partially filled board is not allowed, and selecting, removing, or replacing candidates never counts as an error by itself.
The game gives you exactly one recoverable failure per run. The feedback distinguishes three failure modes: the target is disconnected from the driver, a gear is isolated and not part of the powered component, or a direction conflict exists between two paths that reach the same gear with contradictory signs. Submitting the identical failed assignment again is deduplicated, so retrying the same wrong layout does not consume your remaining chance. A second distinct failed full layout closes the run, and Restart returns you to level one with an empty board, zero score, no failed signatures, and no held candidate.
Keyboard Controls and Replay Reliability
The game supports the full construction loop without a mouse or touch surface. Number keys 1 through 4 hold available candidate gears, and Q, W, E, and T address the four sockets from left to right. Pressing a socket key with a held candidate places that candidate into that socket; pressing a socket key with no held candidate clears the occupied socket. Enter tests a completely filled train, and R restarts. Every pointer target is at least 44 pixels wide, with visible focus and held states, so the same layout can be reproduced on touch, pointer, and keyboard input.
The five levels are deterministic original fixtures. Their candidate radii, tooth counts, socket coordinates, driver dimensions, and target dimensions do not change between runs. Independent tests restate every level literally, complete the exact 200-to-1,000 route, recover from one failed train, deduplicate a repeated failure, trigger the second-failure deadlock, and freeze all terminal actions. The scope is shown beside the board and in the cited methodology: ideal same-module external spur gears only, with torque, power loss, tooth stress, backlash, profile interference, shaft alignment, lubrication, noise, wear, materials, safety factors, tolerances, and dynamic loads deliberately omitted. Everything executes locally in the browser, with no account, download, upload, API, remote model, random service, or hardware permission required.