A change-speed gear set selects among gear pairs to provide different output speeds. Compare three ideal ratios that share the same module and tooth-count sum, so their pitch circles fit one fixed center distance.
Three-Speed Fixed-Center Gear-Set Calculator
Enter input speed, selector position, common tooth-count sum, low-pair driver teeth and module. The worksheet constructs three alternative external gear pairs at one center distance and reports the selected ideal ratio and output-speed magnitude. It does not rate a gearbox or authorize shifting under load.
Equation Used
- All three pairs are ideal external spur gears with one declared common module.
- The common tooth sum S is even, and z is bounded below S/2.
- Exactly one pair transmits at a time; unselected pairs are shown only as available ratios.
- Torque capacity, efficiency, inertia, tooth stress, profile shift, interference, backlash, lubrication, bearings, shafts, clutch/synchronizer geometry, shift timing and safety are excluded.
The selector chooses one of three gear pairs. The common module and tooth-count sum keep center distance constant, while the selected tooth ratio determines ideal output speed.
One of several gear pairs establishes the selected ratio
Multi-speed transmission patents place alternative gear pairs on common shaft axes and use sliding gears, sleeves, clutches or synchronizers to connect one ratio at a time. The selected external pair reverses direction and sets the ideal speed ratio.
The animation is a declared ratio-stack diagram: only the highlighted pair transmits. It does not claim a particular sliding sleeve, dog clutch or synchronizer construction.
A fixed-center ratio-set study
Use this calculator to inspect three ratios that fit one pair of shaft centers. Applying them to a machine, vehicle or power takeoff requires the actual transmission architecture, duty cycle and manufacturer procedures.
Constant center distance and ideal external-mesh ratio
One external mesh reverses rotation. Ideal speed ratio does not establish usable torque or efficiency.
Declared symmetric three-ratio example
For S=100, z=25 and m=2 mm, the pairs are 25:75, 50:50 and 75:25. Every pair has a 100 mm center distance. At 900 rpm input, their ideal output-speed magnitudes are 300, 900 and 2,700 rpm respectively, all opposite the input direction.
Ideal ratios and a working gearbox
Equal center distance makes the three pitch-circle pairs geometrically compatible with the same shaft spacing. A working gearbox also needs suitable tooth geometry, shafts, bearings and a mechanism that selects one transmitting pair. Ideal speed ratios alone do not establish torque capacity, efficiency or a shifting procedure.
Multiple-speed gear questions
Why must every declared pair have the same tooth-count sum?
For standard external gears with common module, that keeps pitch-radius sum and shaft center distance constant.
Does selecting a pair show a physical synchronizer?
No.
Is output torque equal to the displayed ratio times input torque?
Only in an ideal lossless static relation; this calculator does not rate torque.
Multi-speed transmission references
- WO1984000408A1, Multiple Speed Gear Transmission: primary patent documenting a sliding-gear multi-speed transmission with multiple selectively connected ratios on defined shaft axes.
- US20100154573A1, Twin Layshaft Transmission: primary patent explaining that conventional multi-speed transmissions use different selectable gear pairs between input/output shafts and layshafts.
- KHK Stock Spur Gears Technical Data: manufacturer reference defining module, tooth count and mounting or center distance data for spur-gear meshes.
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