Compound change gears set a rotational speed ratio with two gear meshes. The input gear drives one half of a keyed compound pair, and the other half drives the output gear. On a lathe, that ratio can link the spindle to the leadscrew; the actual thread pitch also depends on leadscrew lead and any additional gearing.
Change Gear Motion Interactive Calculator
Adjust all four tooth counts. Pitch diameters and rotation rates update together. The two mesh planes are shown separately to expose both contacts; B and C remain locked to the same angular motion.
Equation Used
- Four external spur gears with compatible tooth form and module.
- B and C are rigidly keyed together without relative motion.
- No extra idler, reversing train or gearbox ratio is included.
- Pitch diameters follow tooth counts; roots and mounting details are illustrative.
- Thread pitch needs the leadscrew lead, which is not an input here.
The two mesh planes are separated visually so both contacts remain visible. B and C share a keyed shaft. Enter the four tooth counts to compare speed ratios; mounting fit, gear strength and thread accuracy require separate checks for the actual machine.
Two meshes and one compound shaft
Input A drives gear B through the first external mesh. B and C share a keyed shaft, so they have the same angular speed. C drives output D through the second external mesh.
The Grizzly G0765 manual illustrates this A/B and C/D arrangement in its secondary threading configuration. The calculator uses the same connection pattern as an educational model, with independently selected tooth counts. It is not a gear-setting chart for that lathe.
The animation separates the rear and front mesh planes to keep both pairs visible. The dashed connection identifies the shared B/C shaft. Tooth counts change pitch diameters as well as speed, and meshing pitch circles remain tangent.
Setting a leadscrew speed relationship
A lathe can use change gears to establish spindle-to-leadscrew motion. A compound pair multiplies two mesh ratios, providing combinations that a single pair cannot achieve with the same available tooth counts.
Actual gear availability, shaft spacing, brackets and any intervening gearbox determine what a machine can accept. The calculator does not infer those constraints from tooth count alone.
Compound speed ratio
For the first mesh, nB/nA = −TA/TB. Since B and C are keyed together, nC = nB. For the second mesh, nD/nC = −TC/TD. Multiplying cancels the two direction reversals: nD/nA = TA TC/(TB TD).
The displayed input/output ratio is the reciprocal, TB TD/(TA TC). Values above one represent a slower output; values below one represent a faster output.
If A turns once per spindle revolution and D directly drives a leadscrew of lead P, then carriage advance per spindle revolution is P times nD/nA. Any other gearing must also be included. The calculator does not supply P, so its output is revolutions per revolution rather than a thread pitch.
Default gear combination
With A = 20, B = 40, C = 20 and D = 50 teeth, the first mesh gives −0.5 output turns per input turn. The second gives −0.4. Together, D makes 0.2 turns per A turn in the same direction, an input/output ratio of 5:1.
For a separate illustrative leadscrew lead of 5 mm/rev, direct connection would produce 1 mm of advance per spindle revolution. That extra lead value is not part of the calculator inputs.
Thread error accumulates over successive revolutions. For example, a generated pitch of 1.51515 mm instead of 1.50000 mm differs by about 0.01515 mm per revolution. Over 20 revolutions, the difference is about 0.303 mm. A close-looking gear ratio alone does not establish acceptable thread fit.
Ratio and physical fit are separate checks
A compatible tooth system is needed for meshing gears. The drawing uses a common illustrative module and 20° involute working flanks; small tooth counts may need profile correction or an undercut assessment.
The visualization automatically repositions the separated mesh pairs. It does not show that a chosen combination fits an existing lathe bracket, nor does it establish backlash, lubrication intervals, fastener torque or tooth load capacity. Follow the particular machine documentation for those details.
Manufacturer reference
- Grizzly G0765 owner’s manual, printed page 41, figures 54–57: A/B and C/D gear connections and the shared keyed B/C bushing.
Calculator questions
Why do B and C rotate together?
They are keyed to the same shaft. Their tooth counts can differ, but their angular motion is identical.
Why do input and output turn in the same direction?
Each external mesh reverses direction. The two reversals cancel.
Where is the idler?
This four-gear model has no separate idler. It follows the two mesh ratios used by the calculator.
Does the output give thread pitch?
No. It gives output revolutions per input revolution. Leadscrew lead and any additional gearing are needed to obtain carriage advance.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
