Brown movement 41 shows a double-oblique, chevron-like tooth arrangement for transmitting rotation. Explore the paired gear bands and calculate ideal driven speed and mesh-event rate from tooth counts and input speed.
Double-Oblique Tooth-Count Calculator
Enter declared driver and driven tooth counts and driver speed. The worksheet reports an ideal external-gear ratio and mesh-event rate only; it does not generate tooth geometry or quantify Brown's qualitative bearing comparison.
Equation Used
- The declared tooth counts define one ideal external gear ratio with opposite rotation.
- Every declared driver tooth produces one ideal mesh event per driver revolution.
- The drawing preserves movement 41's paired double-oblique topology but does not claim a generated tooth surface.
- Module, helix angle, pressure angle, center distance, face width, contact ratio, sliding, thrust balance, backlash, losses, lubrication, heat, loads, bearings, strength, wear, manufacture and safety are excluded.
The double-oblique tooth bands illustrate the gear arrangement. Tooth counts and driver speed determine the ideal rotation ratio and mesh-event rate; tooth contact and thrust balance are not calculated.
Double-oblique teeth give a more continuous bearing
Brown groups movements 40 and 41 together as rotary-to-rotary gears whose oblique teeth give a more continuous bearing than ordinary spur gears. The movement 41 engraving shows the second paired double-oblique or chevron-like form.
The schematic shows the double-oblique pair. Brown's bearing comparison is qualitative; the calculator reports speed ratio and mesh-event rate rather than contact ratio.
A historical oblique-tooth transmission example
The arrangement illustrates rotary transmission with inclined tooth portions meeting in a chevron-like pattern. A working pair also needs compatible tooth geometry, mounting dimensions and load data, which the speed-ratio model does not supply.
Ideal tooth-count relationships
The negative sign records opposite ideal external-mesh rotation. Brown's phrase more continuous bearing is qualitative and is not converted into contact ratio, thrust balance or load capacity.
Declared tooth-count example
For z1=24, z2=48 and n1=720 rpm, ideal driven speed is -360.0 rpm, reduction magnitude is 2.000:1, driven revolutions per driver revolution are -0.500 and ideal mesh-event rate is 288.0 Hz.
Speed ratio and tooth engagement
Tooth counts establish the ideal speed relationship, but do not quantify contact continuity or load sharing between the inclined tooth portions. Contact ratio, thrust balance and strength require a complete tooth geometry and operating conditions.
Oblique-tooth form 2 questions
Does Brown call movement 41 a crossed-skew gear?
No.
Does this calculate helix angle, thrust or contact ratio?
No.
Are the entered tooth counts historical?
No. They are entered values for the ideal ratio calculation.
Oblique-tooth source
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, pages 16-17, movements 40 and 41: primary public-domain plate and caption for the oblique-tooth forms and qualitative bearing statement.
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