This calculator treats the entered positive values as effective rolling-contact radii for an ideal no-slip external pair. It reports reciprocal speed and torque ratios; it does not define or design hyperboloid tooth/contact geometry.
Hyperboloid-on-Hyperboloid Pair Interactive Calculator
Explore ideal tangential-speed matching for two effective contact radii.
Equation Used
- Entered values are positive effective rolling radii at a common contact point.
- External no-slip rolling circles turn in opposite angular directions; their contacting surfaces have the same tangential velocity.
- Lossless steady power transfer for the ideal torque ratio.
- No shaft angle, hyperboloid parameters, tooth/traction geometry, contact ellipse, spin, creepage, normal force, friction, stress, efficiency, lubrication, wear or strength model.
The reference-comparison output reports how far the driver/driven speed ratio lies from a fixed example ratio of 4:1. It is not an accuracy or quality score and does not recommend 4:1 for a design.
Ideal effective-radius rolling contact
At an ideal no-slip contact, tangential speed magnitudes match: omega1 r1=omega2 r2. Therefore driven/driver speed is r1/r2. With lossless steady power, the driven/input torque ratio is reciprocal, r2/r1.
The animation is an abstract pair of effective rolling bodies, not a generated hyperboloid gear or traction-drive design.
Use as a ratio check
The identities can check reciprocal radius, speed and ideal torque ratios. They cannot establish conjugate geometry, shaft placement, contact conditions or load capacity.
Ratio naming matters
The tile labeled driver/driven speed ratio is r2/r1; actual driven revolutions per driver revolution are r1/r2. The ideal driven/driver torque multiplier is r2/r1 before losses.
The difference from the 4:1 example reference is |(r₂/r₁) − 4|/4 × 100%. This is a numerical comparison, not a physical error measurement.
Worked rolling-ratio example
For driver effective radius 1 and driven radius 4, the driver/driven speed ratio is 4:1, the driven body makes 0.25 revolution per driver revolution, and the ideal driven/driver torque ratio is 4. The difference from the fixed 4:1 example reference is zero.
Scope and limitations
Real hyperboloid or crossed-axis drives require the complete pitch surfaces and shaft angle, contact location and curvature, conjugate tooth or traction geometry, sliding/spin and creepage, normal preload and traction coefficient, contact stress, materials, heat treatment, lubrication, efficiency, thermal behavior, bearings/shafts/housing, alignment, backlash, fatigue and manufacturer validation.
Frequently asked questions
Does the ratio design hyperboloid gears?
No. It uses two abstract effective rolling radii, not complete hyperboloid surfaces or tooth geometry.
Why are speed and torque ratios reciprocal?
Equal tangential velocity sets the speed ratio. Under the separate assumption of lossless steady power transfer, increasing torque trades against angular speed.
Is the 4:1 comparison an accuracy error?
No. It is the percentage difference from a fixed example reference. A result of zero does not mean a mechanism is accurate, efficient or suitable.
Calculation basis
Ideal tangent rolling circles have equal contact velocity. Their angular speeds have opposite signs and magnitudes inversely proportional to radius. The calculator reports speed-ratio magnitudes.
Under lossless steady power transfer, torque magnitudes have the reciprocal speed ratio. The fourth result compares the driver/driven speed ratio with a fixed 4:1 example reference. Complete hyperboloid or crossed-axis geometry is outside these two-radius calculations.
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