The Thompson constant-velocity coupling uses a controlled gimbal arrangement intended to keep its control yoke associated with the homokinetic plane between angled shaft axes. This calculator compares ideal Thompson 1:1 transmission with the theoretical speed extrema of one Hooke joint.
Thompson Coupling (CV) Interactive Calculator
Enter shaft-axis angle and constant input speed. The calculator reports ideal kinematic ratios only; it does not rate a product, predict residual error or assess loads and life.
Equation Used
- The single comparison joint is an ideal Hooke joint driven at constant angular speed.
- The Thompson control mechanism perfectly maintains the homokinetic-plane constraint described in the patent.
- The calculator reports the single-joint positive and negative deviations from the input speed, not one symmetric amplitude.
- Torque, inertia, friction, clearance, compliance, bearing limits, vibration and product ratings are omitted.
Controlled Homokinetic Geometry
U.S. Patent 7,144,326 describes a gimbal arrangement whose control mechanism constrains a control yoke in association with the homokinetic plane. That plane bisects the angle between the input and output axes and is perpendicular to the plane containing them.
Under the ideal constraint, instantaneous input and output angular velocities are equal. The illustration is conceptual and does not reproduce every yoke, pin, bearing or control link in a manufactured coupling.
What This Explanatory Calculator Does
A single ideal Hooke joint at a nonzero angle has a periodic output-speed ratio. Its theoretical extrema are cos(beta) and 1/cos(beta). The patent's controlled geometry is intended to impose a constant-velocity characteristic instead.
This tool compares those ideal statements. It does not decide whether a Thompson coupling or any other joint suits a driveline.
Ideal Speed-ratio Comparison
rsingle,min = cos(beta)
rThompson,ideal = 1
The two displayed single-joint percentages are 100(rmax−1) and 100(rmin−1). They are unequal signed deviations; their difference is the peak-to-peak span.
Worked Ideal Comparison
At beta = 20 degrees, cos(beta) ≈ 0.9397. A single ideal Hooke joint therefore ranges from about −6.03% to +6.42% relative to constant input speed. At 1000 rpm input, the ideal Thompson result reports a constant 1000 rpm mean/output speed and zero kinematic deviation.
That zero is an ideal model boundary, not a measured tolerance or accuracy specification.
Model Boundary
- Calculated: ideal single-Hooke-joint speed-ratio extrema, their signed percentage deviations, and ideal Thompson 1:1 output.
- Patent basis: a control mechanism constraining a gimbal/control yoke relative to the homokinetic plane.
- Not calculated: instantaneous waveform phase, torque, bearing loads, friction, clearance, elastic deflection, heat, wear, balance, critical speed, efficiency, residual velocity error, angle or speed rating, durability, vibration, noise, product selection or safety.
Frequently Asked Questions
Why are the single-joint positive and negative values different?
The extrema are reciprocal-related functions, 1/cos(beta) and cos(beta), so their deviations from one are not symmetric.
Is zero Thompson ripple a measured specification?
No. It is the result of the perfect ideal homokinetic constraint.
Does input rpm change the percentage deviations?
No. In this ideal ratio model they depend only on beta; rpm sets the displayed ideal output speed.
Does the calculator show the full speed waveform?
No. It reports only the theoretical extrema of one Hooke joint.
Can it predict vibration or fatigue?
No. It includes no inertia, torque, stiffness, damping, clearance or material model.
Can it select a coupling?
No. Use current manufacturer data and a complete driveline analysis.
References
- Glenn Alexander Thompson, U.S. Patent 7,144,326, Constant velocity coupling and control system therefor: gimbal, control yoke and homokinetic-plane constraint.
- U.S. Patent Application US20040106458A1: detailed embodiments and ideal constant-velocity condition.
- Thompson Couplings, TCVJ brochure: manufacturer description and product-specific information.
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