Weiss CV Joint Mechanism Explained: How It Works, Parts, Geometry, and Uses on Steered Drive Axles

Posted by Robbie Dickson on

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A ball-type constant-velocity joint keeps torque-transmitting elements in an angle-bisecting plane so input and output rotate at the same ideal mean and instantaneous speed. This calculator compares that ideal behavior with a single Hooke joint reference.

Weiss CV Joint Interactive Calculator

Enter articulation angle and shaft phase. Weiss values are ideal invariants; Hooke values are a separate mathematical comparison—not measured joint performance.

0°

Ideal CV speed ratio
--
Ideal bisector-plane angle
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Single-Hooke comparison ratio
--
Single-Hooke ratio span
--

Equation Used

ideal CV ratio=1; ideal ball plane=theta/2; Hooke comparison ratio=cos(theta)/(1-sin^2(theta)cos^2(phi)); Hooke peak-to-peak ratio span=100(sec(theta)-cos(theta)).
The Hooke comparison is not part of the Weiss joint. Actual CV error depends on groove/cage geometry, clearances, elastic deflection, wear and manufacture.
  • Ideal Weiss-type ball constraint holds the ball centers in the bisector plane.
  • The ideal CV ratio is exactly one by model definition.
  • Hooke results describe a separate single-Cardan comparison.
  • Angles are kinematic inputs without torque or speed magnitude.
  • Ball contact, groove geometry, cage loads, friction, efficiency, clearances, wear and strength are omitted.
FIRGELLI Automations - Interactive Mechanism Calculators
Related Video: Double Cardan Joint
Video: Study of double Cardan universal joint 3 by Nguyen Duc Thang (thang010146) on YouTube. Used here to complement the diagram below.
Same mechanism and inputs as the interactive calculator.

Angle-Bisecting CV Principle

U.S. Patent 2,509,969 describes positioning the joint cross in the plane bisecting the shaft angle to secure constant-velocity action. Modern ball-joint patents likewise place torque-transmitting balls in a bisector plane.

What This Calculator Represents

Ideal CV invariants plus a separate Hooke-joint kinematic comparison.

Comparing Shaft Speeds

r_CV=1
beta=theta/2
r_H=cos theta/(1-sin²theta cos²phi)
span=100(sec theta-cos theta)

Worked Comparison

At 30 degrees and phase zero, ideal CV ratio remains 1 and ball-plane angle is 15 degrees; the single-Hooke comparison ratio and span vary with its own relation.

Assumptions and Limits

  • Calculated: ideal CV invariants and single-Hooke comparison.
  • Illustrated: intersecting shafts and bisector-plane balls.
  • Not calculated: real groove closure, forces, contact, friction, efficiency, wear or durability.

Frequently Asked Questions

Does ratio 1 prove a real joint is perfect?

No; it is an ideal invariant.

Is Hooke ripple produced by the Weiss joint?

No; it is a comparison.

Is torque capacity calculated?

No.

Are ball loads included?

No.

Does phase change the ideal CV ratio?

No.

Can this select a joint?

No.

References

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