A Rzeppa constant-velocity joint transfers rotation through six balls between an outer bell and an inner race. A cage keeps the ball centres in the plane normal to the bisector of the two shaft axes. This geometry allows equal input and output speed as the joint bends.
Rzeppa CV Joint Interactive Calculator
See the outer bell, inner race and six-ball cage articulate together. Vary shaft angle, speed and ball-centre radius.
Equation Used
- Six balls constrained to the angle-bisecting plane.
- Ideal equal shaft phase and speed.
- Ball-centre pitch radius is entered.
- No wear, contact stress or torque capacity prediction.
The ideal shaft-speed ratio stays 1:1 as articulation changes. The cage tilt and ball axial travel vary with the joint angle.
Outer bell, inner race, balls and cage
The cutaway removes part of the housing to reveal its grooves, the inner race and the six balls. The shafts remain connected through the joint centre. The cage tilts by half the angle between their axes, keeping the ball centres in the homokinetic plane.
The end-on inset makes all six balls visible throughout rotation. In the ideal meridian-track construction used here, their positions within the cage windows vary slightly through a turn. Real joints use engineered groove offsets, contact profiles and cage clearances; the rendered surfaces simplify those details.
Applications
Fixed ball-type CV joints are commonly used at the wheel end of automotive driveshafts, where steering and suspension movement change the shaft angle. A separate plunging joint can accommodate changes in shaft length. Joint type, allowable angle and service limits must be identified for the particular vehicle.
Ideal constant-velocity geometry
Input and output shaft angular speed are equal. If their articulation angle is β, the cage-plane normal tilts by β/2 from either shaft axis. A ball-centre circle of radius R in that plane has peak-to-peak axial travel 2R sin(β/2) relative to either shaft.
The animated centre-line construction places each ball in both corresponding meridian track planes and in the common bisecting plane. It illustrates the equal-phase constraint rather than calculating manufactured groove flanks. Axial travel is not a clearance or wear allowance.
47° joint angle and 35 mm ball radius
The cage normal is tilted 23.5°. At 1,000 rpm input, ideal output remains 1,000 rpm and one shaft turn takes 0.060 s. The ideal ball axial travel is about 27.912 mm peak to peak.
Changing joint angle changes the geometry, not the ideal 1:1 speed ratio. Zero input speed stops the demonstration.
Keep geometry separate from a wear limit
Ball travel describes how the centres move through the joint. It is not a cage-clearance specification or a wear limit. Use the actual joint manufacturer’s tolerances and service information.
This model does not calculate torque capacity, lubrication performance, contact stress or cage life. The displayed angle range is an exploration range, not approval for any particular joint.
Questions
Why does speed not change when I adjust the angle?
Equal shaft speed is the ideal constant-velocity property. The geometry and ball travel do change.
What is the gold ring?
The windowed cage holding the balls near the bisecting plane.
Can this determine allowable wear?
No. Wear limits depend on the specific component.
Technical references
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