A constant-velocity joint transfers rotation between angled shafts while keeping their instantaneous speeds equal in the ideal model. This illustration shows a six-ball Rzeppa arrangement: balls run between an outer race and an inner race, with a cage maintaining the ball-centre plane. The calculator compares its steady output with the speed variation of a single Hooke joint.
Related actuator design tools
This calculator compares rotary joint speeds. If a separate linear actuator adjusts the shaft alignment in your machine, size that actuator from its linkage geometry, load and required motion.
When comparing a cylinder to an electric actuator, convert the discussion into stroke, force, speed, duty cycle, and installed length. Matching one specification is not enough.
The control method should match the consequence of being wrong. Simple extend/retract switching is fine for many applications, but repeatable stops, synchronized motion, or programmable positions require the right feedback and controller architecture.
- Use loaded speed, not only no-load speed, when timing the motion.
- Confirm voltage, controller rating, and limit-switch behavior before wiring.
- Use feedback when synchronized or repeatable position control is required.
For FIRGELLI actuator control, use the linear actuator wiring diagram generator before wiring the final circuit and compare suitable actuator families in the FIRGELLI linear actuator range. If the machine already has an actuator, the linear actuator replacement finder can help shortlist replacements.
Constant-velocity Joint Interactive Calculator
Change shaft speed and articulation to compare an ideal six-ball CV joint with a single Hooke joint. The cutaway shows the connected races, cage and balls; the graph follows the same rotation position.
Equation Used
- Rigid ideal kinematics at constant input speed and fixed articulation.
- The six balls lie in a plane normal to the shaft-axis bisector. Simplified race surfaces are for explanation, not manufacture.
- No torque capacity, contact stress, friction, durability or vibration threshold is calculated.
- The 0–45 degree slider is an educational comparison range, not a rating for a product.
The ideal CV joint keeps output speed equal to input speed. The Hooke-joint comparison shows a separate construction whose speed varies twice per revolution.
Races, balls and cage
The cutaway exposes the outer cup, the grooved inner race connected to the outgoing shaft, and six steel balls retained by the gold cage. The front portion of the housing and the flexible boot are omitted so that the moving parts remain visible.
The ball centres remain in a plane normal to the bisector of the two shaft axes. The blue and green shaft markers turn together. Changing articulation tilts the output shaft and the intermediate plane; changing RPM changes the displayed rotational rate at a fixed 100-times slowdown.
NTN’s reference drawing identifies the six-ball arrangement. Real joints use specifically designed groove offsets and contact profiles. This model preserves the ideal ball-plane and equal-phase constraints; its rendered surfaces are simplified and do not define a machinable race.
Fixed and plunging joints
CV joints are used where a driveline must transmit rotation through changing alignment. The type depends on whether the connection also needs axial movement. GKN distinguishes fixed-ball joints from plunging designs and provides different ratings for each.
This drawing represents a fixed six-ball joint. It does not simulate plunge, shaft bending, load distribution or a particular vehicle installation. Enter the articulation between the shafts themselves; a steering-wheel angle is not that measurement.
Ideal speed comparison
For the CV joint, nout = nin. For a single Hooke joint, choose input phase theta so that tan(psi) = cos(beta) tan(theta), with psi unwrapped continuously. Differentiating gives nout/nin = cos(beta)/[1 − sin²(beta) sin²(theta)].
At theta=0 degrees the ratio is cos(beta); at 90 degrees it is sec(beta). There are two speed cycles per input revolution. Minimum output is nin cos(beta), maximum output is nin/cos(beta), and peak-to-peak ripple as a percentage of input speed is 100[sec(beta) − cos(beta)].
This percentage is not a symmetric plus/minus deviation about input speed. The upper and lower deviations differ. It also does not predict a vibration level or establish an acceptable operating angle.
The instantaneous curve uses the same cycle-position control as the cutaway. It compares a separate single Hooke joint with the CV construction; the orange variation is not attributed to the balls in this drawing.
Worked speed comparison
At 1,000 RPM input and 40 degrees articulation, the ideal CV output stays at 1,000 RPM. A single Hooke joint varies from approximately 766 RPM to 1,305 RPM, giving 53.9% peak-to-peak ripple relative to input.
At 15 degrees, the calculated peak-to-peak percentage is 6.94%; at 30 degrees it is 28.87%. Peak-to-peak ripple is the full difference between maximum and minimum speed, expressed as a percentage of input speed.
At zero articulation, both constructions give output equal to input and the graph’s two curves coincide. Doubling input speed doubles the minimum and maximum RPM but leaves the percentage ripple unchanged.
What this comparison can establish
The calculator isolates the kinematic distinction between constant output speed and the twice-per-revolution variation of a single Hooke joint. It does not size the joint or compare purchase price, torque rating or service life.
Those properties depend on the particular product, duty and installation. The slider maximum is not a universal maximum working angle. A multiple-joint shaft also cannot be evaluated as a single Hooke joint without considering its complete geometry and phasing.
Questions about the model
Why does changing RPM leave the ripple percentage unchanged?
The extrema scale directly with input speed. Dividing their difference by that speed cancels the RPM term.
Why are there six visible balls?
This cutaway represents the six-ball Rzeppa construction identified in the reference drawing. Other CV-joint constructions exist.
Is 45 degrees a service limit?
No. It is the comparison range of this calculator. Use the rating for the specific joint and installation.
Does the graph show speed variation inside the CV joint?
No. The green line is ideal CV output. The orange curve is a separate single Hooke-joint comparison.
Can these results diagnose a worn driveline?
No. The model has no wear, clearance, loading or vibration measurement inputs.
Construction references
- NTN: EP1512879A1, fixed-type constant-velocity universal joint. Figures 8a/8b show the reference six-ball Rzeppa construction; the description explains the ball plane.
- GKN Automotive: constant-velocity joint portfolio. Distinguishes fixed and plunging joint types and their individual ratings.
The speed comparison is derived explicitly above from the ideal shaft-angle relation. The drawing explains the ball-plane geometry; it does not provide manufacturing dimensions or a product rating.
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