KEVOS® MAKEOS · Power Transmission
Universal-Joint Drive (Single or Double Cardan: Speed, Torque, Inertia)
How much does the output speed of this Cardan shaft fluctuate, is a double-joint arrangement phased correctly, and what peak torque do the joints see?
Kinematic and torque check of a single or double Cardan (Hooke’s) joint drive: the output angle traced through a full turn for each joint, speed ratio extremes and fluctuation at the output and at the intermediate shaft (for a single joint, the limits match the universal joint tool), whether a double joint cancels the fluctuation (equal angles and yokes in phase), peak angular accelerations and the inertia torques they cause, and the peak joint torque against your rating.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Input speed | rpm | Speed of the input shaft. |
| Input torque | N·m | Torque on the input shaft. |
| Arrangement | choice | One joint, or two joints with an intermediate shaft. |
| Joint 1 angle | ° | Angle between the input and the next shaft at joint 1. |
| Joint 2 angle | ° | Angle at joint 2 (double arrangement). |
| Yokes on the intermediate shaft | choice | Whether the yokes on the two ends of the intermediate shaft lie in the same plane. |
| Inertia of the driven side | kg·m² | Inertia of the driven machine at the output shaft. |
| Inertia of the intermediate shaft | kg·m² | Inertia of the intermediate shaft (double arrangement). |
| Largest joint angle allowed | ° | Largest joint angle you accept for the speed and life (your value from the joint maker). |
| Joint torque rating | N·m | Torque rating of the joint for the speed and angle (from the maker). |
Method and formulas
- Joint 1: φ = atan2(sin θ, cos θ cos β₁); ratio dφ ÷ dθ swings between cos β and 1 ÷ cos β (as the universal joint tool).
- Joint 2: in phase ψ = atan2(sin φ cos β₂, cos φ) (cancels joint 1 when β₂ = β₁); out of phase ψ = atan2(sin φ, cos φ cos β₂) (adds to it).
- Angular acceleration α = ω₁² d²ψ ÷ dθ², found point by point; inertia torque = J α.
- Peak joint torque = T₁ × the largest speed ratio’s reciprocal + the intermediate-shaft inertia torque.
- Example: at 15° the output swings 0% and the intermediate shaft 6.935%; the peak joint torque is 111.14 N·m.
Limitations
- Rigid shafts and joints; torsional resonance of the shaft is not checked.
- Friction and joint bearing loads are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a Cardan drive shaft layout
- Confirm a double joint runs at constant velocity
- Find the torque peaks from joint angle and inertia
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Speed limits and fluctuation at the output and intermediate shafts
- Phasing check for constant velocity
- Inertia torques and peak joint torque
Interpreting the result
- Equal angles with in-phase yokes give a constant output speed; any angle difference brings fluctuation back.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2445–2446. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Universal-Joint Drive (Single or Double Cardan: Speed, Torque, Inertia) calculator
