BIZOMAT MAKEOS · Power Transmission
Universal (Cardan) Joint Speed Variation
How much does the output speed of this universal joint vary over each revolution?
Maximum and minimum driven-shaft speed, speed variation and output speed at any rotation angle of a single universal (Cardan) joint working at an angle, with the matching torque variation.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Joint working angle | ° | Angle between the two shafts at the joint. |
| Driving shaft speed | rpm | Constant speed of the driving shaft. |
| Driving shaft position for the instantaneous speed | ° | Rotation of the driving yoke from the position where the driven shaft is fastest. |
| Input torque | N·m | Torque at the driving shaft. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Joint working angle
- What it is
- The angle between the centrelines of the driving and driven shafts at the joint, measured as the deviation from a straight line.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The driven-speed variation grows quickly as the angle increases.
- Get it right
- Measure from straight (0° means the shafts are in line), not the included angle between them.
What this means: Driving shaft speed
- What it is
- The steady rotational speed of the input (driving) shaft. The driven shaft speeds up and slows down twice each turn around this mean.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every output speed scales in direct proportion to the input speed.
What this means: Driving shaft position for the instantaneous sp…
- What it is
- How far the driving yoke has turned, measured from the position where the driven shaft runs fastest, for the instantaneous speed and torque results.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from the fastest position; the slowest position is a quarter turn later.
What this means: Input torque
- What it is
- The torque applied to the driving shaft. The tool shows how the driven torque rises and falls as the speed varies, with power held constant.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The torque at the chosen position scales in direct proportion to the input torque.
Method and formulas
- Maximum driven speed = n sec β; minimum = n cos β (handbook).
- Instantaneous ratio ω₂/ω₁ = cos β ÷ (1 − sin²β sin²θ), θ from the minimum-speed position.
- Torque varies inversely with speed (power constant, losses ignored).
- Example (handbook case): 100 rpm at 25° gives 110.34 and 90.631 rpm, a variation of 19.707 rpm.
Limitations
- Single joint; two joints correctly phased with equal angles cancel the variation.
- Inertia of the driven parts turns the speed variation into torque pulses.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a single universal joint is acceptable for a drive
- Explain vibration from a drive shaft at an angle
- Decide on a double joint or intermediate shaft
Who it is for
- Design engineers
- Maintenance engineers
- Automation engineers
What you get
- Maximum and minimum driven speed
- Total variation
- Instantaneous speed and torque at the chosen position
Interpreting the result
- Angles above about 20–25° should be avoided except at low speed and power; above 45° a single joint does not work well.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2445–2446. Topic reference; no source tables or recommended settings are reproduced.
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Open the Universal (Cardan) Joint Speed Variation calculator