This calculator presents the exact ideal angular-velocity relationship for one Hooke universal joint driven at constant input speed. It does not size or rate a driveline.
Hooke's Angular Shaft Coupling Interactive Calculator
Explore instantaneous and limiting output-speed ratios for a single ideal Hooke joint at an entered shaft angle and constant input RPM.
Equation Used
- One ideal Hooke joint with intersecting input and output axes.
- Constant input angular speed and rigid zero-clearance geometry.
- No second-joint phasing or angle-equality model.
- No torque, inertia, bearing load, friction, backlash, lubrication, vibration, critical-speed, strength, fatigue, life or allowable-angle model.
Kinematics only. The slow deviation is negative because the minimum ratio is cos β; the fast deviation is positive because the maximum is 1/cos β. Neither is a torque, vibration or service-limit calculation.
Single-joint angular kinematics
Two yokes on intersecting shaft axes are connected through orthogonal pins on a cross. At zero shaft angle, input and output rotate together. At nonzero angle, the geometric constraint produces a periodic instantaneous speed ratio even with constant input speed.
The animation uses planar orientation symbols rather than a three-dimensional yoke-and-cross assembly. Read the numerical ratio from the stated equation; the symbols do not establish a physical shaft-phase convention. Playback is slowed for viewing.
Use as a kinematic conversion only
The calculator can quantify ideal single-joint speed variation. Hardware selection and driveline design require manufacturer ratings and complete load, geometry, phasing and dynamic analysis.
Instantaneous ratio and extrema
For shaft angle β and input phase θ, ω2/ω1=cosβ/[1−sin²β sin²θ]. The minimum ratio is cosβ and the maximum is 1/cosβ. The average output speed over a full revolution equals input speed.
Worked example
At β=20° and 1,000 rpm input, the ideal ratio ranges from cos20°≈0.9397 to 1/cos20°≈1.0642. Output therefore ranges from about 939.7 to 1,064.2 rpm while averaging 1,000 rpm over a revolution.
Scope and limitations
A real driveline needs joint-series ratings, torque and transient load, bearing reactions, operating angle and speed limits, lubrication, plunge/slip accommodation, phasing and angle equality for multiple joints, shaft inertia and stiffness, torsional and bending vibration, critical speeds, balance, fatigue and guarding.
Questions
Does a single joint transmit constant speed?
Only at zero shaft angle. Otherwise instantaneous speed varies twice per revolution.
Does this calculator prove two joints cancel ripple?
No. Cancellation additionally requires the correct topology, yoke phasing and equal operating angles.
Is 35 degrees a safe operating angle?
The input range is not a rating. Safe angle and speed come from the actual joint manufacturer and driveline analysis.
Calculation basis and component data
The speed-ratio extrema follow the ideal single-Hooke-joint relationship stated above. They require no assumed torque or hardware rating.
Lovejoy: Universal joints explains that actual joint operation depends on the application’s angle and speed combination. Component selection additionally requires the applicable manufacturer data and load case; this kinematic calculation is not a selection chart.
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