An Oldham coupling connects parallel shafts with a small centre offset through an intermediate disc that slides in two perpendicular directions. Explore the three-part arrangement described by Hiscox and calculate ideal tongue travel, sliding speed and centre motion.
Ideal Oldham Kinematics Calculator
Enter a declared parallel shaft offset and input speed. The worksheet reports exact displacement identities for one ideal orthogonal-slot construction; it does not rate torque, wear, friction, backlash, material, life or alignment tolerance.
Equation Used
- The input and output shaft axes are parallel, with a fixed declared centre offset e.
- The two intermediate-disc sliding directions are exactly perpendicular and rotate together through angle theta.
- The ideal output angle equals the input angle, giving n2=n1.
- Each signed tongue displacement has amplitude e and peak-to-peak travel 2e; the intermediate centre follows a radius-e/2 circle twice per shaft revolution.
- Clearance, backlash, angular or axial misalignment, torque, contact pressure, friction, wear, lubrication, heat, materials, strength, speed limits, manufacture and safety are excluded.
Perpendicular sliding features let the intermediate disc bridge the shaft offset while preserving the ideal 1:1 rotation ratio. Playback runs at a fixed illustrative speed; the speed input changes the calculated maximum sliding speed.
An orthogonal double-splined disc bridges offset parallel shafts
Hiscox item 1287 places double-splined disc B between grooved faceplates A and C on shafts slightly eccentric in alignment. Item 1288 shows the intermediate disc's front and back sliding features at right angles.
In the declared ideal construction, one disc coordinate slides along the input-face direction and the perpendicular coordinate slides along the output-face direction while both shafts retain the same angle.
A historical offset-shaft coupling principle
The coupling accommodates a small parallel offset through sliding at the intermediate disc rather than bending the shafts. This ideal model explains that motion; selecting an actual coupling also requires its permitted offset, torque, speed and operating conditions.
Declared ideal orthogonal-slot kinematics
With u=(cosθ,sinθ) and v=(-sinθ,cosθ), the intermediate centre M lies on both O1+a u and O2+b v. Its locus is a circle of radius e/2 about the midpoint, traversed twice per shaft revolution. Each signed slide coordinate ranges from -e to +e.
Declared kinematics example
For e=6 mm and n1=600 rpm, each tongue's ideal peak-to-peak travel is 12.0 mm, maximum slot speed is 377.0 mm/s, intermediate-centre orbit radius is 3.0 mm and ideal n2/n1 is 1.000.
Kinematic motion and coupling ratings
The ideal motion relations determine travel and sliding speed, but do not establish contact pressure, friction, wear or service life. Those quantities depend on the disc geometry, material, fit, loading and operating conditions. The calculator therefore does not rate a commercial coupling.
Oldham coupling questions
Does the ideal construction preserve a 1:1 velocity ratio?
Yes, under the declared orthogonal, clearance-free constraints.
Does this calculator rate a real coupling?
No.
Are the entered offset and speed historical?
No. They are declared inputs for the ideal kinematic viewer.
Oldham coupling source
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, page 317, items 1287–1288: primary public-domain plate and captions for the grooved faceplates, free-running double-splined disc and right-angle front/back grooves.
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