A cylindrical kinematic pair permits independent translation along and rotation about a common axis. Those two invariant motions distinguish it from revolute, prismatic and screw pairs.
Two-degree Cylindrical Pair Interactive Calculator
Enter a friction coefficient, shaft diameter, engagement length, comparison arm and assumed normal load. Results are calculation and a simple Coulomb estimate—not a jamming, clearance, contact-pressure or bearing design calculation.
Equation Used
- The joint is represented as coaxial cylindrical surfaces with independent axial and angular coordinates.
- The entered load is an assumed normal load at the sliding interface.
- The Coulomb estimate uses a constant entered coefficient and opposes relative sliding.
- L/D and μL/a are dimensionless calculation ratios only.
- Clearance, fit, contact-pressure distribution, edge loading, cocking equilibrium, lubricant regime, speed, temperature, wear, stiffness, strength, seals, bearings, tolerances, jamming and safety are omitted.
Two Independent Motions on One Axis
A cylindrical pair constrains four of a rigid body's six spatial degrees of freedom while leaving translation along the cylinder axis and rotation about that same axis. NASA descriptions of cylindrical joints and cylindrical-surface invariants identify those two motions.
Unlike a screw pair, the two coordinates are not coupled by a lead.
What This Calculator Represents
The animation shows independent axial translation z and rotation θ. The numbers report entered L/D and μL/a ratios plus the elementary Coulomb estimate μN for an entered normal load.
They do not predict whether a real shaft and bore will cock, bind or wear.
Limited Entered-Parameter calculation
entered geometry ratio = L/D
entered comparison index = 100 μL/a
index complement = 100(1 - μL/a)
The final two values are not a universal jamming criterion or safety margin.
Worked Arithmetic Example
For μ=0.12, entered normal load 30 N, L=50 mm, D=25 mm and a=120 mm, the Coulomb estimate is 3.6 N, L/D is 2.00, μL/a is 5.0% and its arithmetic complement is 95.0%.
Assumptions and Limits
- Illustrated motion: independent axial translation and rotation about the common cylinder axis.
- Calculated: μN and dimensionless entered ratios.
- Not calculated: clearance, fit, contact pressure, edge reactions, cocking equilibrium, lubricant regime, seal drag, bearing behavior, deflection, stiffness, strength, wear, tolerances, jamming or safety.
Frequently Asked Questions
How many degrees of freedom does a cylindrical pair have?
Two: translation along and rotation about the common axis.
Are those motions screw-coupled?
No.
Is μN a complete bearing-friction model?
No; it is an elementary Coulomb estimate for an entered normal load.
Does μL/a predict jamming?
No; it is only an entered comparison index here.
Is L/D a universal design limit?
No.
Can this size a shaft, sleeve or bushing?
No.
References
- NASA, Kinematic Alignment Bonding: rotation about and translation along a cylindrical axis are invariant motions.
- NASA internship report: a cylindrical joint permits rotation about an axis and translation along that axis.
- MIT OpenCourseWare, Tribology: Coulomb friction is proportional to normal load for the constant-coefficient model.
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