A cylindrical lower pair permits two independent ideal motions: translation along its common axis and rotation about that axis. A smooth shaft in a matching sleeve illustrates the arrangement. This calculator compares their diameters and shows those motions separately and together.
Cylinder-on-Cylinder Lower Pair Interactive Calculator
Compare measured bore and shaft diameters, then explore independent axial and rotary motion in a cutaway cylindrical joint.
Equation Used
- Coaxial circular bore and shaft at the entered measurement condition.
- Nominal diameter subtraction; no tolerance stack, roundness or thermal model.
- Fixed cutaway sleeve and illustrative shaft length; no end stops or key.
- Gap is magnified in the transverse detail. The main cutaway is illustrative.
Negative clearance means interference. Zero nominal clearance alone does not establish a freely moving fit.
A sleeve guides a shaft along one common axis
The bronze sleeve stays fixed. The blue shaft first slides without rotating, then rotates without sliding, then combines both motions. An end-face marker makes the rotation visible.
The upper half of the sleeve is removed in the drawing to expose the shaft. There is no screw thread coupling angle to position and no key preventing rotation. The ideal joint constrains lateral translation and tilt while retaining axial translation and axial rotation.
What this model represents
The model is useful for understanding a smooth sliding and rotating shaft or sleeve. A keyed quill, a threaded feed or a clamped shaft has additional constraints and cannot automatically be treated as the same two-freedom joint.
The illustration does not specify a real bearing material rating or predict seal behavior. Actual load, speed, lubrication and alignment requirements must be considered separately.
Signed dimensional clearance
Diametral clearance is bore diameter minus shaft diameter. For a concentric cross-section, the radial difference is half the diametral difference. Multiply millimetres by 1000 to express either result in micrometres.
A positive result leaves nominal dimensional clearance. A negative result indicates interference between the undeformed dimensions. A zero result is a line-to-line nominal fit, not proof that the joint will move freely.
The lower drawing magnifies the difference so that these small gaps or overlaps are visible. The displayed numbers remain the entered dimensional differences.
A 25.020 mm bore and 25.000 mm shaft
The diametral difference is 0.020 mm, or 20 µm. The concentric radial difference is 10 µm. Increasing the shaft to 25.030 mm changes the diametral result to −10 µm and the radial result to −5 µm.
The animation stops free sliding for the interference case but retains the cross-section. This does not simulate a press-fitting process, deformation or a finished interference fit.
Nominal geometry is only part of a fit assessment
The appropriate fit depends on actual diameter tolerances, materials, temperature, shape errors, surface condition, lubrication and loading.
Positive nominal clearance does not establish bearing life, a fluid film or freedom from binding. Nor does the ideal pair provide a holding brake or an axial stop.
Cylindrical-pair questions
Are sliding and rotation linked?
No. They are independent coordinates. A helical screw joint instead relates angle to travel through its lead.
Why does the transverse gap look large?
It is deliberately magnified to show differences measured in micrometres.
Why does motion stop at zero or negative clearance?
The entered dimensions do not establish a freely sliding undeformed joint. The illustration retains the geometry instead of showing parts freely passing through interference.
Does the excursion setting change clearance?
No. Clearance comes from the two diameters. Excursion changes the displayed motion range.
Reference
Lynch and Park, Modern Robotics, section 2.2, classifies the cylindrical joint as having two degrees of freedom. Signed radial and diametral differences here follow directly from concentric-circle geometry.
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