An oblique disk on an upright shaft raises and lowers a separate rod resting on its face. Explore Brown item 95 and calculate ideal follower stroke from the contact radius and disk tilt.
Oblique-Plane Stroke Calculator
Enter a declared follower contact radius and disk tilt. The worksheet applies one ideal tilted-plane construction and reports peak-to-peak travel only; it does not size or rate a pump, compressor, cam, follower or bearing.
Equation Used
- The disk face is an ideal rigid plane tilted by the declared angle from a plane normal to the upright shaft.
- The upright point follower remains at declared transverse radius R and stays in contact throughout one revolution.
- The signed displacement is sinusoidal only under this declared plane-and-point construction.
- Disk diameter, rod-end shape, guide clearances, return force, contact load, friction, slip, impact, wear, speed, power, lubrication, bearings, strength, materials, manufacture and safety are excluded.
The rotating tilted disk raises and lowers the upright resting follower. Radius and tilt determine the ideal stroke; contact forces and follower lift-off are not calculated.
An oblique disk lifts a separate upright resting rod
Brown item 95 shows an upright drive shaft carrying a disk whose face is oblique to the horizontal. A second upright rod rests on that face at an offset from the shaft. As the shaft and disk rotate, the local face height beneath the rod rises and falls, so the guided rod reciprocates vertically.
The schematic shows the rod resting on the rotating disk. The entered radius and tilt define the ideal displacement calculation; the drawing is illustrative.
A historical rotary-to-rectilinear motion example
The arrangement illustrates how a rotating tilted surface can produce vertical reciprocation. This model calculates travel alone; a working application also needs a way to maintain follower contact and support the resulting loads.
Declared ideal rotating-plane geometry
The phase origin may be chosen at mid-stroke. Maximum and minimum signed offsets are plus and minus R tan(theta), giving peak-to-peak stroke S. This is a geometry identity for the declared model, not a force or durability calculation.
Declared geometry example
For R=50 mm and theta=15 degrees, ideal half-stroke is 13.40 mm, full stroke is 26.79 mm and S/R is 0.536. These are illustrative declared values.
Follower travel and contact
The stroke equation assumes continuous contact between the rod and an ideal plane. It does not determine the return force needed to maintain that contact, the pressure at the rod end, or the effects of friction and wear. Those quantities require a defined follower shape, loading and operating speed.
Oblique-disk reciprocator questions
Is the rod connected to the disk?
Brown describes the upright rod as resting upon the disk surface; the declared animation therefore shows contact, not a pin joint.
Does the formula predict contact force or follower lift-off?
No.
Are R and theta historical dimensions?
No. They are entered values for the ideal plane model.
Oblique-disk source
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, page 29, item 95: primary public-domain plate and caption for the upright shaft, oblique disk and upright resting rod.
- Brown, 507 Mechanical Movements, Internet Archive scan: independent public-domain scan of the same item and caption.
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