What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis?

In summary, the geometries of two contacting solids that can undergo relative rotation and translation along the same axis should involve complementary shapes that facilitate motion while maintaining contact. Ideal geometries include cylindrical or spherical forms that allow smooth interaction and minimize friction. The design should ensure that the surfaces are engineered for optimal contact area and load distribution, enabling both rotational and translational movement without excessive wear or instability.
  • #1
apcosta
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Thread moved from the technical forums to the schoolwork forums
TL;DR Summary: What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis?

a) Consider two rigid bodies that have a relative motion characterized by a rotation and a translation with respect to the same axis (like a bolt and a nut). The two solids may rotate around a certain axis and translate along the *same* axis (exactly as a bolt and a nut).

b) The two solids are separated by a surface so that the geometries of the two bodies match perfectly at all points of the surface.

c) What is the geometry of such a surface? In other words: what is the geometry of the screw head of a bolt so that it matches perfectly with the nut?
 
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  • #2
apcosta said:
c) What is the geometry of such a surface?
Cylindrical.
Any constant pitch helical thread profile, with its complement, would work if the translation was due to rotation.
 
  • #3
Yes, the translation is due to rotation so that there is a permanent/persistent sliding at all points of the interface. So, you mean "a constant pitch helicoid surface"? Where could I find a proof?
Thank you very much for your fast reaction!
 
  • #4
apcosta said:
b) The two solids are separated by a surface so that the geometries of the two bodies match perfectly at all points of the surface.
That is not true of real helical threads. Most screw threads have truncated crests and troughs, so the opposed thread surfaces do not match exactly, but are easier to cut. Contact between the bodies is only made on one thread flank of the internal body, against the one opposed flank of the external body. There must always be a clearance to allow for tolerance and temperature changes. Without a lubricant film, the sliding surfaces would have high friction, or cold weld together.
Also consider a low friction ball-screw, where the recirculating balls are in the channel between the two bodies. There are gaps between the ball contact lines with the channel, the balls are ancillary bodies, so there is no single surface in contact at all points.

apcosta said:
Where could I find a proof?
The proof will depend on what you are trying to do, and why you need a proof.
 
  • #5
apcosta said:
c) What is the geometry of such a surface? In other words: what is the geometry of the screw head of a bolt so that it matches perfectly with the nut?
Welcome, @apcosta !

What the screw head of a bolt has to do with the nut?

What is guiding the relative movement of one surface respect to the other?
 
  • #6
It seems like you must want something more than that. You could consider that nut and bolt as a single solid and then put a partitioning surface between them with practically any shape remaining in the interior of the combined solid.
CORRECTION: Sorry, I missed the significance of this part: "have a relative motion characterized by a rotation and a translation with respect to the same axis".
 
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  • #7
I think that we can take a segment of any flat curve and uniformly rotate and translate it around and along any axis in space to make such surface, as long as this surface does not intersect itself. Not only "nuts and bolts" with various grooves, but also "corkscrews" with various cross sections.
 
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  • #8
FactChecker said:
It seems like you must want something more than that. You could consider that nut and bolt as a single solid and then put a partitioning surface between them with practically any shape remaining in the interior of the combined solid.
CORRECTION: Sorry, I missed the significance of this part: "have a relative motion characterized by a rotation and a translation with respect to the same axis".
Yes, that last part is fundamental. Thank you for showing interest in this problem!
 
  • #9
apcosta said:
Thank you for showing interest in this problem!
Is this a purely theoretical study, or is there a practical application?

The requirement that the geometry of the two bodies, match perfectly at all points on the contact surface, seems to be an impossible practical relationship, that defeats the purpose of the study.

Spline shafts are designed to allow free linear translation, while preventing rotation.
Hydraulic cylinders control translation, but allow freedom of rotation about the axis.
A cylindrical sleeve, running on a round bar, may meet your requirement.
A screw thread couples the translation to the rotation, but there are many special threads that do not meet the perfect-contact-everywhere requirement.

Can you tell us more about the intended application, or the reason for your interest, in such a mechanism?
 

FAQ: What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis?

What types of geometries are typically used for two contacting solids with relative rotation and translation along the same axis?

The most common geometries for such scenarios are cylindrical and conical shapes. Cylindrical geometries allow for smooth rotational and translational motion, while conical geometries can provide self-centering properties.

How does the choice of geometry affect the friction between the contacting surfaces?

The geometry of the contacting surfaces significantly impacts friction. Cylindrical surfaces tend to have more uniform friction characteristics, while conical surfaces can vary in friction depending on the contact angle and the applied forces. Proper lubrication and surface finish are crucial to managing friction in both geometries.

What are the mechanical considerations for ensuring stability during relative rotation and translation?

Key mechanical considerations include the alignment of the axis, the surface roughness, and the contact pressure distribution. Ensuring that the axis of rotation and translation is well-aligned minimizes wobble and uneven wear. Surface roughness should be optimized to balance friction and wear, and the contact pressure should be evenly distributed to avoid localized stress concentrations.

How does material selection influence the performance of the contacting solids?

Material selection is critical for performance. Harder materials tend to wear less but may increase friction, while softer materials may wear more quickly but can provide smoother motion. The choice of materials should also consider compatibility to avoid galling or corrosion, especially in environments with varying temperatures or exposure to chemicals.

What are the common applications of such contacting solid geometries?

Common applications include bearings, bushings, and mechanical joints in machinery. These geometries are also used in robotics for rotational joints, in automotive components such as drive shafts, and in aerospace for various moving parts. The design ensures that components can move smoothly and reliably while handling the required loads and motions.

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