A more technical term for a "slicing" motion

I seek a word (verb, noun, adverb or adjective) that is suggestive of a particular type of constrained mechanical motion described below by way of example.

It could be a flat planar sheet moving within the imaginary plane that contains it, or it could be a curved sheet moving in a circular motion within an imaginary cylindrical surface. The defining characteristic is that the object in motion does not venture into territory outside a given surface, which contains the object itself in all its potential positions. It is like a small surface moving within another larger surface to which it conforms at all times.

The verb "slice" comes to mind, but nothing is actually being sliced here, and ideally I hope to find a word in a register that is more appropriate for a technical document, like the register of words such as "articulated" or "reciprocating" (as they apply to constrained motion). That said, I'm short on ideas so any related words could be helpful.

• There ought to be something technical in mathematics (geometry) for this - like 'traverse'? SO the sheet traverses within the plane; the curved sheet traverses within the cylinder, etc... Commented Aug 30, 2018 at 18:59
• @JohnFeltz So I could call it a surface-traversing sheet, which may be okay, but it doesn't seem to suggest that the sheet conforms to the same surface it traverses. Or does it? Commented Aug 30, 2018 at 19:04
• @DhruvSaxena The sense here is not at all to traverse a space exhaustively, but to be constrained to a space. And explicitly a surface. Commented Aug 30, 2018 at 19:27
• When I saw the headline I thought of shear but that is not what you are asking. I believe that the action is a sliding one since, one body can only slide on another when it is in contact with it and is, therefore, constrained. As soon as the bodies lose contact with each other they are no longer sliding. Commented Aug 31, 2018 at 10:07

"The curved plate rides along the surface of the cylinder."

Merriam-Webster defines ride as follows:

ride - intransitive verb 1 a : to sit and travel on the back of an animal that one directs

b : to travel in or on a conveyance

2 : to travel as if on a conveyance : be borne rode on a wave of popularity

3 a : to lie moored or anchored a ship rides at anchor

b : sail

c : to move like a floating object the moon rode in the sky

4 : to become supported on a point or surface

5 a : to travel over a surface the car rides well

b : to move on the body shorts that ride up

6 : to continue without interference let it ride

7 a : to be contingent : depend plans on which the future rides

b : to become bet a lot of money riding on the favorite

ride - transitive verb

1 a : to travel on ride a bike ride the bus

b : to move with like a rider ride the waves

2 a : to traverse by conveyance rode 500 miles

b : to ride a horse in ride a race

3 : survive, outlast —usually used with out rode out the gale

4 : to traverse on horseback to inspect or maintain ride fence

5 : to mount in copulation —used of a male animal

6 a : obsess, oppress ridden by anxiety

b : to harass persistently : nag

c : tease, rib

7 : carry, convey

8 : to project over : overlap

9 : to give with (a punch) to soften the impact

10 : to keep in partial engagement by resting a foot continuously on the pedal ride the brakes

This is similar to the sense that a train "rides the rails." In particular definitions 4 and 7 seems to carry the connotation you are looking for.

• Ride, like Slice, seems heavily predicated on an object. To slice implies that there is something being sliced, and to ride implies that there is something being ridden. In this case there may be no material object, only the subject "sliding" along its own extrapolation. Or am I under-appreciating the scope of Ride's meaning? Commented Aug 30, 2018 at 21:23

As for the motion, the words "traverse" or "translocate" can work well for an object moving within or following a surface. However, I don't think that all three of your criteria can be conveyed in a single word (i.e. 1. the mobility, 2. surface constraint, and 3. the object itself). You are describing a mobile/moving surface (object) constrained within another (greater) surface.

(surficial or coplanar)

"sector", "subsector", "section", or "subsection".

Possibly one of these words would suit the technical purpose you have in mind?

https://www.thefreedictionary.com/traverse

https://www.thefreedictionary.com/surficial

https://www.thefreedictionary.com/coplanar

https://www.thefreedictionary.com/sector

https://www.thefreedictionary.com/subsection

While the definitions of Glide don't seem to match the intended meaning, I think it has the requisite connotations.

I suspect this should be asked on mathematics.SE

The best I can offer is a patch and map trace.

Patch
A patch (also called a local surface) is a differentiable mapping x:U->R^n, where U is an open subset of R^2. More generally, if A is any subset of R^2, then a map x:A->R^n is a patch provided that x can be extended to a differentiable map from U into R^n, where U is an open set containing A. Here, x(U) (or more generally, x(A)) is called the map trace of x.

Wolfram Mathworld.