D sliders, also known as P carriages in Studio-Silver Reed language, only move/ push the needles; they do not manipulate any stitches.
The needles are pushed to various working positions, B, C for Studio, D for Brother, depending on the starting position of the needles.
Drop stitch “lace” is also referred to as drive lace in Studio pubs, and summer fair isle in Passap ones.
The first samples of the stitch type I was exposed to were shared at a Passap Seminar that explored the built-in console color separation techniques in the E6000, introduced in 1988. Two passes with no yarn, and both locks were required until the Passap version of the D slider was developed in Australia. The E6000 magazines then began offering designs producing what they named as summer fair isle, and in seminars, added reader techniques that were shared for use when planning to knit designs in 3 or 4 colors.
Many brand-specific magazines provided patterns produced with devices or accessories as they were introduced, with pubs on the topic ebbing and waning with the passage of time.
The first reference I have been able to find on the Studio P carriage dates back to the introduction of the SRP50 ribber in 1978. A grainy copy of the early manual is downloadable and illustrates its use on page 12, applied to drive lace on pages 36-38, and to pile knitting continuing to page 42.
This post is intended to address using sliders on Brother models, in theory, to facilitate the process of dropping stitches when continuous design patterning is in use.
Links to my historical posts on the definition and execution of this “lace” on different machines using varying methods are provided at the bottom.
The resulting knit benefits from the use of yarn that responds to blocking by lying flat and retaining scale differences between the different stitch sizes.
Knitting begins with all stitches on one bed, and loops formed on the opposite bed, that dropped at varying intervals, depending on the intended pattern, to produce elongated stitches between stocking stitch ones.
Dropping the stitches can be achieved manually with any tool on hand, by sliding the ribber carriage only back and forth if loops are formed on it, or with the aid of stitch ditchers/ dumpers.
Maintaining proper needle selection and not having needles accidentally pushed back to the A position, resulting in possible pattern errors, is made easier and quicker with specific tools, often called sliders and sometimes referred to in early manuals as carriages, although they have no moving parts.
Knit bubbles and “stitch ditchers/dumpers” and Brother KMs “pile knitting”/ ribber stitch dropping tools share images of such tools.
Usual dropping sequences in Brother models are made from right to left on needles in B position, with a return of the needles to B after the stitches have been dropped. The next preselection pattern row is made as the paired carriage return to the left, then repeating paired rows.
The appearance in machines that keep the needles in the equivalent of Brother B position after carriage pattern passes, i.e., Studio, Superba, Passap, with the possibility of dropping stitches every row, can produce shapes composed of simple long stitches.
To maintain Brother preselection, if the knit bed is used to form loops for the long stitches, there will be an added knit row on the ribber as the carriages return to the left, with a different final appearance.
I was able to obtain a 3D printed model for the Brother 4.5 mm machine from cults3D at the time of my blog post; the site is often unavailable according to forums, and the present pricing is said to be set to discourage downloads pending resolution in a related court case.
For those without access to 3D printing, this site may be worth exploring for direct purchase of items, ie, the slider, for $21.
The use of the tool is clearly demonstrated here https://www.youtube.com/watch?v=IGjPwGqFJhQ.
Note that sliders presently available are used on knit beds with slotted rails, as in the 930 on the right, and it is open to question if the use is possible on the solid and slightly narrower rails found in earlier electronic and punch card models. Also an issue, if the rail happens to disrupted in any way in the center. 
The Studio slider is shown in the center, and, on the right, the only Brother-produced slider, intended for use on the bulky machine.
The needle butts enter unimpeded and follow the tracks marked with arrows. 
They can be used on both the knit and the ribber beds.
Just as easily, stitches on the ribber can be dropped using only the ribber carriage for 2 passes.
The traditional method in published designs found in punchcard volumes uses alternating black pixels/punched holes to produce the loops that are, in turn, dropped, and all-white/unpunched rows, which allow for the loops being dropped when there is no pattern selection on the top bed.
For the 3D model, it is useful to “read the manual”, or in this case, follow the video.
I chose to mark my slider for future use.
The proper placements on respective needle beds to match the traditional method. 
This top bed placement is wrong, needles are still brought forward, moving right to left, but are left out to D, not B, on the return to the right. 
Beginning with single color samples.
A Studio drive lace published repeat for use with the technique
knit 2 rows, drop, repeat
12X16
test knit on 37 stitches 
results are in hard to read stitch size differences
breaking the common rules and appearance for this type of fabric, a “what if” version, double height, 12X32 
test knit on 50 stitches, 
knit 4 rows, drop, repeat. 
Larger designs can be more effective, 24X22
rendered double height, 24X44 
EOR rendered all white/ erased for traditional use and approach. 
Test knit on 48 stitches. 
I have a perennial curiosity in terms of using nearly anything in a way other than that intended when designed.
This is a first experiment using the 24X44 fair isle design,
with each row selection repeating twice and changing the position of the slider on the needle bed, no blank rows are required.
Stitches are still dropped when moving from right to left.
The slider is turned around and placed on the bed in front of the rail to move stitches forward. Note the relative position of the needle butts and the nub on the slider.
From left to right, to drop stitches, the slider is placed to rest on the rail, with the nub pointing down. 
With the knit carriage set for slip stitch, and the pattern programmed as fair isle, the black pixels or punched holes will be selected forward, when the carriages move to the left, picking up loops on the selected needles on the next carriage pass to the right. 
With carriages on the right, the stitches are dropped.
The small proof of concept. 
A larger test, the first PNG, 20X40 
in brick configuration, doubled in length, 20X80 
and then doubled in width for a guess at better aspect ratio, 40X80. 
After loops are formed, left to right, the slider operates from the right, 
will advance all needles out to E as it moves to the left, 
and drop all loops as it returns to the left.
The needles will be empty and aligned in B.
The next pass will preselect the next row of the design on the top bed, and the process is repeated. 
When planning to drop stitches on the ribber, the designs often include racking to form secondary shapes.
The traditional placement is on the left after loops are formed. 
As the tool moves to the right, needles are raised, moving all loops behind the latches. With its return to the left, loops are dropped, forming the long stitches. 
The stitches on the ribber are hand selected each row, knit, and dropped, with the top bed knitting single rows rather than 2 for each row of the design when the beds are reversed.
This giant swatch shows the results; the stitches in the dropped pattern tend to get larger as they move further away from the knit stitches beside them. 
These were my earlier samples testing my hacked Studio tool, which failed double bed, then reverting to using the uncoupled ribber carriage to drop stitches.
Knitting details in the 2022 post Geometric shapes in drop stitch lace 4, stitch release, added racking. 
A larger test, with the idea begun in a spreadsheet including shapes in black, knit rows in purple, racking positions in green text with row numbers in black: 
keeping it more practical. 
The slider may be used, as described above, the tiny swatch. In my experience, moving the uncoupled ribber carriage back and forth is quicker. 
The difference in the stitch formation that happens with the ribber knitting two rows with automated loop formation patterning for dropped stitches on the top bed, while the top bed knits a single row between formation of loops on hand-selected needles on the ribber, with loops dropped after being formed on each row.
End release may be used on simple geometric shapes that do not contain knit rows. If the repeat or the item being produced is long in the number of rows, it can be performed periodically.
The knit carriage is set to slip in both directions, including on the first preselection row.
End needle selection is canceled.
It is best to use a tightly twisted fiber that does not split.
When programming the number of stitches for the number of needles in work, black pixel columns may be added on as borders on the left and right to stabilize the knit edges.
Contrary to other slip stitch designs, in automating the process, there are mostly blank areas, which will result in knit stitches on the ribber, while the black areas will result in the loops for dropping on the knit bed.
These shapes do not have vertical lines. As selection changes, the initial loops will be held until the last ones in each shape are formed.
The 10X24 repeat chart. 
When there is no needle preselection, rows 7 and 19 of the 24 rows, 
stitches on the knit bed are dropped.
The programmed repeat is 40X24. 
On the 930, the programmed designs match the direction in which they appear on the purl side. 
End release long stitches on the left, compared to those with the traditional paired row method used in the flower shapes on the right. 
Previously published related post links in reverse chronological order, followed by a low- resolution collage of some of the test swatches explored in them
Multiple color drop stitch lace using img2track and more
Revisiting drop/release stitch lace 1
Drop stitch lace using Ayab software 2/ HOP
Tuck stitch/ combination fabrics
Drop stitch lace using Ayab software
Geometric shapes in drop stitch lace 3, end release
Geometric shapes in drop stitch lace 2, Brother KM
Geometric shapes in drop stitch lace 1, Brother KM
Drop stitch lace, 2 colors per row, Passap KM
Drop stitch lace, 2 colors per row, Japanese machines
Revisiting knit “bubbles” brother KM
Brother KMs “pile knitting”/ ribber stitch dropping tools includes a downloadable PDF with instructions published by Brother for their KR 260 compatible slider model
Dropping whole rows:
Long stitches meet transfer lace
A tuck stitch combination fabric
Working with block shapes
More knit bubbles
More play with dropped stitches
Knit bubbles and “stitch ditchers/dumpers”
Working out the kinks in my drop stitch lace saga
If DBJ is preferred, an interesting variation using thick and thin yarns produces a stable and reversible knit with an interesting peek-through evocative of drop stitch lace.