R tidyverse create duplicate rows based on a fixed variable

I have an R dataframe that has start and end measurements for each id. The least possible value for end - start is min_sz = 2 (known difference, but may not actually occur in the data). I wish to create "chunks" based on a fixed value and create duplicate rows for each id, based on the number of chunks that start and end overlap.

If I were to use min_sz = 2 as my chunk size, my calculation and result would look something like this:

min_sz = 2

df = tibble(
  id = c("a", "b", "c", "d", "e", "f", "g", "h", "i", "j"),
  start = c(0, 0, 0, 4, 4, 8, 10, 10, 16, 32),
  end = c(4, 6, 16, 10, 22, 18, 36, 56, 42, 84),
)

df %>% 
  mutate(dur = end - start) %>% 
  mutate(n_min_chunks = dur / min_sz) %>% 
  uncount(n_min_chunks) %>% 
  group_by(id) %>% 
  mutate(row = row_number()) %>% 
  mutate(
    chunk_start = start + (min_sz * (row - 1)),
    chunk_end = start + (min_sz * row),
  )

I wish to apply a similar operation, but for potentially any req_sz that's a multiple of min_sz and includes partial overlaps. If I were to use req_sz = 20 for example, my output should look something like this (note #5 & #6 with partial overlaps "4-20" & "20-22"):

but I've been unable to come up with a mathematical solution that allows me to scale this "chunking" operation.

Any help would be greatly appreciated!

in base R you could write a function to accomplish the same:

explode <- function(data, by){
  f <- function(...){ 
   s <- list(...)[c('start', 'end')]
   mat <- embed(seq((s$start %/% by) * by, (s$end %/% by + 1) * by, by), 2)
   data.frame(...,dur = s$end - s$start, chk_st = mat[,2], chk_ed = mat[,1])
  }
  do.call(rbind, do.call(Map, c(f, data, by = by)))
}


 explode(df, by=20)
    id start end dur chunck_start chunk_end
a    a     0   4   4            0        20
b    b     0   6   6            0        20
c    c     0  16  16            0        20
d    d     4  10   6            0        20
e.1  e     4  22  18            0        20
e.2  e     4  22  18           20        40
f    f     8  18  10            0        20
g.1  g    10  36  26            0        20
g.2  g    10  36  26           20        40
h.1  h    10  56  46            0        20
h.2  h    10  56  46           20        40
h.3  h    10  56  46           40        60
i.1  i    16  42  26            0        20
i.2  i    16  42  26           20        40
i.3  i    16  42  26           40        60
j.1  j    32  84  52           20        40
j.2  j    32  84  52           40        60
j.3  j    32  84  52           60        80
j.4  j    32  84  52           80       100