  The $d$-fold ($d \geq 3$) branched coverings on a disk give an infinite
family of nongeometric embeddings of braid groups into mapping class groups.
  We, in this paper, give new explicit expressions of these braid group
representations into automorphism groups of free groups in terms of the actions
on the generators of free groups.
  We also give a systematic way of constructing and expressing these braid
group representations in terms of a new gadget, called covering groupoid.
  We prove that each generator $\widetilde{\beta}_i$ of braid group inside
mapping class group induced by $d$-fold covering is the product of $d-1$ Dehn
twists on the surface.
