Projection effects on the stellar proper motion of Chamaeleon stars. Upper panels: proper motion distribution of synthetic stars randomly distributed over the fields used in our membership analysis moving with the same space motion of Cha I and Cha II stars. Lower panels: illustrate the expected proper motion distribution of synthetic ϵ Cha and η Cha located in the same fields. We generated a total of 1000 sources in our simulations. We compare the proper motion of the synthetic stars with the observed values for the candidate members previously identified in the literature and members identified in this study (in this case we use the solution with p_in = 0.9, see Table 1). The mean, dispersion and correlation coefficient obtained from each proper motion distribution are indicated in the panels. The solid lines denote the fitted proper motion distributions and the crosses mark the mean proper motion in each case.