gistfile1.rb

  resources :doctors do
    get 'new_schedule', :on => :member
  end
  resources :schedules do
    get 'new_appointment', :on => :member
  end
  resources :appointments
  
# With this /doctors/123/new_schedule will map to DoctorsController#new_schedule
#       and /schedules/321/new_appointment will map to SchedulesController#new_appointment
# And all other normal routes (show, edit, delete) will be simple in form :controller/:id/:action:
#
# doctors/123/show to show doctor with id 123
# schedules/321/edit to edit schedule with id 321 (we dont't need the ID of doctor to find it, so why nesting?)
# appointments/444/delete to delete appointment with id 444
#
# If you still want to show to user the fact of nesting this, you can show this on your page, like when you
# visit appointment 444, you can show something like...
# Doctor <name> > Schedule <title> > Apppointment <title>
# ... in your page
  

we are parsing doctor through schedule?

No, in this case from the point of routes all three resourses are independent and only need one parameter for URL generation.