Q:

What can be the mechanism used in devising a machine that can arrange the dishes properly to make the cleaning faster in the messes/hotels

In hotels/messes the used plates are often placed haphazardly, and the workers need to pick
the plates carefully to clean them. This leads to longer washing times and longer waiting times for customers.
what new mechanical/electronic devices can be designed to solve this problem and it can arrange the dishes properly
to make the cleaning faster in the messes. I just want to know the mechanism that be used in working of such devices.
Please suggest some ideas about it.

A:

Some of this depends on how tough the dishes are.  While taking a lot of room, I can see possibilitiles in a conveyer sorter.
Concept one:
Dishes are dumped onto a conveyer that is on a sideways slant.  Operator initially only has to see that they are one layer deep.  Use of multiple belts runing side by side at different speeds and textures may be able to spread out a pile of dishes into a single layer.  Side slope lets them drift to the bottom and form a single line of dishes.
Magnet picks up the cutlery.
Bar set more than a plate thick and running diagonally gets cups and glasses to slide out of the way of the plates.  This creates a second stream of dishes.
Since the plateware is now in a line with one edge against the side of the conveyor, a set of micro-switches, or photo switches at appropriate distances can trigger a door on the side of the conveyor.  Using delay timers ensures the right door is opened.
Concept 2.
Robot arm:
Robot has to be able to distinguish size right side up plate from upside down.  And recongize a glass in various orientations.  In addition has to be able to tell what objects are on top of other objects.
Handling for cutlery is an electro magnet.  Handling for plates is a vacuum suction cup.
Normal process for a plate:

Determine if plate is on top.  (complete rim visible.
Center suction cup with servos.
Place on plate
Apply suction
Pick up plate
If necessary invert plate. (2nd suction cup arm or ramp that flips it over?  First takes more mechanics, second takes more room, and requires longer reach for servos)
Stack plate.

Cups and glasses are more difficult.
You have an additional problem in sorting out used food, napkins, and things that don't belong.  (People leaving glasses, wallets, phones...  They shouldn't be in the bus trays, but they often are.)
Concept 3:  Special dishes.  Each style of dish  has at least 3 steel tags embedded in the bottom.  dish lifters have magnets in the same patterns as the dishes. Each lifter only lifts one kind of dish.  Dishes that don't get picked up go over a roller that flips them over for another pass.  Not sure if this can be made to work with glasses.

Look at how trash sorters work, and the mechanisms on canning and bottling lines for further inspiration.

I've worked in an industrial kitchen and it's pretty fast.   We had the smallest Hobart dishwasher.  We had a dozen trays in various spike configuations, A tray would hold 20 plates, 36 cups, or a layer of cutlery.  Rack the dishes, spray the worst of the food residue off of them. open dishwasher tunnel. slide tray in, pushing washed tray out. Close tunnel.  Hit start.  60 second wash, 20 second rinse.
We used two operators, one on the dirty side, one on the clean side.  90 seconds was enough to have the next tray ready.  On the clean side, the dishes were hot enough they air dried in under a minute, so there was a queue on that side too.  At any given time tray A was being loaded.  B was waiting for the dishwasher.  C was in the dishwasher, D was drying, E was being unloaded.  The net result was about 3-5 seconds per plate/cup and about half that for cutlery.
Net result was that two people had no problem at all keeping up with a double serving line.

Larger dishwashers have open tunnels without doors.  They are longer, and have curtains, and a conveyor.  Wash chamber and rinse chamber are separate reducing clean water use.  Heat is scavenaged from the dryer chamber to prewarm the incoming water.  They are somewhat faster, but mostly more energy efficient.

One of the keys is to have enough dishes.  We solved a lot of delays by buying another case of cups. (Cups would disappear into the dorms...)
Another key is to get people to do some of their own bussing.  We had a garbage can with a lid with a 6" hole in it, and some really strong magnets underneath to salvage cutlery, 3 buckets for knives, forks, spoons, bus trays for plates, cups.  This helped a lot, and most people cooperated with the system.  Pre-sorting like this probably sped us up about 20%
Dishwasher is a minimum wage job.  If minimum wage is \$10/hour and your mess is open 16 hours a day, then labour for two operators is \$320/day.  If you can eliminate both operators, then you are saving about \$100K/year.  What is your estimated cost?  Expected maintenance?  It still requires an operator.  Is that still a min-wage job?  You have reduced 2 people to 1 part time more expensive person.
Dishwashing is a critical system.  It stops, and everything else stops as soon as you run out of clean dishes.  You need dual systems that can keep up.  Or you need a backup system (sinks and dishwashers.)
Dishwasher personnel are multi-talented.  They also wash pots and serving trays during the slow periods, mop floors, wipe tables.  These jobs need doing too.  You want to hire people for full shifts.  You do not want them standing around.
If things are really slow your dishwasher can put on a clean shirt and bus tables, take orders, deliver coffee / water / soda refills.

