Can computers on other LAN networks, access a printer that is connected to a router through a switch.explanation is given below.

here is a sketch

s1,s2,s3 3 switches are separated to 3 different networks in a LAN. (using subnettings )

let's say the printer on the s1 switch is connected to the switch through a pc and it is not a netowrk printer.(even if it is,it won't change anything here,I think(?) )

So my question is, We know that all 2pc and the printer are connected to that Router (thorugh s1 switch). Therefore all the device get the same IP address right?so how can the computers on s2 and s3 reconganize the printer in the s1 switch specifically if all the machines on the s1 has the same IP to out side netowrks? yes,printer will be shared so any other pc on diffrent netowrks can use that printer.

Do I need to use another router ofr the printer to give it a diffrent IP, in this case?
hope I was clear .

All of these hosts on the network will be able to communicate with each other through the router. The router would have to have three vlans setup and route between the vlans. Hosts on each vlan (subnet) would send packets to their default gateway (the router), in order for the packets to traverse the vlans.

You only need one router in the diagram if the router is capable of defining multiple segments. IF it isnt, yes, multiple routers would be added to the design.

Let's say the router is a modern one capble of everything a router can do. If so,how does this(reconganizing the printer sperately) work ? port forwarding ?or something?

Ok, so a router is actually a pretty basic device. All TCP/IP devices have what is called a routing table. This routing table has information about how to move packets out of the system. A router is no different. A router will populate information into this table about the interfaces it has, and other route information it has shared with other routers on the network.

Going back to your example, this router has three subnets defined. Therefore the router has three interfaces (they can be three logical interfaces on one NIC, or three seperate NICs). In any case, the router has been configured with three IPs on three interfaces, each on its own subnet. Each of these IPs now becomes the "default gateway" for hosts on each subnet.

When a computer on subnet2 needs to send a print job to the printer on subnet1, the computer on subnet2 needs to figure out what subnet the printer is located on. It compares the destination IP with its own IP in a process called ANDing. It determines that the destion host (the printer) is located on a remote subnet, therefore it sends the packets to its gateway. The gateway receives that packets and looks at its routing table and performs the same ANDing process to determine where the destination host is located. This process continues until the packets reach the destination host.

I have a summary written up in more detail about this process. Feel free to read over it.