In an earlier entry, I noted:

Any coin design is composed of a number of design elements. During the process of producing a coin die, each design element is engraved on individual punches. Eventually, these design elements are embossed on a matrix to form a single composite design. The matrix is then used to manufacture the individual dies employed in the minting of coins.
In pre-modern times, the artist creating the coin design would have to carry out his work on the same scale as the coins that would eventually be produced. Today, the artist prepares a much larger scale model in plaster or similar material. When the plaster piece is finished, the remaining steps in the production process are purely mechanical.

The design of the plaster scale model is transferred to the punches that will be employed in the production of the matrix. This process is made possible by the invention of the pantograph. The pantograph is a mechanical device with a pointer fixed to one arm and a cutter fixed to another arm. While moving the pointer across a scale model, the pantograph will control the process of engraving the metal body at the other end, eventually reproducing the pattern of the scale model. Through this process, a punch of the appropriate size is obtained.

This technology allows for punches of different sizes to be obtained from the same scale model, simply by adjusting the pantograph. Thus, it allows for coins with the same basic design elements, but differing diameter, to be minted from dies that have been obtained through parallel processes, all reproducing a single original design element. E.g. the Ashoka sculpture on individual coins of different denominations and sizes may emanate from the same original model.

We should remember, that there are a number of steps in the process of transferring the design from the plaster model to the coin dies, and the details of this process may vary, depending on time and place.

Apart from the obviously improved efficiency in industrialized coin production, the pantograph also makes possible a much more detailed and precise coin design, compared with pre-modern coins. The challenges for artists and craftsmen are different today from those in pre-modern times. And the outcome of their efforts should be appreciated from a different perspective.

Pudukkottai pre-modern
Pudukkottai modern
Two 'kasu' coins from Pudukkottai (a place in Tamil Nadu in Southern India). The coin above is pre-modern, while the one below was minted in a modern mint (Birmingham or Kolkata) somewhere between 1889 and 1947. The machine struck kasu from Pudukkottai is the only modern coin from Tamil Nadu that was not issued by (although with the consent of) the British administration.

See also this Wikipedia article on the pantograph.