The circuit is very simple : one single transistor is driven by one of Arduino's output. The transistor in turn drives the relay whose moving anchor is modified into a larger clapper to hit the bell.
The pin strips help keep the board steady on your Arduino. I used a few more than actually necessary.
Arduino is interfaced to the PC through a serial port emulated by a USB interface, that is, a regular USB cable connecting Arduino's board and the PC is actually seen by both parties as a serial link.
runs on the PC and reads PC's time of day every second. At the hour and half hour it sends a string of "#" characters through the USB/serial port, the number of "#" characters being the number of strikes of the bell.
is connected on the other end of the serial port and receives the string of "#" characters : it simply has to count them and drive one of its digital output once per strike.
Now come the hardare part do be soldered: the output of Arduino drives a transistor which in turn drives the relay whose moving anchor is modified into a clapper. Simple as it sounds.
The circuit is herebelow:
The NPN transistor has three pins, they shouldn't be swapped: different transistors have different pinouts.
The 1000 Ohm resistor limits the current into the Base of the transistor, the diode at the relay's coil is necessary to preserve the transistor from inverse large voltage spikes generated by the relay when it opens. The diode has a polarity, look for the black ring at its cathode.
Only three connections are needed with Arduino.
In case a large realay is used, a medium power transistor would be needed and an external supply for the circuit below would be needed. In this case connect to Arduino only GND and "To Arduino digital pin 8". BW, on every respectable Arduino board, the pin name are clearly labeled at the conectors, you can't be wrong.