I am currently working on a project for school and we are creating a mock pavlock although much simpler. We basically want a microcontroller to be able to keep time and shock at specific times. We currently have the RTC and microcontroller working together, but we are a little stumped as to how to use the controller to produce the shock. I've been reading other posts about how to produce a shock, but how would we be able to adapt that circuit for a microcontroller? We are also using a lipo battery so it can only produce a max voltage of 3.7
Take a look at flyback transformers. These can boost a low voltage up to a high enough voltage to shock someone. Many novelties like shocking lighters use flyback transformers to generate the shock. Here is a very cheap one on amazon...
Maybe try to get a hold of one of these an open it up to see how it works, and the even salvage parts from it. You can use a transistor to generate the input current to the transformer under the control of a micro-controller.
Another way to generate high voltages with a micro-controller is to use a diode based voltage multiplier...
If you connect the input of one of these multipliers to a GPIO pin of the micro-controller, you can charge up the multiplier by toggling the output pin up and down. If you pick small capacitors, you can limit the amount of energy stored in the system to help keep it safe.
Finally, you can generate high voltages by physically hitting a peizo element with something like a solenoid. This is how barbeque lighters generate their spark. Try to find one of these lighters and open it up and play with the striking mechanism inside to see how it works.
Of course be careful too.
To make an electrical shock you ought to learn some about human body model. I think making a circuit similar to ESD guns that is one of EMC engineers tools is enough for your need.
make a battery based high voltage generator source like the following diagram that is based on a simple NE555 oscillator chip http://1.bp.blogspot.com/-PKz_3voZMiQ/Tlxinj5p3NI/AAAAAAAABMM/HO8R6Lvr6pE/s1600/ET_Flyback_basic.gif
Isolate the transformer input pins (as low voltage region) and all other low voltage circuits including the system casing from output pins according to your generated voltage. for each kV you need to have at least one millimeter isolation (or using special materials for reducing the isolation mandatory space)
connect the high voltage source to the output with an micro controller controlled relay as discharge switch and proper RC network that you can see at the following picture http://www.compliance-club.com/archive/keitharmstrong/991215a.jpg
make a program on a micro controller circuit board that is able to read a trigger switch on its GPIO and set proper command on another GPIO pin that is connected to discharge switch relay
Due to radiated EMI that may generate by your simple ESD gun you have to protect your controller chip vital pins (such as reset) with proper 1nF capacitors