HP rated toggle switches can be a legitimate part of an automation project, provided your budget includes a little bit of funding for a post-doc student to operate them.
Here's your design constraints:
The Arduino output is limited to a few volts dc - and not a lot of current.
This is absolutely not enough to drive your induction motor.
It is enough to drive a small relay (look through the product range of any Arduino supplier and you'll find a selection of relay modules, complete with built-in interface circuits).
The sort of relay you can drive with an Arduino is almost certainly not big enough to switch your motor (induction motors are nasty loads which draw large currents on starting and generate large voltage spikes when shut down. Neither feature is kind to relay contacts). As Petronila recommended, the way to get round this is to switch the motor using a contactor - a high power relay specially designed to withstand the horrors inflicted on it by a motor load.
You are unlikely to find a contactor you can drive directly from the Arduino, but you should be able to switch power to it using an Arduino-driven relay.
If you choose your components carefully, you should be able to work with:
[ul]
[li]Arduino (and its power supply)[/li]
[li]Relay module for the Arduino (and its power supply - it will need one to drive the onboard interface circuit. Choose carefully and you will be able to run the relay module off the same supply as your Arduino). Make sure the relay is rated to handle mains voltages and has a current rating several times the current drawn by the contactor coil - coils are another nasty load. A relay module that offers "opto-isolation" between the input and the relay is vastly preferable to one which doesn't [/li]
[li]A contactor with a 220V ac coil and contacts that exceed your motor rating.[/li]
[/ul]
Program and wire the Arduino to drive the relay. Wire the relay contacts to switch a 220V mains supply to the contactor coil and use the contactor contacts to switch the 220V mains supply to the motor.
For all that this "control driving relay driving contactor driving load" daisy chain arrangement may sound a bit cobbled together, it is exactly the way that many industrial motor control panels are designed. Draw it out, and you'll find it's less complicated than it sounds.
A.