All of the parts of your brake system are continually exposed to road spray and salt (if you live in a wintery climate). Brake wear generates dust from the rotors and pads wearing away. As a result, the braking mechanisms can get rusty and dirty. The first part of applying brake lubricant is cleaning them up.
Use a die grinder to clear away any rust on parts where you plan to apply lubricant. Grind just until you get to bare metal. Then put a bucket or pan underneath the brake assembly and spray the entire brake mechanism with brake cleaner. This will carry away the brake dust and drip down into the pan, which avoids the dust contaminating the air. This is especially important if, for some reason, you're working on old asbestos brakes. Once the brake cleaner has drained away, collect it and store it for proper recycling or disposal.
Brake lubricant usually comes in a tube or a small canister. Most mechanics just apply it where needed with a finger, but if you'd like more precision, you can use a wooden tongue depressor. Remember to only apply a thin coating where needed. Overlubrication of the brakes results in lubricant dripping or spraying into places where it's undesirable, and could reduce the effectiveness of the brakes.
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