When engineers start talking about job titles, it always drives me crazy. I think people should be less focused on their title and more focused on what they're really doing. And I'm not saying you should sit in the engine room and be quiet.
If you're a mechanical engineer, and you want to learn more about software, then raise your hand and say, "I want to learn more about software because I realize it's a huge part of how the world's going to move forward."
You can better position yourself by working on projects that may include this component or by finding colleagues working on software and let it be known that you want to learn more. Find ways to offer your assistance. Be available nights, weekends, whatever it takes.
Let it be known that you want to take on more responsibility. When people ask you for help, the answer is yes. However, if you don’t know how to do it, be transparent. Say, “Hey, I'm not really sure, but I know I can learn.” Try and position yourself to become who you want to be.
In my view, the busy people at your company will always be busy, and they’ll only get busier. Why? Because people want to lean on people who can get stuff done. Asking how you can learn new skills is a lot more constructive than saying “I want to be the project manager” or “I need to make more money.”
On that note, don’t ever say, "I want to do this, or I'm going to leave the company." I can't stand when people give me ultimatums. Typically, I'll open the door for them to leave if they want to leave. Making threats and demands isn’t helpful. If you genuinely feel that you’re being underpaid, it's important to raise that with your manager, but not in a way that says you need to get paid more or you’re going to quit. You can’t build relationships and trust with threats.
I’ve never asked for a promotion in my life. Ask how you can expand your current role and responsibilities at your company. Keep raising your hand to learn new skills and take on new challenges. Focus on those more than your job title, and the promotions will follow.