Your second sentence ("Yesterday I worked on my chest") is good. Your first and third sentences feel like they are missing words. Here are some similar and natural-sounding alternatives:
1. I like to work on my biceps.
2. I like to work my biceps hard.
3. I work on my biceps every day.
4. I work biceps and triceps at the gym.
5. That machine really works your biceps!
6. That machine is for working on your biceps.
The verbs "work on" and "work" are subtly different here. They can both be correct depending on the supporting words and intended meaning. In this context, "work on" means "spend time on" or "improve," and "work" (when combined with a possessive pronoun like "my") means something like "cause to work hard." In my fourth sentence without the possessive pronoun, "work" is more like "exercise."
Using "work my biceps" in this context is more colloquial and carries the feeling of treating your muscles as a separate entity from yourself. You are forcing them (your muscles) to work hard. This is fine to use and sounds natural, especially if you add something for emphasis like "hard", "really", or an exclamation mark. However, in some sentences it might sound a little boastful.
It sounds weird to say "That machine works on your biceps" because the biceps are yours, not the machine's. You use the machine to work on your biceps.
