tie someone down to something—restrict a person to the terms of an agreement, etc.:
- If he tries to cheat, we must tie him down to his contract.
tie someone up with something—
1. connect or associate a person with smth.:
- Isn’t this company closely tied up with the continental industry?
2. fully involve a person with smth.:
- I’m afraid I can’t help you now—I’m too tied up with other things.
Note: The expression is not equivalent in meaning to the phrase rope someone into something—persuade or induce a person to do smth.:
- I was roped into the school dancing troupe and we performed in front of an audience.