AlignPosition with offset (or weld without following orientation)

My goal is a part that follows another. Weld constraint would work, but when the player rotates, then the part rotates around it too, that’s the problem.

Problem Example

I thought about using AlignPosition but I cant set an offset it, so it just goes inside the player (with applyCenterOfMass, otherwise the part would be rotating like crazy.)

This is what I want to achieve with constraints:

Example (WITH RUNSERVICE)

The reason I want to use constraints is because I’ll be changing the position of the part constantly and I’ll have many more parts, so i want to avoid using script for this.