How would I get these joints simulating correctly?

[Aaa_Aaa]

You’re probably looking for Inverse or Forward Kinematics, and there’s a great list of resources in this answer from @ben: Does three.js supports FK (forward kinematics) and IK (Inverse kinematics)?

This will whet your appetite: https://github.com/notrueblood/FABRIK-for-threejs-and-beyond and this: https://jsantell.github.io/THREE.IK/