Quick question? How do you incorporate constraints into Jacobian for solving IK problems? For instance how do you keep the segments together when representing an arm? Because initially IK gives you a set of rotations necessary to reach the goal and I am trying to add constraints so to also get a set of translations required to keep the bones connected together at all times. Any ideas? Thanks

"Forward kinematics" takes joint angles and gives an end-effector orientation. For serial manipulators it is computed as the product of a bunch of transformations, which can be represented nicely in homogeneous coordinates.

"Inverse kinematics" takes an end-effector orientation and gives joint angles that will achieve it.

The constraints, you can see, are implied. We're not representing the arm as a bunch of rigid bodies with some connection constraints. We're representing it in the generalized coordinates given by the joint angles. There's simply no way to even represent a configuration in which the segments are disconnected.