This paper presents a new approach for an online solution of the inverse kinematics problem based on nonlinear optimization for robots with joint physical constraints. The inverse kinematics problem is stated as a constrained nonlinear optimization problem and is solved using Kuhn--Tucker conditions analysis. The nonlinear multivariable optimization problem is locally converted into independent local linear constrained subproblems and each subproblem is analytically solved. For each joint, position limits and velocity limits are considered as physical constraints. The proposed structure benefits from a very low complexity design. The proposed method is fast and requires few calculations. The convergence of the proposed algorithm is proven based on the Lyapunov function. While keeping the algorithm stable, it can navigate the manipulator to a desired position under joint physical limits. The algorithm is simulated on a 7-DOF PA-10 manipulator. Results indicate good efficiency for the proposed structure in constrained path planning of joint space.