In this paper, a novel self-calibration method is developed for a camera attached to a mechanical system with known kinematics. An innovative least squares estimator is developed to compute the unknown intrinsic and extrinsic camera calibration parameters while an adaptive parameterized error prediction formulation is presented to compensate for the unknown pixel coordinates of the static objects projection. The estimator is based on a Lyapunov stability analysis which verifies convergence of the signals provided a persistent excitation condition is satisfied. Simulation results with and without additive pixel noise are also provided to illustrate the performance and robustness of the algorithm.