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Many mechanical systems such as vehicles, robots and space structures are comprised of a lot of interconnected components. The motion of the components is constrained because of mechanical joints or specified motion trajectories. Multibody dynamics is one of effective methods to analyze nonlinear dynamic behavior for such systems. On the other hand, it is quite difficult to obtain all parameters required for numerical simulation by only direct measurement in complex mechanical systems. Therefore, parameter estimation and identification techniques are crucial for simulation in practical problems. This study aims to develop a parameter estimation technique based on the adjoint method which can be applied to mathematical models used in the multibody dynamics, namely, differential algebraic equations. In addition, a feature extraction technique based on the proper orthogonal decomposition is incorporated into the parameter estimation method in order to evaluate effect of model uncertainties on an accuracy of the parameter estimation, because the joint components often involve model uncertainties due to inherent physical characteristics such as friction, contact and so on. The validity of the present method is discussed by numerical experiments using the rigid multibody systems.