In this work, we consider adaptive control of time-varying mechanical systems. First, we derive the dynamics of time-varying mechanical systems under the assumption that the generalized constraints on the system do not depend on time but the system parameters such as masses and payloads are time-varying. A compact parameterization of the dynamics of the system is obtained based on the rate of change of parameters being a polynomial in time. Based on this parameterization, adaptation laws for the time-varying parameters is proposed. To test the proposed adaptive controllers, an experimental platform consisting of a two-link robot with a time-varying payload is designed. The designed experimental platform mimics pouring/filling operations in industry, where the payload is time-varying. Experimental results demonstrate the effectiveness of the proposed adaptive control designs.