Robot manipulation in a physically-constrained environment requires compliant manipulation. Compliant manipulation is a manipulation skill to adjust hand motion based on the force imposed by the environment. Recently, reinforcement learning (RL) has been applied to solve household operations involving compliant manipulation. However, previous RL methods have primarily focused on designing a policy for a specific operation that limits their applicability and requires separate training for every new operation. We propose a constraint-aware policy that is applicable to various unseen manipulations by grouping several manipulations together based on the type of physical constraint involved. The type of physical constraint determines the characteristic of the imposed force direction; thus, a generalized policy is trained in the environment and reward designed on the basis of this characteristic. This paper focuses on two types of physical constraints: prismatic and revolute joints. Experiments demonstrated that the same policy could successfully execute various compliant-manipulation operations, both in the simulation and reality. We believe this study is the first step toward realizing a generalized household-robot.