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This paper presents a method of estimating both 3-D shapes and moving poses of an articulated object from a monocular image sequence. Instead of using direct depth data, prior loose knowledge about the object, such as possible ranges of joint angles, lengths or widths of parts, and some relationships between them, are referred as system constraints. This paper first points out that the estimate by Kalman filter essentially converge to a wrong state for non-linear unobservable systems. Thus the paper proposes an alternative method based on a set-membership-based estimation including dynamics. The method limits the depth ambiguity by considering loose constraint knowledge represented as inequalities and provides the shape recovery of articulated objects. Effectiveness of the framework is shown by experiments. [ABSTRACT FROM AUTHOR]