A framework is proposed for model-based monocular vision covering not only conventional 3-D rigid models, but also flexible structures made up of 3-D rigid bodies connected by rotational joints. Pose-estimation problems from a single view are defined and discussed according to this object model composed of rigid bodies and rotational axes, respectively represented by sets of unit vectors and by single unit vectors. The authors define primitive problems as those which are solvable, but which would be unsolvable if any vector in the problem were invisible. A theorem is derived to extract a primitive problem family, members of which correspond to models containing rigid bodies and invisible rotational axes. Two generic rotation-estimation algorithms applicable to this problem family are also constructed. Experimental results from several primitive problems show the effectiveness of the proposed framework.