This work continues the approach to sensor-based robot motion planning in an unknown environment first studied in [2,3] and further developed for various configurations of planar robot arms in [4,10]. The main idea of the approach is to reduce the problem to the analysis of simple closed curves on an appropriate two-dimensional (2d) manifold. We extend the same ideas to simple 3d arms with two revolute joints whose endpoints travel along 2d manifolds whereas their bodies operate in a "normal" 3d space. For such an arm, a path planning algorithm is described, its convergence is shown, and an example of the algorithm performance is given.