In this paper the capabilities of a proposed serial, multi-link, snake-like, planar manipulator with highly restricted joint motion (only three states per joint) have been studied. Two different types of problem namely reach-the-point and follow-the-path problems, have been solved for such a manipulator when the number of links is assumed unlimited. The reach-the-point problem has been solved also for the case of fixed number of links. By adopting a coded representation of the configuration a set of transformation rules has been developed to decide whether two different configurations lead to the same point in the work-space. This avoids the time-consuming evaluation of trigonometric functions involved in actually computing the tip location.