In this paper, we consider a routing problem of a single grasp-and-delivery robot with unit capacity, which is working at an assembly line of printed circuit boards. The grasp-and-delivery robot arranges n identical pins from their current configuration to the next required configuration by transferring the pins one by one. A cycle of the assembly contains such a transition from a configuration to an another configuration. The n pins support a printed circuit board from underneath to prevent it from overbending, while an automated manipulator embeds a number of electronic parts onto the printed circuit board from above. Let m be the number of printed circuit boards to be processed. Given an initial configuration of the pins and a permutable set of m required configurations, the routing problem asks to find a processing order of the m printed circuit boards (i.e., a sequence of the m configurations) and a transfer route of the grasp-and-delivery robot which minimize the route length over all m cycles. In this paper, we first design a polynomial time approximation algorithm with factor four to the cyclic routing problem with a non-permutable set of configurations (i.e., with a fixed processing order of printed circuit boards). Then, by employing its procedure, we show that the cyclic routing problem with a permutable set of configurations admits a polynomial time approximation algorithm with factor eight.