For realizing a versatile, flexible robotic assembly system in the manufacturing domain, a versatile robotic hand which can grasp variously shaped parts accurately is essential. In our research, we assume a robotic hand with multiple parallel stick fingers, and aim to design an optimal mechanism of the hand as a versatile robotic hand for assembly tasks, which is as simple as possible with minimally necessary degrees of freedom and number of fingers. One of the minimum solution is a chuck-type hand. In this paper, as fundamental research toward optimal design of the hand, we address a chuck-type hand with three parallel stick fingers, and propose a geometrical method to find candidate positions of the fingers contacting a target part under the constraint of the hand mechanism. The validity and utility of the proposed method is verified through some numerical examples.