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Dry self-assembly process has been proposed and demonstrated experimentally to be a potentially effective way for vast microchips assembly on a silicon substrate. In this method, each microchip is engraved on its bottom with a pattern of a higher rod peg and a lower uniquely orienting feature. On the silicon substrate, a matrix of counterpart pattern is grooved to capture the pattern features on microchips when the silicon substrate is subjected an orbital motion. In this paper, we proposed a model for the dry self-assembly process and theoretically investigated the effect of a few important parameters on the yield rate of production. Firstly, we derived out the motion of microchips before and after being trapped by the patterned features on the silicon substrate. When the silicon substrate is subjected an orbital motion, a microchip on the substrate is found to be maintaining a cycle motion with the same radius as the substrate but its rotational speed depends on the coefficient of friction between the chip and the substrate. After the rod peg of a chip is trapped on the substrate, the chip rotates around the hole on the substrate as well as rotates itself. The relative rotational speed is same as the substrate. But the self-rotational speed is upper bounded by the rotational speed of the substrate times the ratio of radius between the hole and the rod and varies with the coefficient of friction. Secondly, we numerically studied the effect of a few parameters on the yield rate. The result shows that yield rate increases with the radius of orbital motion of the substrate. Before the chip is trapped by a hole, yield rate depends on the region of the ratio between the rotational speed and a critical speed which is defined by the coefficient of friction and the radius of the orbital motion. In some regions, the matching rates are very high, while in other regions the matching rates are low. It indicates that increasing the rotational speed of motor is not a good way to- improve the yield rate. After the chip is trapped by a hole, the yield rate depends on the region of the ratio of radius between the hole and the rod peg. Our model predicted the experimental observation very well. Our model helps to archive a rapid and reliable dry self-assembly process with high yield rate.