Prismatic part may have a representative geometry of complicated shaped parts. In the case of assembly of prismatic parts, the difficulty is further amplified due to asymmetry of the part geometry. To overcome these problems, we have made a geometric analysis for the assembly of prismatic parts and developed a vibratory assembly wrist which could compensate not only the lateral positioning errors but also the rotational positioning error. We have also adopted an active strategy based upon neural networks for the purpose of improving the performance of the vibratory assembly wrist. We presented the geometric analysis for the assembly of prismatic parts and the mechanisms which help the vibratory assembly to accomplish the hole search successfully. We have studied the developed vibratory wrist and the assembly performances of the wrist. The performances were discussed via a series of experiments. And we presented the need of the active strategy to execute the assembly in the passive-active combination method. An active algorithm based upon neural networks was applied to accomplish the vibratory assembly of the passive-active combination method. The performances of the neural networks were investigated through a series of simulations using experimental data. The results showed that the active strategy could compensate a greater part of the initial positioning error and then the vibratory wrist could accomplish the assembly of prismatic parts with small reaction forces and a short search time.