In the traditional $(K,L,M_T,M_U,N)$ partially connected linear network, a central server stores a library of N files and connects to $K+L-1$ transmitters, each equipped with a cache of size $M_T$. Each user is connected to L neighboring transmitters and is equipped with a local cache of size $M_U$. Motivated by practical scenarios in which users can access multiple cache nodes, this paper considers a $(K,L,r,M_T,M_C,N)$ multiaccess cache-assisted partially connected linear network, where each user can access r neighboring cache nodes under a cyclic wrap-around topology, and each cache node has a storage capacity of $M_C$. We propose a general construction framework based on placement delivery arrays (PDAs). The analysis shows that, when the Maddah-Ali and Niesen (MN) scheme is employed and r is sufficiently large, the achieved normalized delivery time (NDT) approaches that of existing schemes for the traditional partially connected linear network. Moreover, under the same aggregate cache size accessible to each user, numerical results demonstrate that, as the cache size ratio increases, the gap between the NDT achieved by the proposed scheme and that of the traditional partially connected linear network scheme gradually diminishes, while the proposed scheme requires a smaller subpacketization level.