To enable distributed multiple mobile manipulator systems to complete collaborative tasks safely and stably, this article investigates and presents a motion generation scheme that considers both orientation and position coordination based on a distributed recurrent neural network. Moreover, physical limits are also considered. Specifically, the orientation and position coordination constraints and physical limits are modeled separately as equality and inequality constraints with coupled variables. Subsequently, a motion generation scheme for multiple mobile manipulators based on quadratic programming is established. Finally, a distributed linear variational inequality-based primal-dual neural network is constructed to solve the motion generation scheme and obtain the motion trajectories of all the mobile manipulators. The simulation results demonstrate that the hybrid orientation and position collaboration motion generation scheme effectively addresses the position and orientation coordination problem for multiple mobile manipulator systems. Compared to other schemes, the proposed scheme based on a distributed computing structure greatly enhances the stability of the system. Additionally, the proposed approach introduces orientation coordination and physical limits, which increases the practicality of the system.