Currently available algorithms developed for planning robot motion paths in configuration spaces with both obstacle avoidance constraints and end-effector pose constraints suffer from low sampling rates, long computation times, and requirements for specific manipulator structures. The present work addresses this issue by developing an improved sampling-type motion planning algorithm based on a modified form of the rapidly-exploring random tree (RRT) algorithm. The sampling process is based on the standard premise that the constrained manifold is continuous within a particular range. Therefore, configurations that meet the specific constraints associated with a proscribed motion planning task are sampled in advance, and those configurations meeting the constraints are stored in an offline configuration dataset that is employed exclusively in the RRT process. Accordingly, the proposed algorithm facilitates a greatly streamlined motion planning process for manipulators with high degrees of freedom. The computational speed and planning precision of the algorithm are further enhanced by introducing a target bias mechanism and applying an adaptive mechanism to improve the obstacle collision detection performance. The high motion-planning performance of the proposed algorithm is verified by comparisons with the performances of other state-of-the-art RRT-based algorithms based on numerical simulations.